From dcc2d3481cbc9e7a86e80468f954dfe241ccafbb Mon Sep 17 00:00:00 2001 From: cuda-quantum-bot Date: Thu, 30 Jan 2025 05:31:49 +0000 Subject: [PATCH] Docs preview for PR #2458. --- pr-2458/CMakeLists.txt | 2 +- ...ications_python_logical_aim_sqale_38_0.png | Bin 0 -> 128920 bytes ...ications_python_logical_aim_sqale_56_0.png | Bin 0 -> 137263 bytes pr-2458/_sources/api/default_ops.rst.txt | 4 +- .../_sources/api/languages/cpp_api.rst.txt | 17 + .../_sources/api/languages/python_api.rst.txt | 2 + .../python/deutschs_algorithm.ipynb.txt | 49 +- .../digitized_counterdiabatic_qaoa.ipynb.txt | 24 +- .../python/hadamard_test.ipynb.txt | 34 +- .../applications/python/krylov.ipynb.txt | 48 +- .../python/logical_aim_sqale.ipynb.txt | 1356 ++++++++++++ .../python/vqe_advanced.ipynb.txt | 2 +- .../python/executing_kernels.ipynb.txt | 2 +- .../executing_photonic_kernels.ipynb.txt | 171 ++ pr-2458/_sources/releases.rst.txt | 52 +- pr-2458/_sources/using/applications.rst.txt | 5 +- 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If it is applied to a qum where the number of photons is already at the maximum value, the operation has no effect. -:math:`U|0\rangle → |1\rangle, U|1\rangle → |2\rangle, U|2\rangle → |3\rangle, \cdots, U|d\rangle → |d\rangle` +:math:`C|0\rangle → |1\rangle, C|1\rangle → |2\rangle, C|2\rangle → |3\rangle, \cdots, C|d\rangle → |d\rangle` where :math:`d` is the qudit level. .. tab:: Python @@ -674,7 +674,7 @@ This operation reduces the number of photons in a qumode up to a minimum value o 0 representing the vacuum state. If it is applied to a qumode where the number of photons is already at the minimum value 0, the operation has no effect. -:math:`U|0\rangle → |0\rangle, U|1\rangle → |0\rangle, U|2\rangle → |1\rangle, \cdots, U|d\rangle → |d-1\rangle` +:math:`A|0\rangle → |0\rangle, A|1\rangle → |0\rangle, A|2\rangle → |1\rangle, \cdots, A|d\rangle → |d-1\rangle` where :math:`d` is the qudit level. .. tab:: Python diff --git a/pr-2458/_sources/api/languages/cpp_api.rst.txt b/pr-2458/_sources/api/languages/cpp_api.rst.txt index b16e570f53..34487dbefb 100644 --- a/pr-2458/_sources/api/languages/cpp_api.rst.txt +++ b/pr-2458/_sources/api/languages/cpp_api.rst.txt @@ -35,6 +35,14 @@ Common .. doxygenclass:: cudaq::observe_result :members: +.. doxygenstruct:: cudaq::observe_options + :members: + +.. doxygenfunction:: cudaq::observe(const observe_options &options, QuantumKernel &&kernel, spin_op H, Args &&...args) +.. doxygenfunction:: cudaq::observe(std::size_t shots, QuantumKernel &&kernel, spin_op H, Args &&...args) +.. doxygenfunction:: cudaq::observe(QuantumKernel &&kernel, spin_op H, Args &&...args) +.. doxygenfunction:: cudaq::observe(QuantumKernel &&kernel, const SpinOpContainer &termList, Args &&...args) + .. doxygenclass:: cudaq::ExecutionContext :members: @@ -53,6 +61,13 @@ Common .. doxygenclass:: cudaq::sample_result :members: +.. doxygenstruct:: cudaq::sample_options + :members: + +.. doxygenfunction:: cudaq::sample(const sample_options &options, QuantumKernel &&kernel, Args &&...args) +.. doxygenfunction:: cudaq::sample(std::size_t shots, QuantumKernel &&kernel, Args &&...args) +.. doxygenfunction:: cudaq::sample(QuantumKernel &&kernel, Args&&... args) + .. doxygenclass:: cudaq::SimulationState .. doxygenstruct:: cudaq::SimulationState::Tensor @@ -89,6 +104,8 @@ Common .. doxygenfunction:: cudaq::draw(QuantumKernel &&kernel, Args&&... args) +.. doxygenfunction:: cudaq::get_state(QuantumKernel &&kernel, Args&&... args) + .. doxygenclass:: cudaq::Resources .. doxygentypedef:: cudaq::complex_matrix::value_type diff --git a/pr-2458/_sources/api/languages/python_api.rst.txt b/pr-2458/_sources/api/languages/python_api.rst.txt index d84ddc427c..3c26a73e6d 100644 --- a/pr-2458/_sources/api/languages/python_api.rst.txt +++ b/pr-2458/_sources/api/languages/python_api.rst.txt @@ -157,6 +157,8 @@ Data Types .. autoclass:: cudaq.operator.cudm_state.CuDensityMatState :members: +.. autoclass:: cudaq.operator.helpers.InitialState + .. autofunction:: cudaq.operator.cudm_state.to_cupy_array .. autoclass:: cudaq::SampleResult diff --git a/pr-2458/_sources/applications/python/deutschs_algorithm.ipynb.txt b/pr-2458/_sources/applications/python/deutschs_algorithm.ipynb.txt index feaacacd9d..b1e281a0af 100644 --- a/pr-2458/_sources/applications/python/deutschs_algorithm.ipynb.txt +++ b/pr-2458/_sources/applications/python/deutschs_algorithm.ipynb.txt @@ -13,17 +13,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We have a function which takes in a bit and outputs a bit. This can be represented as $f: \\{0,1\\} \\longrightarrow \\{0,1\\}$. \n", + "Deutsch's Algorithm is a concise demonstration of the differences in computational complexity between classical and quantum algorithms for certain problems. For Desutch's algorithm, we begin with a function which takes in a bit and outputs a bit. This can be represented as $f: \\{0,1\\} \\longrightarrow \\{0,1\\}$. \n", + "The function $f$ has the property that it either constant or balanced. The goal of Deutsch's Algorithm is to determine whether our given function is constant or whether it is balanced. \n", "\n", - "The function $f$ has a property; either it is constant or balanced. \n", + "A constant function is \"A balanced function is a function such that the outputs are the same regardless of the inputs, i.e., if $f(0) = 0$ then $f(1) = 1$ or if $f(0) = 1$ then $f(1) = 0$.\n\", the outputs are the same regardless of the inputs, i.e., in the case of $f: \\{0,1\\} \\longrightarrow \\{0,1\\}$, there are are two ways in which this can occur: $f(0) = f(1) = 0$ or $f(0) = f(1) = 1$.\n", "\n", - "If constant, the outputs are the same regardless of the inputs, i.e., $f(0) = f(1) = 0$ or $f(0) = f(1) = 1$.\n", - "\n", - "If balanced, the ouputs are balanced across their possibilities, i.e, if $f(0) = 0$ then $f(1) = 1$ or if $f(0) = 1$ then $f(1) = 0$.\n", - "\n", - "The question we would like to answer is if the function is constant or balanced. \n", + "A balanced function is defined such that the ouputs are balanced across their possibilities, i.e., if $f(0) = 0$ then $f(1) = 1$ or if $f(0) = 1$ then $f(1) = 0$.\n", " \n", - "Classically, if we are given a function $f$, we can solve to find its property via the code below: \n" + "Classically, if we are given a function $f: \\{0,1\\} \\longrightarrow \\{0,1\\}$, we can determine if it is constant or balanced by evaluating the function at $0$ and at $1$. This is carried out in the code below: \n" ] }, { @@ -96,11 +93,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "If you step through the `if` statements above, one can see that we require 2 calls to the function to determine its property. That is, we have to query $f$ twice.\n", + "If you step through the `if` statements above, you may notice that we require 2 calls to the function to determine its property. That is, we have to query $f$ twice.\n", "\n", - "The claim is that Deutsch's algorithm can solve for this property with 1 function evalulation, demonstrating quantum advantage. \n", + "The claim is that Deutsch's Algorithm can determine if a given function is constant or balanced with just 1 function evalulation, demonstrating quantum advantage. \n", "\n", - "Below we first go through the math and then the implementation in CUDA Quantum. \n", + "Below we first outline Deutsch's Algorithm and work through the math to verify that it does as promised. Then, we provide the implementation in CUDA-Q. \n", "\n" ] }, @@ -130,7 +127,7 @@ "\n", "\n", "\n", - "Suppose we have $f(x): \\{0,1\\} \\longrightarrow \\{0,1\\}$. We can compute this function on a quantum computer using oracles which we treat as black box functions that yield the output with an appropriate sequence of logic gates. \n", + "Suppose we have $f(x): \\{0,1\\} \\longrightarrow \\{0,1\\}$. We can compute this function on a quantum computer using oracles which we treat as black box functions that yield the output with an appropriate sequence of logical gates. \n", "\n", "Above you see an oracle represented as $U_f$ which allows us to transform the state $\\ket{x}\\ket{y}$ into: \n", "\n", @@ -140,7 +137,7 @@ "\\end{aligned}\n", "$$\n", "\n", - "If $y = 0$, then $U_f\\ket{x}\\ket{y} = U_f\\ket{x}\\ket{0} = \\ket{x}\\ket{0 \\oplus f(x)} = \\ket{x}\\ket{f(x)}$ since $f(x)$ can either be $0/1$ and $0 \\oplus 0 = 0$ and $0 \\oplus 1 = 1$.\n", + "If $y = 0$, then $U_f\\ket{x}\\ket{y} = U_f\\ket{x}\\ket{0} = \\ket{x}\\ket{0 \\oplus f(x)} = \\ket{x}\\ket{f(x)}$, since $f(x)$ can either be $0$ or $1$ and $0 \\oplus 0 = 0$ and $0 \\oplus 1 = 1$.\n", "\n", "This is remarkable because by setting $\\ket{y} = \\ket{0}$, we can extract the value of $f(x)$ by measuring the value of the second qubit. \n", " \n", @@ -213,7 +210,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Deutschs' Algorithm: \n", + "## Deutsch's Algorithm: \n", "\n", "Our aim is to find out if $f: \\{0,1\\} \\longrightarrow \\{0,1\\}$ is a constant or a balanced function? If constant, $f(0) = f(1)$, and if balanced, $f(0) \\neq f(1)$.\n", "\n", @@ -296,18 +293,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/usr/local/lib/python3.10/dist-packages/qutip/__init__.py:66: UserWarning: The new version of Cython, (>= 3.0.0) is not supported.\n", - " warnings.warn(\n" - ] - } - ], + "outputs": [], "source": [ "# Import the CUDA-Q package and set the target to run on NVIDIA GPUs.\n", "\n", @@ -391,6 +379,17 @@ "elif np.array(result)[0] == '1':\n", " print('f(x) is a balanced function')" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This algorithm can be generalized to determine if a $n$-bit function $f:{0,1}^n\\longrightarrow {0,1}$ is constant or a balanced with only $\\frac{n}{2}$ function evaluations, for $n$ even. A function if balanced if half of the inputs map to $0$ and half map to $1$. \n", + "\n", + "Here we must assume that the function that we are given is either constant or balanced since there are $n$-bit functions that are neither constant, nor balanced. For instance the $2$-bit function $f(b_0,b_1) = \\max(b_0,b_1)$ is neither balanced, nor constant.\n", + "\n", + "A hint on how you might approach this problem is to first solve the problem for $n=2$ and see if you can then use that approach to handle $n$-bit functions for larger values of $n$." + ] } ], "metadata": { diff --git a/pr-2458/_sources/applications/python/digitized_counterdiabatic_qaoa.ipynb.txt b/pr-2458/_sources/applications/python/digitized_counterdiabatic_qaoa.ipynb.txt index 35dcb5778a..a3043b7a1b 100644 --- a/pr-2458/_sources/applications/python/digitized_counterdiabatic_qaoa.ipynb.txt +++ b/pr-2458/_sources/applications/python/digitized_counterdiabatic_qaoa.ipynb.txt @@ -8,7 +8,7 @@ "\n", "Drugs often work by binding to an active site of a protein, inhibiting or activating its function for some therapeutic purpose. Finding new candidate drugs is extremely difficult. The study of molecular docking helps guide this search and involves the prediction of how strongly a certain ligand (drug) will bind to its target (usually a protein). \n", "\n", - "One of the primary challenges to molecular docking arises from the many geometric degrees of freedom present in proteins and ligands, making it difficult to predict the optimal orientation and assess if the drug is a good candidate or not. One solution is to formulate the problem as a mathematical optimization problem where the optimal solution corresponds to the most likely ligand-protein configuration. This optimization problem can be solved on a quantum computer using methods like the Quantum Approximate Optimization Algorithm (QAOA). This tutorial demonstrates how this [paper](https://arxiv.org/pdf/2308.04098) used digitized-counteradiabatic (DC) QAOA to study molecular docking. This tutorial assumes you have an understanding of QAOA, if not, please see the CUDA-Q MaxCut tutorial found [here](https://nvidia.github.io/cuda-quantum/latest/examples/python/tutorials/qaoa.html)\n", + "One of the primary challenges to molecular docking arises from the many geometric degrees of freedom present in proteins and ligands, making it difficult to predict the optimal orientation and assess if the drug is a good candidate or not. One solution is to formulate the problem as a mathematical optimization problem where the optimal solution corresponds to the most likely ligand-protein configuration. This optimization problem can be solved on a quantum computer using methods like the Quantum Approximate Optimization Algorithm (QAOA). This tutorial demonstrates how this [paper](https://arxiv.org/pdf/2308.04098) used digitized-counteradiabatic (DC) QAOA to study molecular docking. This tutorial assumes you have an understanding of QAOA, if not, please see the CUDA-Q MaxCut tutorial found [here](https://nvidia.github.io/cuda-quantum/latest/applications/python/qaoa.html).\n", "\n", "The next section provides more detail on the problem setup followed by CUDA-Q implementations below." ] @@ -25,10 +25,10 @@ "\n", "\n", "There are 6 key steps:\n", - "1. The experimental protein and ligand structures are determined and used to select pharmacores, or an important chemical group that will govern the chemical interactions,\n", - "2. T wo labeled distance graphs (LAGs) of size $N$ and $M$ represent the protein and the ligand, respectively. Each node corresponds to a pharmacore and each edge weight corresponds to the distance between pharmacores.\n", + "1. The experimental protein and ligand structures are determined and used to select pharmacores, or an important chemical group that will govern the chemical interactions.\n", + "2. Two labeled distance graphs (LAGs) of size $N$ and $M$ represent the protein and the ligand, respectively. Each node corresponds to a pharmacore and each edge weight corresponds to the distance between pharmacores.\n", "3. A $M*N$ node binding interaction graph (BIG) is created from the LAGs. Each node in the BIG graph corresponds to a pair of pharmacores, one from the ligand and the other from the protein. The existence of edges between nodes in the BIG graph are determined from the LAGs and correspond to interactions that can feesibly coexist. Therefore, cliques in the graph correspond to mutually possible interactions. \n", - "4. The problem is mapped to a QAOA circuit and corresponding Hamiltonian, and the ground state solution is determined.\n", + "4. The problem is mapped to a QAOA circuit and corresponding Hamiltonian. From there, the ground state solution is determined.\n", "5. The ground state will produce the maximum weighted clique which corresponds to the best (most strongly bound) orientation of the ligand and protein.\n", "6. The predicted docking structure is interpreted from the QAOA result and is used for further analysis.\n" ] @@ -50,16 +50,14 @@ "source": [ "import cudaq\n", "from cudaq import spin\n", - "import numpy as np\n", - "\n", - "# cudaq.set_target('nvidia')" + "import numpy as np\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The block below defines two of the BIG data sets from the paper. The first is a smaller example, but it can be swapped with the commented out example below at your discretion. The weights are specified for each node based on the nature of the ligand and protein pharmacores represented by the node" + "The block below defines two of the BIG data sets from the paper. The first is a smaller example, but it can be swapped with the commented out example below at your discretion. The weights are specified for each node based on the nature of the ligand and protein pharmacores represented by the node." ] }, { @@ -77,7 +75,7 @@ } ], "source": [ - "# The two graphs input from the paper\n", + "# The two graph inputs from the paper\n", "\n", "# BIG 1\n", "\n", @@ -113,12 +111,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Next, the Hamiltonian is constructed. \n", + "Next, the Hamiltonian is constructed: \n", "\n", "$$H = \\frac{1}{2}\\sum_{i \\in V}w_i(\\sigma^z_i - 1) + \\frac{P}{4} \\sum_{(i,j) \\notin E, i \\neq j} (\\sigma^z_i -1)(\\sigma^z_j - 1) $$\n", "\n", "\n", - "The first term concerns the vertices and the weights of the given pharmacores. The second term is a penalty term that penalizes edges of the graph with no interactions. The penalty $P$ is set by the user and is defined as 6 in the cell above. The function below returns the Hamiltonina as a CUDA-Q `spin_op` object.\n", + "The first term concerns the vertices and the weights of the given pharmacores. The second term is a penalty term that penalizes edges of the graph with no interactions. The penalty $P$ is set by the user and is defined as 6 in the cell above. The function below returns the Hamiltonian as a CUDA-Q `spin_op` object.\n", "\n" ] }, @@ -208,7 +206,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The kernel below defines a DC-QAOA circuit. What makes the approach \"DC\" is the inclusion of additional counteradiabatic terms to better drive the optimization to the ground state. These terms are digitized and applied as additional operations following each QAOA layer. The increase in parameters is hopefully offset by requiring fewer layers. In this example, the DC terms are additional parameterized $Y$ operations applied to each qubit. These can be commented out to run conventional QAOA." + "The kernel below defines a DC-QAOA circuit. What makes the approach \"DC\" is the inclusion of additional counteradiabatic terms to better drive the optimization to the ground state. These terms are digitized and applied as additional operations following each QAOA layer. The increase in parameters is hopefully offset by requiring fewer layers. In this example, the DC terms are the additional parameterized $Y$ operations applied to each qubit. These can be commented out to run conventional QAOA." ] }, { @@ -246,7 +244,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The classical optimizer for the QAOA procedure can be specified as one of the build in CUDA-Q optimizers, in this case Nelder Mead. The parameter count is defined for DC-QAOA, but can be swapped with the commented line below for conventional QAOA." + "The classical optimizer for the QAOA procedure can be specified as one of the built-in CUDA-Q optimizers, in this case Nelder Mead. The parameter count is defined for DC-QAOA, but can be swapped with the commented line below for conventional QAOA." ] }, { diff --git a/pr-2458/_sources/applications/python/hadamard_test.ipynb.txt b/pr-2458/_sources/applications/python/hadamard_test.ipynb.txt index 8199b74d6b..1d1f781d59 100644 --- a/pr-2458/_sources/applications/python/hadamard_test.ipynb.txt +++ b/pr-2458/_sources/applications/python/hadamard_test.ipynb.txt @@ -6,14 +6,14 @@ "source": [ "# Using the Hadamard Test to Determine Quantum Krylov Subspace Decomposition Matrix Elements\n", "\n", - "The Hadamard test, is a quantum algorithm for estimating the expectation values and is a useful subroutine for a number of quantum applications ranging from estimation of molecular ground state energies to quantum semidefinite programming. This tutorial will briefly introduce the Hadamard test, and demonstrate how it can be implemented in CUDA-Q and then parallelized for a Quantum Krylov Subspace Diagonalization application.\n", + "The Hadamard test is a quantum algorithm for estimating expectation values and is a useful subroutine for a number of quantum applications ranging from estimation of molecular ground state energies to quantum semidefinite programming. This tutorial will briefly introduce the Hadamard test, demonstrate how it can be implemented in CUDA-Q, and then parallelized for a Quantum Krylov Subspace Diagonalization application.\n", "\n", "The Hadamard test is performed using a register with an ancilla qubit in the $\\ket{0}$ state and a prepared quantum state $\\ket{\\psi}$, the following circuit can be used to extract the expectation value from measurement of the ancilla.\n", "\n", "\n", "![Htest](./images/htest.png)\n", "\n", - "The key insight is to note that $$P(0) = \\frac{1}{2} \\left[ I + Re \\bra{\\psi} O \\ket{\\phi} \\right]$$ and $$P(1) = \\frac{1}{2} \\left[ I - Re \\bra{\\psi} O \\ket{\\phi} \\right]$$ so their difference is equal to $$P(0)-P(1) = Re \\bra{\\psi} O \\ket{\\phi}$$\n", + "The key insight is that $$P(0) = \\frac{1}{2} \\left[ I + Re \\bra{\\psi} O \\ket{\\phi} \\right]$$ and $$P(1) = \\frac{1}{2} \\left[ I - Re \\bra{\\psi} O \\ket{\\phi} \\right]$$ so their difference is equal to $$P(0)-P(1) = Re \\bra{\\psi} O \\ket{\\phi}.$$\n", "\n", "\n", "More details and a short derivation can be found [here](https://en.wikipedia.org/wiki/Hadamard_test)." @@ -26,17 +26,17 @@ "What if you want to perform the Hadamard test to compute an expectation value like $\\bra{\\psi} O \\ket{\\phi}$, where $\\ket{\\psi}$ and $\\ket{\\phi}$ are different states and $O$ is a Pauli Operator? This is a common subroutine for the QKSD, where matrix elements are determined by computing expectation values between different states.\n", "\n", "Defining $O$ as \n", - "$$O = X_1X_2$$\n", + "$$O = X_1X_2,$$\n", "\n", "and given the fact that\n", - "$$\\ket{\\psi} = U_{\\psi}\\ket{0} \\qquad \\ket{\\phi} = U_{\\phi}\\ket{0}$$\n", + "$$\\ket{\\psi} = U_{\\psi}\\ket{0} \\qquad \\ket{\\phi} = U_{\\phi}\\ket{0},$$\n", "\n", - "We can combine the state preparation steps into the operator resulting in\n", - "$$\\bra{\\psi}O\\ket{\\phi} = \\bra{0}U_\\psi^\\dagger O U_\\phi\\ket{0}$$\n", - "Which corresponds to the following circuit\n", + "we can combine the state preparation steps into the operator resulting in\n", + "$$\\bra{\\psi}O\\ket{\\phi} = \\bra{0}U_\\psi^\\dagger O U_\\phi\\ket{0},$$\n", + "which corresponds to the following circuit.\n", "![Htest2](./images/htestfactored.png)\n", "\n", - "By preparing this circuit, and repeatedly measuring the ancilla qubit, allows for estimation of the expectation value as $$P(0)-P(1) = Re \\bra{\\psi} O \\ket{\\phi}$$\n", + "By preparing this circuit, and repeatedly measuring the ancilla qubit, we estimate the expectation value as $$P(0)-P(1) = Re \\bra{\\psi} O \\ket{\\phi}.$$\n", "\n", "\n", "The following sections demonstrate how this can be performed in CUDA-Q." @@ -53,7 +53,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Before performing the Hadamard test, lets determine the exact expectation value by performing the matrix multiplications explicitly. The code below builds two CUDA-Q kernels corresponding to $\\ket{\\psi} = \\frac{1}{\\sqrt{2}}\\begin{pmatrix}1 \\\\ 0 \\\\ 1 \\\\ 0\\end{pmatrix}$ and $\\ket{\\phi} = \\begin{pmatrix}0 \\\\ 1 \\\\ 0 \\\\ 0\\end{pmatrix}$" + "Before performing the Hadamard test, let's determine the exact expectation value by performing the matrix multiplications explicitly. The code below builds two CUDA-Q kernels corresponding to $\\ket{\\psi} = \\frac{1}{\\sqrt{2}}\\begin{pmatrix}1 \\\\ 0 \\\\ 1 \\\\ 0\\end{pmatrix}$ and $\\ket{\\phi} = \\begin{pmatrix}0 \\\\ 1 \\\\ 0 \\\\ 0\\end{pmatrix}.$" ] }, { @@ -87,7 +87,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The state vectors can be accessed using the `get_state` command and printed as numpy arrays" + "The state vectors can be accessed using the `get_state` command and printed as numpy arrays:" ] }, { @@ -118,7 +118,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The Hamiltonian operator ($O$ in the derivation above) is defined as a CUDA-Q spin operator and converted to a matrix withe the `to_matrix`. The following line of code performs the explicit matrix multiplications to produce the exact expectation value." + "The Hamiltonian operator ($O$ in the derivation above) is defined as a CUDA-Q spin operator and converted to a matrix with `to_matrix`. The following line of code performs the explicit matrix multiplications to produce the exact expectation value." ] }, { @@ -208,7 +208,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The CUDA-Q Sample method computes 100000 sample ancilla measurements and uses them to estimate the expectation value. The standard error is provided as well. Try increasing the sample size and note the convergence of the expectation value and the standard error towards the numerical result." + "The CUDA-Q `sample` method computes 100000 sample ancilla measurements, and from them we can estimate the expectation value. The standard error is provided as well. Try increasing the sample size and note the convergence of the expectation value and the standard error towards the numerical result." ] }, { @@ -249,9 +249,9 @@ "\n", "![Htest3](./images/QKSD.png)\n", "\n", - "This method can be easily parallelized and multiple QPUs, if available could compute the matrix elements asynchronously. The CUDA-Q `mqpu` backend allows you to simulate a computation across multiple simulated QPUs. The code below demonstrates how.\n", + "This method can be easily parallelized, and multiple QPUs, if available, could compute the matrix elements asynchronously. The CUDA-Q `mqpu` backend allows you to simulate a computation across multiple simulated QPUs. The code below demonstrates how.\n", "\n", - "First, the Hadamard test circuit is defined, but this time the $\\ket{\\psi}$ and $\\ket{\\phi}$ states contain parameterized rotations so that multiple states can be quickly generated for the sake of example." + "First, the Hadamard test circuit is defined, but this time the $\\ket{\\psi}$ and $\\ket{\\phi}$ states contain parameterized rotations so that multiple states can be quickly generated, for the sake of example." ] }, { @@ -302,7 +302,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -314,7 +314,7 @@ } ], "source": [ - "cudaq.set_target(\"nvidia-mqpu\")\n", + "cudaq.set_target(\"nvidia\", option=\"mqpu\")\n", "\n", "target = cudaq.get_target()\n", "qpu_count = target.num_qpus()\n", @@ -354,7 +354,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The four matrix elements are shown below and now be classically processed to produce the eigenvalues." + "The four matrix elements are shown below and can be classically processed to produce the eigenvalues." ] }, { diff --git a/pr-2458/_sources/applications/python/krylov.ipynb.txt b/pr-2458/_sources/applications/python/krylov.ipynb.txt index 1954212c02..183a13d691 100644 --- a/pr-2458/_sources/applications/python/krylov.ipynb.txt +++ b/pr-2458/_sources/applications/python/krylov.ipynb.txt @@ -7,39 +7,45 @@ "source": [ "# Multi-reference Quantum Krylov Algorithm - $H_2$ Molecule\n", "\n", - "The multireference selected quantum Krylov (MRSQK) algorithm is defined in [this paper](https://arxiv.org/pdf/1911.05163) and was developed as a low-cost alternative to quantum phase estimation. This tutorial will demonstrate how this algorithm can be implemented in CUDA-Q and accelerated using multiple GPUs. The CUDA-Q Hadamard test tutorial might provide helpful background information for understanding this tutorial.\n", + "The multireference selected quantum Krylov (MRSQK) algorithm is defined in [this paper](https://arxiv.org/pdf/1911.05163) and was developed as a low-cost alternative to quantum phase estimation. This tutorial will demonstrate how this algorithm can be implemented in CUDA-Q and accelerated using multiple GPUs. The [CUDA-Q Hadamard test tutorial](https://nvidia.github.io/cuda-quantum/latest/applications/python/hadamard_test.html) might provide helpful background information for understanding this tutorial.\n", "\n", "The algorithm works by preparing an initial state, and then defining this state in a smaller subspace constructed with a basis that corresponds to Trotter steps of the initial state. This subspace can be diagonalized to produce an approximate energy for the system without variational optimization of any parameters.\n", "\n", "In the example below, the initial guess is the ground state of the diagonalized Hamiltonian for demonstration purposes. In practice one could use a number of heuristics to prepare the ground state such as Hartree Fock or CISD. A very promising ground state preparation method which can leverage quantum computers is the linear combination of unitaries (LCU). LCU would allow for the state preparation to occur completely on the quantum computer and avoid storing an inputting the exponentially large state vector.\n", "\n", "\n", - "Regardless of the method used for state preparation, the procedure begins by selecting a $d$ dimensional basis of reference states ${\\Phi_0 \\cdots \\Phi_d}$ where each is a linear combination of slater determinants. \n", + "Regardless of the method used for state preparation, the procedure begins by selecting a $d$-dimensional basis of reference states ${\\Phi_0 \\cdots \\Phi_d},$ where each is a linear combination of Slater determinants: \n", "\n", - "$$ \\ket{\\Phi_I} = \\sum_{\\mu} d_{\\mu I}\\ket{\\phi_{\\mu}} $$\n", + "$$ \\ket{\\Phi_I} = \\sum_{\\mu} d_{\\mu I}\\ket{\\phi_{\\mu}}. $$\n", "\n", "\n", - "From this, a non-orthogonal Krylov Space $\\mathcal{K} = \\{\\psi_{0} \\cdots \\psi_{N}\\}$ is constructed by applying a family of $s$ unitary operators on each of the $d$ reference states resulting in $d*s = N$ elements in the Krylov space where, \n", - "$$ \\ket{\\psi_{\\alpha}} \\equiv \\ket{\\psi_I^{(n)}} = \\hat{U}_n\\ket{\\Phi_I} $$\n", + "From this, a non-orthogonal Krylov Space $\\mathcal{K} = \\{\\psi_{0} \\cdots \\psi_{N}\\}$ is constructed by applying a family of $s$ unitary operators on each of the $d$ reference states resulting in $d*s = N$ elements in the Krylov space where \n", + "$$ \\ket{\\psi_{\\alpha}} \\equiv \\ket{\\psi_I^{(n)}} = \\hat{U}_n\\ket{\\Phi_I}, $$\n", "\n", "Therefore, the general quantum state that we originally set out to describe is\n", "\n", - "$$ \\ket{\\Psi} = \\sum_{\\alpha} c_{\\alpha}\\ket{\\psi_{\\alpha}} = \\sum_{I=0}^d \\sum_{n=0}^s c_I^{(n)}\\hat{U}_n\\ket{\\Phi_I} $$\n", + "$$ \\ket{\\Psi} = \\sum_{\\alpha} c_{\\alpha}\\ket{\\psi_{\\alpha}} = \\sum_{I=0}^d \\sum_{n=0}^s c_I^{(n)}\\hat{U}_n\\ket{\\Phi_I}. $$\n", "\n", "The energy of this state can be obtained by solving the generalized eigenvalue problem\n", - "$$ \\boldsymbol{Hc}=\\boldsymbol{Sc}E $$\n", + "$$ \\boldsymbol{Hc}=\\boldsymbol{Sc}E, $$\n", "\n", - "Where the elements of the overlap and Hamiltonian matrix are\n", + "where the elements of the overlap are\n", "\n", "$$S_{\\alpha \\beta} = \\braket{\\psi_{\\alpha}|\\psi_{\\beta}} = \\braket{\\Phi_I|\\hat{U}_m^{\\dagger}\\hat{U}_n|\\Phi_J}$$ \n", "\n", - "$$H_{\\alpha \\beta} = \\braket{\\psi_{\\alpha}|\\hat{H}|\\psi_{\\beta}} = \\braket{\\Phi_I|\\hat{U}_m^{\\dagger}\\hat{H}\\hat{U}_n|\\Phi_J}$$\n", + "and Hamiltonian matrix is\n", "\n", - "These matrix elements are computed using a quantum computer and the Hadamard test with a circuit shown below for the case of the overlap matrix elements (The Hamiltonian matrix elements circuit would include controlled application of the Hamiltonian in the circuit). Once the matrices are constructed, the diagonalization is performed classically to produce an estimate for the ground state in question.\n", + "$$H_{\\alpha \\beta} = \\braket{\\psi_{\\alpha}|\\hat{H}|\\psi_{\\beta}} = \\braket{\\Phi_I|\\hat{U}_m^{\\dagger}\\hat{H}\\hat{U}_n|\\Phi_J}.$$\n", + "\n", + "The matrix elements for $S$ are computed with the Hadamard test with a circuit shown below for the case of the overlap matrix elements. \n", "\n", "![Htest](./images/krylovcircuit.png)\n", "\n", - "The $2\\sigma_+$ term refers to measurement of the expectation value of this circuit with the $X+iY$ operator. \n" + "The $2\\sigma_+$ term refers to measurement of the expectation value of this circuit with the $X+iY$ operator.\n", + "\n", + "The Hamiltonian matrix elements are computed with a circuit that includes controlled application of the Hamiltonian. Once the $H$ and $S$ matrices are constructed, the diagonalization is performed classically to produce an estimate for the ground state in question.\n", + "\n", + "\n" ] }, { @@ -140,7 +146,7 @@ " return result\n", "\n", "\n", - "#Build the lists of coefficients and Pauli Words from H2 Hamiltonian\n", + "# Build the lists of coefficients and Pauli Words from the H2 Hamiltonian\n", "coefficient = termCoefficients(hamiltonian)\n", "pauli_string = termWords(hamiltonian)\n", "\n", @@ -153,7 +159,7 @@ "id": "74b4c079-8837-47ae-a484-52ec5f4a160e", "metadata": {}, "source": [ - "In the case of this example, the unitary operators that build the Krylov subspace are first-order Trotter operations at different time steps. The performance here could potentially be improved by increasing the size of the time step, using a higher order Trotter approximation, or using other sorts of approximations. The CUDA-Q kernels below define the unitary operations that construct the $\\psi$ basis. Each receives the target qubits, the time step, and components of the Hamiltonian." + "In this example, the unitary operators that build the Krylov subspace are first-order Trotter operations at different time steps. The performance here could potentially be improved by increasing the size of the time step, using a higher order Trotter approximation, or using other sorts of approximations. The CUDA-Q kernels below define the unitary operations that construct the $\\psi$ basis. Each receives the target qubits, the time step, and components of the Hamiltonian." ] }, { @@ -300,11 +306,11 @@ "\n", "The cell below computes the overlap matrix. This can be done in serial or in parallel, depending on the `multi_gpu` specification. First, an operator is built to apply the identity to the overlap matrix circuit when `apply_pauli` is called. Next, the `wf_overlap` array is constructed which will hold the matrix elements. \n", "\n", - "Next, a pair of nested loops, iterate over the time steps defined by the dimension of the subspace. Each m,n combination corresponds to computation of an off-diagonal matrix element of the overlap matrix $S$ using the Hadamard test. This is accomplished by calling the CUDA-Q `observe` function with the X and Y operators, along with the time steps, the components of the Hamiltonian matrix, and the initial state vector `vec`.\n", + "Next, a pair of nested loops iterate over the time steps defined by the dimension of the subspace. Each m,n combination corresponds to computation of an off-diagonal matrix element of the overlap matrix $S$ using the Hadamard test. This is accomplished by calling the CUDA-Q `observe` function with the X and Y operators, along with the time steps, the components of the Hamiltonian matrix, and the initial state vector `vec`.\n", "\n", "The observe function broadcasts over the two provided operators $X$ and $Y$ and returns a list of results. The `expectation` function returns the expectation values which are summed and stored in the matrix.\n", "\n", - "The multi-gpu case completes the same steps, expect for `observe_async` is used. This allows for the $X$ and $Y$ observables to be evaluated at the same time on two different simulated QPUs. In this case, the results are stored in lists corresponding to the real an imaginary parts, and then accessed later with the `get` command to build $S$\n" + "The multi-gpu case completes the same steps, except the `observe_async` command is used. This allows for the $X$ and $Y$ observables to be evaluated at the same time on two different simulated QPUs. In this case, the results are stored in lists corresponding to the real and imaginary parts. These are then accessed later with the `get` command to build $S$.\n" ] }, { @@ -541,19 +547,19 @@ "id": "1917bd58-4ce3-4e3e-9ccf-096577c0da14", "metadata": {}, "source": [ - "### Determining the ground state energy of the Subspace\n", + "### Determining the ground state energy of the subspace\n", "\n", "The final step is to solve the generalized eigenvaulue problem with the overlap and Hamiltonian matrices constructed using the quantum computer. The procedure begins by diagonalizing $S$ with the transform $$S = U\\Sigma U^{\\dagger}$$\n", "\n", - "The eigenvectors $v$ and eigenvalues $s$ are used to construct a new matrix $X'$\n", + "The eigenvectors $v$ and eigenvalues $s$ are used to construct a new matrix $X':$\n", "\n", - "$$ X' = S ^{\\frac{-1}{2}} = \\sum_k v_{ki} \\frac{1}{\\sqrt{s_k}} v_{kj}$$\n", + "$$ X' = S ^{\\frac{-1}{2}} = \\sum_k v_{ki} \\frac{1}{\\sqrt{s_k}} v_{kj}.$$\n", "\n", - "The $X'$ matrix diagonalizes $H$\n", + "The matrix $X'$ diagonalizes $H:$\n", "\n", - "$$ X'^{\\dagger}HX' = ES^{\\frac{1}{2}}C$$\n", + "$$ X'^{\\dagger}HX' = ES^{\\frac{1}{2}}C.$$\n", "\n", - "Using the eigenvectors of $H'$, ($^{\\frac{1}{2}}C$), the original eigenvectors to the problem can be found by left multiplying by $S^{\\frac{-1}{2}}C$" + "Using the eigenvectors of $H'$, ($^{\\frac{1}{2}}C$), the original eigenvectors to the problem can be found by left multiplying by $S^{\\frac{-1}{2}}C.$" ] }, { diff --git a/pr-2458/_sources/applications/python/logical_aim_sqale.ipynb.txt b/pr-2458/_sources/applications/python/logical_aim_sqale.ipynb.txt new file mode 100644 index 0000000000..f51bd10294 --- /dev/null +++ b/pr-2458/_sources/applications/python/logical_aim_sqale.ipynb.txt @@ -0,0 +1,1356 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Anderson Impurity Model ground state solver on Infleqtion's Sqale" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ground state quantum chemistry—computing total energies of molecular configurations to within chemical accuracy—is perhaps the most highly-touted industrial application of fault-tolerant quantum computers. Strongly correlated materials, for example, are particularly interesting, and tools like dynamical mean-field theory (DMFT) allow one to account for the effect of their strong, localized electronic correlations. These DMFT models help predict material properties by approximating the system as a single site impurity inside a “bath” that encompasses the rest of the system. Simulating such dynamics can be a tough task using classical methods, but can be done efficiently on a quantum computer via quantum simulation.\n", + "\n", + "In this notebook, we showcase a workflow for preparing the ground state of the minimal single-impurity Anderson model (SIAM) using the Hamiltonian Variational Ansatz for a range of realistic parameters. As a first step towards running DMFT on a fault-tolerant quantum computer, we will use logical qubits encoded in the `[[4, 2, 2]]` code. Using this workflow, we will obtain the ground state energy estimates via noisy simulation, and then also execute the corresponding optimized circuits on Infleqtion's gate-based neutral-atom quantum computer, making the benefits of logical qubits apparent. More details can be found in our [paper](https://arxiv.org/abs/2412.07670)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This demo notebook uses CUDA-Q (`cudaq`) and a CUDA-QX library, `cudaq-solvers`; let us first begin by importing (and installing as needed) these packages:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "try:\n", + " import cudaq_solvers as solvers\n", + " import cudaq\n", + " import matplotlib.pyplot as plt\n", + "except ImportError:\n", + " print(\"Installing required packages...\")\n", + " %pip install --quiet 'cudaq-solvers' 'matplotlib'\n", + " print(\"Installed `cudaq`, `cudaq-solvers`, and `matplotlib` packages.\")\n", + " print(\"You may need to restart the kernel to import newly installed packages.\")\n", + " import cudaq_solvers as solvers\n", + " import cudaq\n", + " import matplotlib.pyplot as plt\n", + "\n", + "from collections.abc import Mapping, Sequence\n", + "import numpy as np\n", + "from scipy.optimize import minimize\n", + "import os" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Performing logical Variational Quantum Eigensolver (VQE) with CUDA-QX" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To prepare our ground state quantum Anderson impurity model circuits (referred to as AIM circuits in this notebook for short), we use VQE to train an ansatz to minimize a Hamiltonian and obtain optimal angles that can be used to set the AIM circuits. As described in our [paper](https://arxiv.org/abs/2412.07670), the associated restricted Hamiltonian for our SIAM can be reduced to,\n", + "$$ \n", + "\\begin{equation}\n", + "H_{(U, V)} = U (Z_0 Z_2 - 1) / 4 + V (X_0 + X_2),\n", + "\\end{equation}\n", + "$$\n", + "where $U$ is the Coulomb interaction and $V$ the hybridization strength. In this notebook workflow, we will optimize over a 2-dimensional grid of Hamiltonian parameter values, namely $U\\in \\{1, 5, 9\\}$ and $V\\in \\{-9, -1, 7\\}$ (with all values assumed to be in units of eV), to ensure that the ansatz is generally trainable and expressive, and obtain 9 different circuit layers identified by the key $(U, V)$. We will simulate the VQE on GPU (or optionally on CPU if you do not have GPU access), enabled by CUDA-Q, in the absence of noise:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "if cudaq.num_available_gpus() == 0:\n", + " cudaq.set_target(\"qpp-cpu\", option=\"fp64\")\n", + "else:\n", + " cudaq.set_target(\"nvidia\", option=\"fp64\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This workflow can be easily defined in CUDA-Q as shown in the cell below, using the CUDA-QX Solvers library (which accelerates quantum algorithms like the VQE):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def ansatz(n_qubits: int) -> cudaq.Kernel:\n", + " # Create a CUDA-Q parameterized kernel\n", + " paramterized_ansatz, variational_angles = cudaq.make_kernel(list)\n", + " qubits = paramterized_ansatz.qalloc(n_qubits)\n", + "\n", + " # Using |+> as the initial state:\n", + " paramterized_ansatz.h(qubits[0])\n", + " paramterized_ansatz.cx(qubits[0], qubits[1])\n", + "\n", + " paramterized_ansatz.rx(variational_angles[0], qubits[0])\n", + " paramterized_ansatz.cx(qubits[0], qubits[1])\n", + " paramterized_ansatz.rz(variational_angles[1], qubits[1])\n", + " paramterized_ansatz.cx(qubits[0], qubits[1])\n", + " return paramterized_ansatz\n", + "\n", + "\n", + "def run_logical_vqe(cudaq_hamiltonian: cudaq.SpinOperator) -> tuple[float, list[float]]:\n", + " # Set seed for easier reproduction\n", + " np.random.seed(42)\n", + "\n", + " # Initial angles for the optimizer\n", + " init_angles = np.random.random(2) * 1e-1\n", + "\n", + " # Obtain CUDA-Q Ansatz\n", + " num_qubits = cudaq_hamiltonian.get_qubit_count()\n", + " variational_kernel = ansatz(num_qubits)\n", + "\n", + " # Perform VQE optimization\n", + " energy, params, _ = solvers.vqe(\n", + " variational_kernel,\n", + " cudaq_hamiltonian,\n", + " init_angles,\n", + " optimizer=minimize,\n", + " method=\"SLSQP\",\n", + " tol=1e-10,\n", + " )\n", + " return energy, params" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constructing circuits in the `[[4,2,2]]` encoding" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `[[4,2,2]]` code is a quantum error detection code that uses four physical qubits to encode two logical qubits. In this notebook, we will construct two variants of quantum circuits: physical (bare, unencoded) and logical (encoded). These circuits will be informed by the Hamiltonian Variational Ansatz described earlier. To measure all the terms in our Hamiltonian, we will measure the data qubits in both the $Z$- and $X$-basis, as allowed by the `[[4,2,2]]` logical gateset. Full details on the circuit constructions are outlined in our [paper](https://arxiv.org/abs/2412.07670)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below, we create functions to build our CUDA-Q AIM circuits, both physical and logical versions. As we consider noisy simulation in this notebook, we will include some noisy gates. Here, for simplicity, we will just register a custom identity gate -- to be later used as a noisy operation to model readout error: " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "cudaq.register_operation(\"meas_id\", np.identity(2))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def aim_physical_circuit(\n", + " angles: list[float], basis: str, *, ignore_meas_id: bool = False\n", + ") -> cudaq.Kernel:\n", + " kernel = cudaq.make_kernel()\n", + " qubits = kernel.qalloc(2)\n", + "\n", + " # Bell state prep\n", + " kernel.h(qubits[0])\n", + " kernel.cx(qubits[0], qubits[1])\n", + "\n", + " # Rx Gate\n", + " kernel.rx(angles[0], qubits[0])\n", + "\n", + " # ZZ rotation\n", + " kernel.cx(qubits[0], qubits[1])\n", + " kernel.rz(angles[1], qubits[1])\n", + " kernel.cx(qubits[0], qubits[1])\n", + "\n", + " if basis == \"z_basis\":\n", + " if not ignore_meas_id:\n", + " kernel.for_loop(\n", + " start=0, stop=2, function=lambda q_idx: getattr(kernel, \"meas_id\")(qubits[q_idx])\n", + " )\n", + " kernel.mz(qubits)\n", + " elif basis == \"x_basis\":\n", + " kernel.h(qubits)\n", + " if not ignore_meas_id:\n", + " kernel.for_loop(\n", + " start=0, stop=2, function=lambda q_idx: getattr(kernel, \"meas_id\")(qubits[q_idx])\n", + " )\n", + " kernel.mz(qubits)\n", + " else:\n", + " raise ValueError(\"Unsupported basis provided:\", basis)\n", + " return kernel" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def aim_logical_circuit(\n", + " angles: list[float], basis: str, *, ignore_meas_id: bool = False\n", + ") -> cudaq.Kernel:\n", + " kernel = cudaq.make_kernel()\n", + " qubits = kernel.qalloc(6)\n", + "\n", + " kernel.for_loop(start=0, stop=3, function=lambda idx: kernel.h(qubits[idx]))\n", + " kernel.cx(qubits[1], qubits[4])\n", + " kernel.cx(qubits[2], qubits[3])\n", + " kernel.cx(qubits[0], qubits[1])\n", + " kernel.cx(qubits[0], qubits[3])\n", + "\n", + " # Rx teleportation\n", + " kernel.rx(angles[0], qubits[0])\n", + "\n", + " kernel.cx(qubits[0], qubits[1])\n", + " kernel.cx(qubits[0], qubits[3])\n", + " kernel.h(qubits[0])\n", + "\n", + " if basis == \"z_basis\":\n", + " if not ignore_meas_id:\n", + " kernel.for_loop(\n", + " start=0, stop=5, function=lambda idx: getattr(kernel, \"meas_id\")(qubits[idx])\n", + " )\n", + " kernel.mz(qubits)\n", + " elif basis == \"x_basis\":\n", + " # ZZ rotation and teleportation\n", + " kernel.cx(qubits[3], qubits[5])\n", + " kernel.cx(qubits[2], qubits[5])\n", + " kernel.rz(angles[1], qubits[5])\n", + " kernel.cx(qubits[1], qubits[5])\n", + " kernel.cx(qubits[4], qubits[5])\n", + " kernel.for_loop(start=1, stop=5, function=lambda idx: kernel.h(qubits[idx]))\n", + " if not ignore_meas_id:\n", + " kernel.for_loop(\n", + " start=0, stop=6, function=lambda idx: getattr(kernel, \"meas_id\")(qubits[idx])\n", + " )\n", + " kernel.mz(qubits)\n", + " else:\n", + " raise ValueError(\"Unsupported basis provided:\", basis)\n", + " return kernel" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the circuit definitions above, we can now define a function that automatically runs the VQE and constructs a dictionary containing all the AIM circuits we want to submit to hardware (or noisily simulate):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def generate_circuit_set(ignore_meas_id: bool = False) -> object:\n", + " u_vals = [1, 5, 9]\n", + " v_vals = [-9, -1, 7]\n", + " circuit_dict = {}\n", + " for u in u_vals:\n", + " for v in v_vals:\n", + " qubit_hamiltonian = (\n", + " 0.25 * u * cudaq.spin.z(0) * cudaq.spin.z(1)\n", + " - 0.25 * u\n", + " + v * cudaq.spin.x(0)\n", + " + v * cudaq.spin.x(1)\n", + " )\n", + " _, opt_params = run_logical_vqe(qubit_hamiltonian)\n", + " angles = [float(angle) for angle in opt_params]\n", + " print(f\"Computed optimal angles={angles} for U={u}, V={v}\")\n", + "\n", + " tmp_physical_dict = {}\n", + " tmp_logical_dict = {}\n", + " for basis in (\"z_basis\", \"x_basis\"):\n", + " tmp_physical_dict[basis] = aim_physical_circuit(\n", + " angles, basis, ignore_meas_id=ignore_meas_id\n", + " )\n", + " tmp_logical_dict[basis] = aim_logical_circuit(\n", + " angles, basis, ignore_meas_id=ignore_meas_id\n", + " )\n", + "\n", + " circuit_dict[f\"{u}:{v}\"] = {\n", + " \"physical\": tmp_physical_dict,\n", + " \"logical\": tmp_logical_dict,\n", + " }\n", + " print(\"\\nFinished building optimized circuits!\")\n", + " return circuit_dict" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Computed optimal angles=[1.5846845738799267, 1.5707961678256028] for U=1, V=-9\n", + "Computed optimal angles=[4.588033710930825, 4.712388365176642] for U=1, V=-1\n", + "Computed optimal angles=[-1.588651490745171, 1.5707962742876598] for U=1, V=7\n", + "Computed optimal angles=[1.64012940802256, 1.5707963354922125] for U=5, V=-9\n", + "Computed optimal angles=[2.1293956916868737, 1.5707963294715355] for U=5, V=-1\n", + "Computed optimal angles=[-1.6598458659836037, 1.570796331040382] for U=5, V=7\n", + "Computed optimal angles=[1.695151467539617, 1.5707960973500679] for U=9, V=-9\n", + "Computed optimal angles=[2.4149519241823376, 1.5707928509325972] for U=9, V=-1\n", + "Computed optimal angles=[-1.7301462729177735, 1.570796033796985] for U=9, V=7\n", + "\n", + "Finished building optimized circuits!\n" + ] + } + ], + "source": [ + "sim_circuit_dict = generate_circuit_set()\n", + "circuit_layers = sim_circuit_dict.keys()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Setting up submission and decoding workflow " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this section, we define various helper functions that will play a role in generating the associated energies of the AIM circuits based on the circuit samples (in the different bases), as well as decode the logical circuits with post-selection informed by the `[[4,2,2]]` code:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "def _num_qubits(counts: Mapping[str, float]) -> int:\n", + " for key in counts:\n", + " if key.isdecimal():\n", + " return len(key)\n", + " return 0\n", + "\n", + "\n", + "def process_counts(\n", + " counts: Mapping[str, float],\n", + " data_qubits: Sequence[int],\n", + " flag_qubits: Sequence[int] = (),\n", + ") -> dict[str, float]:\n", + " new_data: dict[str, float] = {}\n", + " for key, val in counts.items():\n", + " if not all(key[i] == \"0\" for i in flag_qubits):\n", + " continue\n", + "\n", + " new_key = \"\".join(key[i] for i in data_qubits)\n", + "\n", + " if not set(\"01\").issuperset(new_key):\n", + " continue\n", + "\n", + " new_data.setdefault(new_key, 0)\n", + " new_data[new_key] += val\n", + "\n", + " return new_data\n", + "\n", + "\n", + "def decode(counts: Mapping[str, float]) -> dict[str, float]:\n", + " \"\"\"Decode physical counts into logical counts. Should be called after `process_counts`.\"\"\"\n", + "\n", + " if not counts:\n", + " return {}\n", + "\n", + " num_qubits = _num_qubits(counts)\n", + " assert num_qubits % 4 == 0\n", + "\n", + " physical_to_logical = {\n", + " \"0000\": \"00\",\n", + " \"1111\": \"00\",\n", + " \"0011\": \"01\",\n", + " \"1100\": \"01\",\n", + " \"0101\": \"10\",\n", + " \"1010\": \"10\",\n", + " \"0110\": \"11\",\n", + " \"1001\": \"11\",\n", + " }\n", + "\n", + " new_data: dict[str, float] = {}\n", + " for key, val in counts.items():\n", + " physical_keys = [key[i : i + 4] for i in range(0, num_qubits, 4)]\n", + " logical_keys = [physical_to_logical.get(physical_key) for physical_key in physical_keys]\n", + " if None not in logical_keys:\n", + " new_key = \"\".join(logical_keys)\n", + " new_data.setdefault(new_key, 0)\n", + " new_data[new_key] += val\n", + "\n", + " return new_data\n", + "\n", + "\n", + "def ev_x(counts: Mapping[str, float]) -> float:\n", + " ev = 0.0\n", + "\n", + " for k, val in counts.items():\n", + " ev += val * ((-1) ** int(k[0]) + (-1) ** int(k[1]))\n", + "\n", + " total = sum(counts.values())\n", + " ev /= total\n", + " return ev\n", + "\n", + "\n", + "def ev_xx(counts: Mapping[str, float]) -> float:\n", + " ev = 0.0\n", + "\n", + " for k, val in counts.items():\n", + " ev += val * (-1) ** k.count(\"1\")\n", + "\n", + " total = sum(counts.values())\n", + " ev /= total\n", + " return ev\n", + "\n", + "\n", + "def ev_zz(counts: Mapping[str, float]) -> float:\n", + " ev = 0.0\n", + "\n", + " for k, val in counts.items():\n", + " ev += val * (-1) ** k.count(\"1\")\n", + "\n", + " total = sum(counts.values())\n", + " ev /= total\n", + " return ev\n", + "\n", + "\n", + "def aim_logical_energies(\n", + " data_ordering: object, counts_list: Sequence[dict[str, float]]\n", + ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n", + " counts_data = {\n", + " data_ordering[i]: decode(\n", + " process_counts(\n", + " counts,\n", + " data_qubits=[1, 2, 3, 4],\n", + " flag_qubits=[0, 5],\n", + " )\n", + " )\n", + " for i, counts in enumerate(counts_list)\n", + " }\n", + " return _aim_energies(counts_data)\n", + "\n", + "\n", + "def aim_physical_energies(\n", + " data_ordering: object, counts_list: Sequence[dict[str, float]]\n", + ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n", + " counts_data = {\n", + " data_ordering[i]: process_counts(\n", + " counts,\n", + " data_qubits=[0, 1],\n", + " )\n", + " for i, counts in enumerate(counts_list)\n", + " }\n", + " return _aim_energies(counts_data)\n", + "\n", + "\n", + "def _aim_energies(\n", + " counts_data: Mapping[tuple[int, int, str], dict[str, float]],\n", + ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n", + " evxs: dict[tuple[int, int], float] = {}\n", + " evxxs: dict[tuple[int, int], float] = {}\n", + " evzzs: dict[tuple[int, int], float] = {}\n", + " totals: dict[tuple[int, int], float] = {}\n", + "\n", + " for key, counts in counts_data.items():\n", + " h_params, basis = key\n", + " key_a, key_b = h_params.split(\":\")\n", + " u, v = int(key_a), int(key_b)\n", + " if basis.startswith(\"x\"):\n", + " evxs[u, v] = ev_x(counts)\n", + " evxxs[u, v] = ev_xx(counts)\n", + " else:\n", + " evzzs[u, v] = ev_zz(counts)\n", + "\n", + " totals.setdefault((u, v), 0)\n", + " totals[u, v] += sum(counts.values())\n", + "\n", + " energies = {}\n", + " uncertainties = {}\n", + " for u, v in evxs.keys() & evzzs.keys():\n", + " string_key = f\"{u}:{v}\"\n", + " energies[string_key] = u * (evzzs[u, v] - 1) / 4 + v * evxs[u, v]\n", + "\n", + " uncertainty_xx = 2 * v**2 * (1 + evxxs[u, v]) - u * v * evxs[u, v] / 2\n", + " uncertainty_zz = u**2 * (1 - evzzs[u, v]) / 2\n", + "\n", + " uncertainties[string_key] = np.sqrt(\n", + " (uncertainty_zz + uncertainty_xx - energies[string_key] ** 2) / (totals[u, v] / 2)\n", + " )\n", + "\n", + " return energies, uncertainties\n", + "\n", + "\n", + "def _get_energy_diff(\n", + " bf_energies: dict[str, float],\n", + " physical_energies: dict[str, float],\n", + " logical_energies: dict[str, float],\n", + ") -> tuple[list[float], list[float]]:\n", + " physical_energy_diff = []\n", + " logical_energy_diff = []\n", + "\n", + " # Data ordering following `bf_energies` keys\n", + " for layer in bf_energies.keys():\n", + " physical_sim_energy = physical_energies[layer]\n", + " logical_sim_energy = logical_energies[layer]\n", + " true_energy = bf_energies[layer]\n", + " u, v = layer.split(\":\")\n", + " print(f\"Layer=({u}, {v}) has brute-force energy of: {true_energy}\")\n", + " print(f\"Physical circuit of layer=({u}, {v}) got an energy of: {physical_sim_energy}\")\n", + " print(f\"Logical circuit of layer=({u}, {v}) got an energy of: {logical_sim_energy}\")\n", + " print(\"-\" * 72)\n", + "\n", + " if logical_sim_energy < physical_sim_energy:\n", + " print(\"Logical circuit achieved the lower energy!\")\n", + " else:\n", + " print(\"Physical circuit achieved the lower energy\")\n", + " print(\"-\" * 72, \"\\n\")\n", + "\n", + " physical_energy_diff.append(\n", + " -1 * (true_energy - physical_sim_energy)\n", + " ) # Multiply by -1 since negative energies\n", + " logical_energy_diff.append(-1 * (true_energy - logical_sim_energy))\n", + " return physical_energy_diff, logical_energy_diff" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def submit_aim_circuits(\n", + " circuit_dict: object,\n", + " *,\n", + " folder_path: str = \"future_aim_results\",\n", + " shots_count: int = 1000,\n", + " noise_model: cudaq.mlir._mlir_libs._quakeDialects.cudaq_runtime.NoiseModel | None = None,\n", + " run_async: bool = False,\n", + ") -> dict[str, list[dict[str, int]]] | None:\n", + " if run_async:\n", + " os.makedirs(folder_path, exist_ok=True)\n", + " else:\n", + " aim_results = {\"physical\": [], \"logical\": []}\n", + "\n", + " for layer in circuit_dict.keys():\n", + " if run_async:\n", + " print(f\"Posting circuits associated with layer=('{layer}')\")\n", + " else:\n", + " print(f\"Running circuits associated with layer=('{layer}')\")\n", + "\n", + " for basis in (\"z_basis\", \"x_basis\"):\n", + " if run_async:\n", + " u, v = layer.split(\":\")\n", + "\n", + " tmp_physical_results = cudaq.sample_async(\n", + " circuit_dict[layer][\"physical\"][basis], shots_count=shots_count\n", + " )\n", + " file = open(f\"{folder_path}/physical_{basis}_job_u={u}_v={v}_result.txt\", \"w\")\n", + " file.write(str(tmp_physical_results))\n", + " file.close()\n", + "\n", + " tmp_logical_results = cudaq.sample_async(\n", + " circuit_dict[layer][\"logical\"][basis], shots_count=shots_count\n", + " )\n", + " file = open(f\"{folder_path}/logical_{basis}_job_u={u}_v={v}_result.txt\", \"w\")\n", + " file.write(str(tmp_logical_results))\n", + " file.close()\n", + " else:\n", + " tmp_physical_results = cudaq.sample(\n", + " circuit_dict[layer][\"physical\"][basis],\n", + " shots_count=shots_count,\n", + " noise_model=noise_model,\n", + " )\n", + " tmp_logical_results = cudaq.sample(\n", + " circuit_dict[layer][\"logical\"][basis],\n", + " shots_count=shots_count,\n", + " noise_model=noise_model,\n", + " )\n", + " aim_results[\"physical\"].append({k: v for k, v in tmp_physical_results.items()})\n", + " aim_results[\"logical\"].append({k: v for k, v in tmp_logical_results.items()})\n", + " if not run_async:\n", + " print(\"\\nCompleted all circuit sampling!\")\n", + " return aim_results\n", + " else:\n", + " print(\"\\nAll circuits submitted for async sampling!\")" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "def _get_async_results(\n", + " layers: object, *, folder_path: str = \"future_aim_results\"\n", + ") -> dict[str, list[dict[str, int]]]:\n", + " aim_results = {\"physical\": [], \"logical\": []}\n", + " for layer in layers:\n", + " print(f\"Retrieving all circuits counts associated with layer=('{layer}')\")\n", + " u, v = layer.split(\":\")\n", + " for basis in (\"z_basis\", \"x_basis\"):\n", + " file = open(f\"{folder_path}/physical_{basis}_job_u={u}_v={v}_result.txt\", \"r\")\n", + " tmp_physical_results = cudaq.AsyncSampleResult(str(file.read()))\n", + " physical_counts = tmp_physical_results.get()\n", + "\n", + " file = open(f\"{folder_path}/logical_{basis}_job_u={u}_v={v}_result.txt\", \"r\")\n", + " tmp_logical_results = cudaq.AsyncSampleResult(str(file.read()))\n", + " logical_counts = tmp_logical_results.get()\n", + "\n", + " aim_results[\"physical\"].append({k: v for k, v in physical_counts.items()})\n", + " aim_results[\"logical\"].append({k: v for k, v in logical_counts.items()})\n", + "\n", + " print(\"\\nObtained all circuit samples!\")\n", + " return aim_results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Running a CUDA-Q noisy simulation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this section, we will first explore the performance of the physical and logical circuits under the influence of a device noise model. This will help us predict experimental results, as well as understand the dominant error sources at play. Such a simulation can be achieved via CUDA-Q's density matrix simulator: " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "cudaq.reset_target()\n", + "cudaq.set_target(\"density-matrix-cpu\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "def get_device_noise(\n", + " depolar_prob_1q: float,\n", + " depolar_prob_2q: float,\n", + " *,\n", + " readout_error_prob: float | None = None,\n", + " custom_gates: list[str] | None = None,\n", + ") -> cudaq.mlir._mlir_libs._quakeDialects.cudaq_runtime.NoiseModel:\n", + " noise = cudaq.NoiseModel()\n", + " depolar_noise = cudaq.DepolarizationChannel(depolar_prob_1q)\n", + "\n", + " noisy_ops = [\"z\", \"s\", \"x\", \"h\", \"rx\", \"rz\"]\n", + " for op in noisy_ops:\n", + " noise.add_all_qubit_channel(op, depolar_noise)\n", + "\n", + " if custom_gates:\n", + " custom_depolar_channel = cudaq.DepolarizationChannel(depolar_prob_1q)\n", + " for op in custom_gates:\n", + " noise.add_all_qubit_channel(op, custom_depolar_channel)\n", + "\n", + " # Two qubit depolarization error\n", + " p_0 = 1 - depolar_prob_2q\n", + " p_1 = np.sqrt((1 - p_0**2) / 3)\n", + "\n", + " k0 = np.array(\n", + " [[p_0, 0.0, 0.0, 0.0], [0.0, p_0, 0.0, 0.0], [0.0, 0.0, p_0, 0.0], [0.0, 0.0, 0.0, p_0]],\n", + " dtype=np.complex128,\n", + " )\n", + " k1 = np.array(\n", + " [[0.0, 0.0, p_1, 0.0], [0.0, 0.0, 0.0, p_1], [p_1, 0.0, 0.0, 0.0], [0.0, p_1, 0.0, 0.0]],\n", + " dtype=np.complex128,\n", + " )\n", + " k2 = np.array(\n", + " [\n", + " [0.0, 0.0, -1j * p_1, 0.0],\n", + " [0.0, 0.0, 0.0, -1j * p_1],\n", + " [1j * p_1, 0.0, 0.0, 0.0],\n", + " [0.0, 1j * p_1, 0.0, 0.0],\n", + " ],\n", + " dtype=np.complex128,\n", + " )\n", + " k3 = np.array(\n", + " [[p_1, 0.0, 0.0, 0.0], [0.0, p_1, 0.0, 0.0], [0.0, 0.0, -p_1, 0.0], [0.0, 0.0, 0.0, -p_1]],\n", + " dtype=np.complex128,\n", + " )\n", + " kraus_channel = cudaq.KrausChannel([k0, k1, k2, k3])\n", + "\n", + " noise.add_all_qubit_channel(\"cz\", kraus_channel)\n", + " noise.add_all_qubit_channel(\"cx\", kraus_channel)\n", + "\n", + " if readout_error_prob is not None:\n", + " # Readout error modeled with a Bit flip channel on identity before measurement\n", + " bit_flip = cudaq.BitFlipChannel(readout_error_prob)\n", + " noise.add_all_qubit_channel(\"meas_id\", bit_flip)\n", + " return noise" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, with our example noise model defined above, we can synchronously & noisily sample all of our AIM circuits by passing `noise_model=cudaq_noise_model` to the workflow containing function `submit_aim_circuits()`:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "# Example parameters that can model execution on hardware at the high, simulation, level:\n", + "# Take single-qubit gate depolarization rate: ~0.2% or better (fidelity ≥99.8%)\n", + "# Take two-qubit gate depolarization rate: ~1–2% (fidelity ~98–99%)\n", + "cudaq_noise_model = get_device_noise(0.002, 0.02, readout_error_prob=0.02)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running circuits associated with layer=('1:-9')\n", + "Running circuits associated with layer=('1:-1')\n", + "Running circuits associated with layer=('1:7')\n", + "Running circuits associated with layer=('5:-9')\n", + "Running circuits associated with layer=('5:-1')\n", + "Running circuits associated with layer=('5:7')\n", + "Running circuits associated with layer=('9:-9')\n", + "Running circuits associated with layer=('9:-1')\n", + "Running circuits associated with layer=('9:7')\n", + "\n", + "Completed all circuit sampling!\n" + ] + } + ], + "source": [ + "aim_sim_data = submit_aim_circuits(sim_circuit_dict, noise_model=cudaq_noise_model)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "data_ordering = []\n", + "for key in circuit_layers:\n", + " for basis in (\"z_basis\", \"x_basis\"):\n", + " data_ordering.append((key, basis))" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "sim_physical_energies, sim_physical_uncertainties = aim_physical_energies(\n", + " data_ordering, aim_sim_data[\"physical\"]\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "sim_logical_energies, sim_logical_uncertainties = aim_logical_energies(\n", + " data_ordering, aim_sim_data[\"logical\"]\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To analyze our simulated energy results in the above cells, we will compare them to the brute-force computed exact ground state energies for the AIM Hamiltonian. For simplicity, these are already stored in the dictionary `bf_energies` below:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "bf_energies = {\n", + " \"1:-9\": -18.251736027394713,\n", + " \"1:-1\": -2.265564437074638,\n", + " \"1:7\": -14.252231964940428,\n", + " \"5:-9\": -19.293350575766127,\n", + " \"5:-1\": -3.608495283014149,\n", + " \"5:7\": -15.305692796870582,\n", + " \"9:-9\": -20.39007993367173,\n", + " \"9:-1\": -5.260398644698076,\n", + " \"9:7\": -16.429650912487233,\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the above metric, we can assess the performance of the logical circuits against the physical circuits by considering how far away the respective energies are from the brute-force expected energies. The cell below computes these energy deviations:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Layer=(1, -9) has brute-force energy of: -18.251736027394713\n", + "Physical circuit of layer=(1, -9) got an energy of: -15.929\n", + "Logical circuit of layer=(1, -9) got an energy of: -17.46016175277361\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(1, -1) has brute-force energy of: -2.265564437074638\n", + "Physical circuit of layer=(1, -1) got an energy of: -1.97\n", + "Logical circuit of layer=(1, -1) got an energy of: -2.176531948420889\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(1, 7) has brute-force energy of: -14.252231964940428\n", + "Physical circuit of layer=(1, 7) got an energy of: -12.268\n", + "Logical circuit of layer=(1, 7) got an energy of: -13.26321740664324\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(5, -9) has brute-force energy of: -19.293350575766127\n", + "Physical circuit of layer=(5, -9) got an energy of: -16.8495\n", + "Logical circuit of layer=(5, -9) got an energy of: -18.46681284816878\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(5, -1) has brute-force energy of: -3.608495283014149\n", + "Physical circuit of layer=(5, -1) got an energy of: -3.1965000000000003\n", + "Logical circuit of layer=(5, -1) got an energy of: -3.4531715120183297\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(5, 7) has brute-force energy of: -15.305692796870582\n", + "Physical circuit of layer=(5, 7) got an energy of: -13.336\n", + "Logical circuit of layer=(5, 7) got an energy of: -14.341784541550897\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(9, -9) has brute-force energy of: -20.39007993367173\n", + "Physical circuit of layer=(9, -9) got an energy of: -17.802\n", + "Logical circuit of layer=(9, -9) got an energy of: -19.339249509416753\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(9, -1) has brute-force energy of: -5.260398644698076\n", + "Physical circuit of layer=(9, -1) got an energy of: -4.8580000000000005\n", + "Logical circuit of layer=(9, -1) got an energy of: -5.1227150992242025\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(9, 7) has brute-force energy of: -16.429650912487233\n", + "Physical circuit of layer=(9, 7) got an energy of: -14.3635\n", + "Logical circuit of layer=(9, 7) got an energy of: -15.448422736181264\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n" + ] + } + ], + "source": [ + "sim_physical_energy_diff, sim_logical_energy_diff = _get_energy_diff(\n", + " bf_energies, sim_physical_energies, sim_logical_energies\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Both physical and logical circuits were subject to the same noise model, but the `[[4,2,2]]` provides additional information that can help overcome some errors. Visualizing the computed energy differences from the above the cell, our noisy simulation provides a preview of the benefits logical qubits can offer:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(11, 7), dpi=200)\n", + "\n", + "layer_labels = [(int(key.split(\":\")[0]), int(key.split(\":\")[1])) for key in bf_energies.keys()]\n", + "plot_labels = [str(item) for item in layer_labels]\n", + "\n", + "plt.errorbar(\n", + " plot_labels,\n", + " sim_physical_energy_diff,\n", + " yerr=sim_physical_uncertainties.values(),\n", + " ecolor=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n", + " color=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n", + " capsize=4,\n", + " elinewidth=1.5,\n", + " fmt=\"o\",\n", + " markersize=8,\n", + " markeredgewidth=1,\n", + " label=\"Physical\",\n", + ")\n", + "\n", + "plt.errorbar(\n", + " plot_labels,\n", + " sim_logical_energy_diff,\n", + " yerr=sim_logical_uncertainties.values(),\n", + " color=(0, 177 / 255.0, 152 / 255.0),\n", + " ecolor=(0, 177 / 255.0, 152 / 255.0),\n", + " capsize=4,\n", + " elinewidth=1.5,\n", + " fmt=\"o\",\n", + " markersize=8,\n", + " markeredgewidth=1,\n", + " label=\"Logical\",\n", + ")\n", + "\n", + "ax.set_xlabel(\"Hamiltonian Parameters (U, V)\", fontsize=18)\n", + "ax.set_ylabel(\"Energy above true ground state (in eV)\", fontsize=18)\n", + "ax.set_title(\"CUDA-Q AIM Circuits Simulation (lower is better)\", fontsize=20)\n", + "ax.legend(loc=\"upper right\", fontsize=18.5)\n", + "plt.xticks(fontsize=16)\n", + "plt.yticks(fontsize=16)\n", + "\n", + "ax.axhline(y=0, color=\"black\", linestyle=\"--\", linewidth=2)\n", + "plt.ylim(\n", + " top=max(sim_physical_energy_diff) + max(sim_physical_uncertainties.values()) + 0.2, bottom=-0.2\n", + ")\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Running logical AIM on Infleqtion's hardware " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The entire workflow we've seen thus far can be seamlessly executed on real quantum hardware as well. CUDA-Q has integration with Infleqtion's gate-based neutral atom quantum computer, [Sqale](https://arxiv.org/html/2408.08288v2), allowing execution of CUDA-Q kernels on neutral-atom hardware via Infleqtion’s cross-platform Superstaq compiler API that performs low-level compilation and optimization under the hood. Indeed, the AIM research results seen in [our paper](https://arxiv.org/abs/2412.07670) were obtained via this complete end-to-end workflow.\n", + "\n", + "To do so, users can obtain a Superstaq API key from [superstaq.infleqtion.com](https://superstaq.infleqtion.com/) to gain access to Infleqtion's neutral-atom simulator, with [pre-registration](https://www.infleqtion.com/sqale-preregistration) open for access to Infleqtion’s neutral atom QPU." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As a tutorial, let us reproduce the workflow we've run so far but on Infleqtion's QPU. We begin with the same GPU-enhanced VQE to generate the AIM circuits:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "cudaq.reset_target()\n", + "\n", + "if cudaq.num_available_gpus() == 0:\n", + " cudaq.set_target(\"qpp-cpu\", option=\"fp64\")\n", + "else:\n", + " cudaq.set_target(\"nvidia\", option=\"fp64\")" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Computed optimal angles=[1.5846845738799267, 1.5707961678256028] for U=1, V=-9\n", + "Computed optimal angles=[4.588033710930825, 4.712388365176642] for U=1, V=-1\n", + "Computed optimal angles=[-1.588651490745171, 1.5707962742876598] for U=1, V=7\n", + "Computed optimal angles=[1.64012940802256, 1.5707963354922125] for U=5, V=-9\n", + "Computed optimal angles=[2.1293956916868737, 1.5707963294715355] for U=5, V=-1\n", + "Computed optimal angles=[-1.6598458659836037, 1.570796331040382] for U=5, V=7\n", + "Computed optimal angles=[1.695151467539617, 1.5707960973500679] for U=9, V=-9\n", + "Computed optimal angles=[2.4149519241823376, 1.5707928509325972] for U=9, V=-1\n", + "Computed optimal angles=[-1.7301462945564499, 1.570796044872433] for U=9, V=7\n", + "\n", + "Finished building optimized circuits!\n" + ] + } + ], + "source": [ + "device_circuit_dict = generate_circuit_set(\n", + " ignore_meas_id=True\n", + ") # Setting `ignore_meas_id=True` drops the noisy-identity gate from earlier" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And now, we change backends! Before selecting an Infleqtion machine in CUDA-Q, we must first set our Superstaq API key, like so:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "# os.environ['SUPERSTAQ_API_KEY'] = \"api_key\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we declare the type of execution we would like on Infleqtion's machine based on the keyword options specified:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "cudaq.reset_target()\n", + "\n", + "# Set the following to run on Infleqtion's Sqale QPU:\n", + "cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\")\n", + "\n", + "# Set the following to run an ideal dry-run on Infleqtion's Sqale QPU:\n", + "# cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\", method=\"dry-run\")\n", + "\n", + "# Set the following to run a device-realistic noisy simulation of Infleqtion's Sqale QPU:\n", + "# cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\", method=\"noise-sim\")\n", + "\n", + "# Set the following to run a local, ideal emulation:\n", + "# cudaq.set_target(\"infleqtion\", emulate=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With that, we're all set! That simple change instructs our AIM circuits to execute on Infleqtion's QPU (or simulator). Due to the general queue wait time of running on hardware, we optionally recommend enabling the `run_async=True` flag to asynchronously sample the circuits. This will allow the cell to be executed and not wait synchronously until all the jobs are complete, allowing other classical code to be run in the meantime. When using `run_async`, an optional directory to store the job information can be specified with `folder_path` (this will be important to later retrieve the job results from the same directory)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Posting circuits associated with layer=('1:-9')\n", + "Posting circuits associated with layer=('1:-1')\n", + "Posting circuits associated with layer=('1:7')\n", + "Posting circuits associated with layer=('5:-9')\n", + "Posting circuits associated with layer=('5:-1')\n", + "Posting circuits associated with layer=('5:7')\n", + "Posting circuits associated with layer=('9:-9')\n", + "Posting circuits associated with layer=('9:-1')\n", + "Posting circuits associated with layer=('9:7')\n", + "\n", + "All circuits submitted for async sampling!\n" + ] + } + ], + "source": [ + "submit_aim_circuits(\n", + " device_circuit_dict, folder_path=\"hardware_aim_future_results\", shots_count=1000, run_async=True\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the above cell execution, all the circuits will post to execute on QPU. We can then return at a later time to retrieve the job results with the cell below:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Retrieving all circuits counts associated with layer=('1:-9')\n", + "Retrieving all circuits counts associated with layer=('1:-1')\n", + "Retrieving all circuits counts associated with layer=('1:7')\n", + "Retrieving all circuits counts associated with layer=('5:-9')\n", + "Retrieving all circuits counts associated with layer=('5:-1')\n", + "Retrieving all circuits counts associated with layer=('5:7')\n", + "Retrieving all circuits counts associated with layer=('9:-9')\n", + "Retrieving all circuits counts associated with layer=('9:-1')\n", + "Retrieving all circuits counts associated with layer=('9:7')\n", + "\n", + "Obtained all circuit samples!\n" + ] + } + ], + "source": [ + "aim_device_data = _get_async_results(circuit_layers, folder_path=\"hardware_aim_future_results\")" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "physical_energies, physical_uncertainties = aim_physical_energies(\n", + " data_ordering, aim_device_data[\"physical\"]\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "logical_energies, logical_uncertainties = aim_logical_energies(\n", + " data_ordering, aim_device_data[\"logical\"]\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Layer=(1, -9) has brute-force energy of: -18.251736027394713\n", + "Physical circuit of layer=(1, -9) got an energy of: -17.626499999999997\n", + "Logical circuit of layer=(1, -9) got an energy of: -17.69666562801761\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(1, -1) has brute-force energy of: -2.265564437074638\n", + "Physical circuit of layer=(1, -1) got an energy of: -2.1415\n", + "Logical circuit of layer=(1, -1) got an energy of: -2.2032104443266585\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(1, 7) has brute-force energy of: -14.252231964940428\n", + "Physical circuit of layer=(1, 7) got an energy of: -12.9955\n", + "Logical circuit of layer=(1, 7) got an energy of: -13.76919450035401\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(5, -9) has brute-force energy of: -19.293350575766127\n", + "Physical circuit of layer=(5, -9) got an energy of: -18.331\n", + "Logical circuit of layer=(5, -9) got an energy of: -18.85730052910377\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(5, -1) has brute-force energy of: -3.608495283014149\n", + "Physical circuit of layer=(5, -1) got an energy of: -3.476\n", + "Logical circuit of layer=(5, -1) got an energy of: -3.5425689231532203\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(5, 7) has brute-force energy of: -15.305692796870582\n", + "Physical circuit of layer=(5, 7) got an energy of: -14.043500000000002\n", + "Logical circuit of layer=(5, 7) got an energy of: -14.795918428433312\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(9, -9) has brute-force energy of: -20.39007993367173\n", + "Physical circuit of layer=(9, -9) got an energy of: -19.4715\n", + "Logical circuit of layer=(9, -9) got an energy of: -19.96524696701215\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(9, -1) has brute-force energy of: -5.260398644698076\n", + "Physical circuit of layer=(9, -1) got an energy of: -4.973\n", + "Logical circuit of layer=(9, -1) got an energy of: -5.207315773582224\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n", + "Layer=(9, 7) has brute-force energy of: -16.429650912487233\n", + "Physical circuit of layer=(9, 7) got an energy of: -15.182\n", + "Logical circuit of layer=(9, 7) got an energy of: -16.241375689575516\n", + "------------------------------------------------------------------------\n", + "Logical circuit achieved the lower energy!\n", + "------------------------------------------------------------------------ \n", + "\n" + ] + } + ], + "source": [ + "physical_energy_diff, logical_energy_diff = _get_energy_diff(\n", + " bf_energies, physical_energies, logical_energies\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As before, we use the same metric of comparing against the true ground state energies; however, this time, both the physical and logical circuits are fully exposed to real hardware noise. Yet, we expect the use of logical qubits afforded to us by the `[[4,2,2]]` code to achieve energies closer to the true ground state than the bare physical circuits (up to a certain error threshold). And indeed they do! Visually, we can plot the energy deviations of both the physical and logical circuits from the cell above and observe that the logical circuits are able to outperform the physical circuits by obtaining much lower energies, demonstrating the power of error detection and the beginning possibilities of fault-tolerant quantum computation: " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(11, 7), dpi=200)\n", + "\n", + "plt.errorbar(\n", + " plot_labels,\n", + " physical_energy_diff,\n", + " yerr=physical_uncertainties.values(),\n", + " ecolor=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n", + " color=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n", + " capsize=4,\n", + " elinewidth=1.5,\n", + " fmt=\"o\",\n", + " markersize=8,\n", + " markeredgewidth=1,\n", + " label=\"Physical\",\n", + ")\n", + "plt.errorbar(\n", + " plot_labels,\n", + " logical_energy_diff,\n", + " yerr=logical_uncertainties.values(),\n", + " color=(0, 177 / 255.0, 152 / 255.0),\n", + " ecolor=(0, 177 / 255.0, 152 / 255.0),\n", + " capsize=4,\n", + " elinewidth=1.5,\n", + " fmt=\"o\",\n", + " markersize=8,\n", + " markeredgewidth=1,\n", + " label=\"Logical\",\n", + ")\n", + "\n", + "ax.set_xlabel(\"Hamiltonian Parameters (U, V)\", fontsize=18)\n", + "ax.set_ylabel(\"Energy above true ground state (in eV)\", fontsize=18)\n", + "ax.set_title(\"CUDA-Q AIM Infleqtion Hardware Execution (lower is better)\", fontsize=20)\n", + "ax.legend(loc=\"upper left\", fontsize=18.5)\n", + "plt.xticks(fontsize=16)\n", + "plt.yticks(fontsize=16)\n", + "\n", + "ax.axhline(y=0, color=\"black\", linestyle=\"--\", linewidth=2)\n", + "plt.ylim(top=max(physical_energy_diff) + max(physical_uncertainties.values()) + 0.2, bottom=-0.2)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pr-2458/_sources/applications/python/vqe_advanced.ipynb.txt b/pr-2458/_sources/applications/python/vqe_advanced.ipynb.txt index 188df3af45..3135b93829 100644 --- a/pr-2458/_sources/applications/python/vqe_advanced.ipynb.txt +++ b/pr-2458/_sources/applications/python/vqe_advanced.ipynb.txt @@ -331,7 +331,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "[\u001b[38;2;255;000;000mwarning\u001b[0m] Target \u001b[38;2;000;000;255mnvidia-mqpu\u001b[0m: \u001b[38;2;000;000;255mThis target is deprecating. Please use the 'nvidia' target with option 'mqpu,fp32' or 'mqpu' (fp32 is the default precision option) by adding the command line option '--target-option mqpu,fp32' or passing it as cudaq.set_target('nvidia', option='mqpu,fp32') in Python. Please refer to CUDA-Q \u001b]8;;https://nvidia.github.io/cuda-quantum/latest/using/backends/platform.html#nvidia-mqpu-platform\u001b\\documentation\u001b]8;;\u001b\\ for more information.\u001b[0m\n" + "[\u001b[38;2;255;000;000mwarning\u001b[0m] Target \u001b[38;2;000;000;255mnvidia-mqpu\u001b[0m: \u001b[38;2;000;000;255mThis target is deprecating. Please use the 'nvidia' target with option 'mqpu,fp32' or 'mqpu' (fp32 is the default precision option) by adding the command line option '--target-option mqpu,fp32' or passing it as cudaq.set_target('nvidia', option='mqpu,fp32') in Python. Please refer to CUDA-Q \u001b]8;;https://nvidia.github.io/cuda-quantum/latest/using/backends/platform\u001b\\documentation\u001b]8;;\u001b\\ for more information.\u001b[0m\n" ] } ], diff --git a/pr-2458/_sources/examples/python/executing_kernels.ipynb.txt b/pr-2458/_sources/examples/python/executing_kernels.ipynb.txt index 66a7afee3b..0d3250c8c1 100644 --- a/pr-2458/_sources/examples/python/executing_kernels.ipynb.txt +++ b/pr-2458/_sources/examples/python/executing_kernels.ipynb.txt @@ -78,7 +78,7 @@ "source": [ "Note that there is a subtle difference between how `sample` is executed with the target device set to a simulator or with the target device set to a QPU. In simulation mode, the quantum state is built once and then sampled $s$ times where $s$ equals the `shots_count`. In hardware execution mode, the quantum state collapses upon measurement and hence needs to be rebuilt over and over again.\n", "\n", - "There are a number of helpful tools that can be found in the API [here](https://nvidia.github.io/cuda-quantum/latest/api/languages/python_api.html#cudaq.SampleResult) to process the `Sample_Result` object produced by `sample`." + "There are a number of helpful tools that can be found in the [API docs](https://nvidia.github.io/cuda-quantum/latest/api/languages/python_api) to process the `Sample_Result` object produced by `sample`." ] }, { diff --git a/pr-2458/_sources/examples/python/executing_photonic_kernels.ipynb.txt b/pr-2458/_sources/examples/python/executing_photonic_kernels.ipynb.txt new file mode 100644 index 0000000000..62e8901c98 --- /dev/null +++ b/pr-2458/_sources/examples/python/executing_photonic_kernels.ipynb.txt @@ -0,0 +1,171 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Executing Quantum Photonic Circuits \n", + "\n", + "In CUDA-Q, there are 2 ways in which one can execute quantum photonic kernels: \n", + "\n", + "1. `sample`: yields measurement counts \n", + "3. `get_state`: yields the quantum statevector of the computation \n", + "\n", + "## Sample\n", + "\n", + "Quantum states collapse upon measurement and hence need to be sampled many times to gather statistics. The CUDA-Q `sample` call enables this: \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import cudaq\n", + "import numpy as np\n", + "\n", + "qumode_count = 2\n", + "\n", + "# Define the simulation target.\n", + "cudaq.set_target(\"orca-photonics\")\n", + "\n", + "# Define a quantum kernel function.\n", + "\n", + "\n", + "@cudaq.kernel\n", + "def kernel(qumode_count: int):\n", + " level = qumode_count + 1\n", + " qumodes = [qudit(level) for _ in range(qumode_count)]\n", + "\n", + " # Apply the create gate to the qumodes.\n", + " for i in range(qumode_count):\n", + " create(qumodes[i]) # |00⟩ -> |11⟩\n", + "\n", + " # Apply the beam_splitter gate to the qumodes.\n", + " beam_splitter(qumodes[0], qumodes[1], np.pi / 6)\n", + "\n", + " # measure all qumodes\n", + " mz(qumodes)\n", + "\n", + "\n", + "result = cudaq.sample(kernel, qumode_count, shots_count=1000)\n", + "\n", + "print(result)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Get state\n", + "\n", + "The `get_state` function gives us access to the quantum statevector of the computation." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import cudaq\n", + "import numpy as np\n", + "\n", + "qumode_count = 2\n", + "\n", + "# Define the simulation target.\n", + "cudaq.set_target(\"orca-photonics\")\n", + "\n", + "# Define a quantum kernel function.\n", + "\n", + "\n", + "@cudaq.kernel\n", + "def kernel(qumode_count: int):\n", + " level = qumode_count + 1\n", + " qumodes = [qudit(level) for _ in range(qumode_count)]\n", + "\n", + " # Apply the create gate to the qumodes.\n", + " for i in range(qumode_count):\n", + " create(qumodes[i]) # |00⟩ -> |11⟩\n", + "\n", + " # Apply the beam_splitter gate to the qumodes.\n", + " beam_splitter(qumodes[0], qumodes[1], np.pi / 6)\n", + "\n", + " # measure some of all qumodes if need to be measured\n", + " # mz(qumodes)\n", + "\n", + "\n", + "# Compute the statevector of the kernel\n", + "result = cudaq.get_state(kernel, qumode_count)\n", + "\n", + "print(np.array(result))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The statevector generated by the `get_state` command follows little-endian convention for associating numbers with their digit string representations, which places the least significant digit on the right. That is, for the example of a 2-qumode system of level 3 (in which possible states are 0, 1, and 2), we have the following translation between integers and digit string:\n", + "$$\\begin{matrix} \n", + "\\text{Integer} & \\text{digit string representation}\\\\\n", + "& \\text{least significant bit on right}\\\\\n", + "0 = \\textcolor{blue}{0}*3^1 + \\textcolor{red}{0}*3^0 & \\textcolor{blue}{0}\\textcolor{red}{0} \\\\\n", + "1 = \\textcolor{blue}{0}*3^1 + \\textcolor{red}{1}*3^0 & \\textcolor{blue}{0}\\textcolor{red}{1}\\\\\n", + "2 = \\textcolor{blue}{0}*3^1 + \\textcolor{red}{2}*3^0 & \\textcolor{blue}{0}\\textcolor{red}{2}\\\\\n", + "3 = \\textcolor{blue}{1}*3^1 + \\textcolor{red}{0}*3^0 & \\textcolor{blue}{1}\\textcolor{red}{0} \\\\\n", + "4 = \\textcolor{blue}{1}*3^1 + \\textcolor{red}{1}*3^0 & \\textcolor{blue}{1}\\textcolor{red}{1} \\\\\n", + "5 = \\textcolor{blue}{1}*3^1 + \\textcolor{red}{2}*3^0 & \\textcolor{blue}{1}\\textcolor{red}{2} \\\\\n", + "6 = \\textcolor{blue}{2}*3^1 + \\textcolor{red}{0}*3^0 & \\textcolor{blue}{2}\\textcolor{red}{0} \\\\\n", + "7 = \\textcolor{blue}{2}*3^1 + \\textcolor{red}{1}*3^0 & \\textcolor{blue}{2}\\textcolor{red}{1} \\\\\n", + "8 = \\textcolor{blue}{2}*3^1 + \\textcolor{red}{2}*3^0 & \\textcolor{blue}{2}\\textcolor{red}{2} \n", + "\\end{matrix}\n", + "$$\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Parallelization Techniques\n", + "\n", + "The most intensive task in the computation is the execution of the quantum photonic kernel hence each execution function: `sample`, and `get_state` can be parallelized given access to multiple quantum processing units (multi-QPU). We emulate each QPU with a CPU." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(cudaq.__version__)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/pr-2458/_sources/releases.rst.txt b/pr-2458/_sources/releases.rst.txt index 6a8a353462..8e455ff9dd 100644 --- a/pr-2458/_sources/releases.rst.txt +++ b/pr-2458/_sources/releases.rst.txt @@ -4,12 +4,56 @@ CUDA-Q Releases **latest** -The latest version of CUDA-Q is on the main branch of our `GitHub repository `__ and is also available as a Docker image. More information about installing the nightly builds can be found :doc:`here ` +The latest version of CUDA-Q is on the main branch of our `GitHub repository `__ +and is also available as a Docker image. More information about installing the nightly builds can be found +:doc:`here ` - `Docker image (nightly builds) `__ - `Documentation `__ - `Examples `__ +**0.9.1** + +This release adds support for using +`Amazon Braket `__ and +`Infeqtion's Superstaq `__ as backends. + +Starting with this release, all C++ quantum kernels will be processed by the `nvq++` compiler regardless of whether +they run on a simulator or on a quantum hardware backend. This change is largely non-breaking, but language constructs +that are not officially supported within quantum kernels will now lead to a compilation error whereas previously they +could be used when executing on a simulator only. The previous behavior can be forced by passing the `--library-mode` +flag to the compiler. Please note that if you do so, however, the code will never be executable outside of a simulator +and may not be supported even on simulators. + +- `Docker image `__ +- `Python wheel `__ +- `C++ installer `__ +- `Documentation `__ +- `Examples `__ + +The full change log can be found `here `__. + +**0.9.0** + +We are very excited to share a new toolset added for modeling and manipulating the dynamics of physical systems. +The new API allows to define and execute a time evolution under arbitrary operators. For more information, take +a look at the `docs `__. +The 0.9.0 release furthermore includes a range of contribution to add new backends to CUDA-Q, including backends +from `Anyon Technologies `__, +`Ferimioniq `__, and +`QuEra Computing `__, +as well as updates to existing backends from `ORCA `__ +and `OQC `__. +We hope you enjoy the new features - also check out our new notebooks and examples to dive into CUDA-Q. + +- `Docker image `__ +- `Python wheel `__ +- `C++ installer `__ +- `Documentation `__ +- `Examples `__ + +The full change log can be found `here `__. + **0.8.0** The 0.8.0 release adds a range of changes to improve the ease of use and performance with CUDA-Q. @@ -17,7 +61,7 @@ The changes listed below highlight some of what we think will be the most useful to know about. While the listed changes do not capture all of the great contributions, we would like to extend many thanks for every contribution, in particular those from external contributors. -- `Docker image `__ +- `Docker image `__ - `Python wheel `__ - `C++ installer `__ - `Documentation `__ @@ -30,7 +74,7 @@ The full change log can be found `here `__. +`here `__. It furthermore adds a range of bug fixes and changes the Python wheel installation instructions. - `Docker image `__ @@ -46,7 +90,7 @@ The full change log can be found `here `, giving you access to our most powerful GPU-accelerated simulators even if you don't have an NVIDIA GPU. With 0.7.0, we have furthermore greatly increased expressiveness of the Python and C++ language frontends. -Check out our `documentation `__ +Check out our `documentation `__ to get started with the new Python syntax support we have added, and `follow our blog `__ to learn more about the new setup and its performance benefits. diff --git a/pr-2458/_sources/using/applications.rst.txt b/pr-2458/_sources/using/applications.rst.txt index 572187128f..b3119decf4 100644 --- a/pr-2458/_sources/using/applications.rst.txt +++ b/pr-2458/_sources/using/applications.rst.txt @@ -22,7 +22,8 @@ Applications that give an in depth view of CUDA-Q and its applications in Python /applications/python/quantum_teleportation.ipynb /applications/python/quantum_volume.ipynb /applications/python/readout_error_mitigation.ipynb + /applications/python/vqe.ipynb /applications/python/vqe_advanced.ipynb /applications/python/hadamard_test.ipynb - /applications/python/vqe.ipynb - \ No newline at end of file + /applications/python/logical_aim_sqale.ipynb + diff --git a/pr-2458/_sources/using/backends/backends.rst.txt b/pr-2458/_sources/using/backends/backends.rst.txt index e5a8c9b087..9ee2bbbbbf 100644 --- a/pr-2458/_sources/using/backends/backends.rst.txt +++ b/pr-2458/_sources/using/backends/backends.rst.txt @@ -12,11 +12,12 @@ CUDA-Q Backends **The following is a comprehensive list of the available targets in CUDA-Q:** +* :ref:`anyon ` * :ref:`braket ` * :ref:`density-matrix-cpu ` * :ref:`fermioniq ` +* :ref:`infleqtion ` * :ref:`ionq ` -* :ref:`anyon ` * :ref:`iqm ` * :ref:`nvidia ` * :ref:`nvidia-fp64 ` @@ -35,6 +36,6 @@ CUDA-Q Backends * :ref:`tensornet-mps ` .. deprecated:: 0.8 - The `nvidia-fp64`, `nvidia-mgpu`, `nvidia-mqpu`, and `nvidia-mqpu-fp64` targets can be + The `nvidia-fp64`, `nvidia-mgpu`, `nvidia-mqpu`, and `nvidia-mqpu-fp64` targets can be enabled as extensions of the unified `nvidia` target (see `nvidia` :ref:`target documentation `). These target names might be removed in a future release. \ No newline at end of file diff --git a/pr-2458/_sources/using/backends/dynamics.rst.txt b/pr-2458/_sources/using/backends/dynamics.rst.txt index a5b8c056b8..6e6e48e567 100644 --- a/pr-2458/_sources/using/backends/dynamics.rst.txt +++ b/pr-2458/_sources/using/backends/dynamics.rst.txt @@ -84,6 +84,8 @@ For example, we can plot the Pauli expectation value for the above simulation as In particular, for each time step, `evolve` captures an array of expectation values, one for each observable. Hence, we convert them into sequences for plotting purposes. +Examples that illustrate how to use the ``dynamics`` target are available +in the `CUDA-Q repository `__. Operator +++++++++++ @@ -272,4 +274,45 @@ backend target. If the output is a '`None`' string, it indicates that your Torch installation does not support CUDA. In this case, you need to install a CUDA-enabled Torch package via other mechanisms, e.g., building Torch from source or using their Docker images. - \ No newline at end of file + +Multi-GPU Multi-Node Execution ++++++++++++++++++++++++++++++++ + +.. _cudensitymat_mgmn: + +CUDA-Q ``dynamics`` target supports parallel execution on multiple GPUs. +To enable parallel execution, the application must initialize MPI as follows. + + +.. tab:: Python + + .. literalinclude:: ../../snippets/python/using/backends/dynamics.py + :language: python + :start-after: [Begin MPI] + :end-before: [End MPI] + + .. code:: bash + + mpiexec -np python3 program.py + + where ``N`` is the number of processes. + + +By initializing the MPI execution environment (via `cudaq.mpi.initialize()`) in the application code and +invoking it via an MPI launcher, we have activated the multi-node multi-GPU feature of the ``dynamics`` target. +Specifically, it will detect the number of processes (GPUs) and distribute the computation across all available GPUs. + + +.. note:: + The number of MPI processes must be a power of 2, one GPU per process. + +.. note:: + Not all integrators are capable of handling distributed state. Errors will be raised if parallel execution is activated + but the selected integrator does not support distributed state. + +.. warning:: + As of cuQuantum version 24.11, there are a couple of `known limitations `__ for parallel execution: + + - Computing the expectation value of a mixed quantum state is not supported. Thus, `collapse_operators` are not supported if expectation calculation is required. + + - Some combinations of quantum states and quantum many-body operators are not supported. Errors will be raised in those cases. diff --git a/pr-2458/_sources/using/backends/hardware.rst.txt b/pr-2458/_sources/using/backends/hardware.rst.txt index 366e837173..33f4907cec 100644 --- a/pr-2458/_sources/using/backends/hardware.rst.txt +++ b/pr-2458/_sources/using/backends/hardware.rst.txt @@ -112,6 +112,128 @@ To see a complete example for using Amazon Braket backends, take a look at our : The ``cudaq.observe`` API is not yet supported on the `braket` target. +Infleqtion +================================== + +.. _infleqtion-backend: + +Infleqtion is a quantum hardware provider of gate-based neutral atom quantum computers. Their backends may be +accessed via `Superstaq `__, Infleqtion’s cross-platform software API +that performs low-level compilation and cross-layer optimization. To get started users can create a Superstaq +account by following `these instructions `__. + +For access to Infleqtion's neutral atom quantum computer, Sqale, +`pre-registration `__ is now open. + +Setting Credentials +````````````````````````` + +Programmers of CUDA-Q may access Infleqtion backends from either C++ or Python. Generate +an API key from your `Superstaq account `__ and export +it as an environment variable: + +.. code:: bash + + export SUPERSTAQ_API_KEY="superstaq_api_key" + +Submission from C++ +````````````````````````` + +To target quantum kernel code for execution on Infleqtion's backends, +pass the flag ``--target infleqtion`` to the ``nvq++`` compiler. + +.. code:: bash + + nvq++ --target infleqtion src.cpp + +This will take the API key and handle all authentication with, and submission to, Infleqtion's QPU +(or simulator). By default, quantum kernel code will be submitted to Infleqtion's Sqale +simulator. + +To execute your kernels on a QPU, pass the ``--infleqtion-machine`` flag to the ``nvq++`` compiler +to specify which machine to submit quantum kernels to: + +.. code:: bash + + nvq++ --target infleqtion --infleqtion-machine cq_sqale_qpu src.cpp ... + +where ``cq_sqale_qpu`` is an example of a physical QPU. + +To run an ideal dry-run execution on the QPU, additionally pass ``dry-run`` with the ``--infleqtion-method`` +flag to the ``nvq++`` compiler: + +.. code:: bash + + nvq++ --target infleqtion --infleqtion-machine cq_sqale_qpu --infleqtion-method dry-run src.cpp ... + +To noisily simulate the QPU instead, pass ``noise-sim`` to the ``--infleqtion-method`` flag like so: + +.. code:: bash + + nvq++ --target infleqtion --infleqtion-machine cq_sqale_qpu --infleqtion-method noise-sim src.cpp ... + +Alternatively, to emulate the Infleqtion machine locally, without submitting through the cloud, +you can also pass the ``--emulate`` flag to ``nvq++``. This will emit any target +specific compiler diagnostics, before running a noise free emulation. + +.. code:: bash + + nvq++ --emulate --target infleqtion src.cpp + +To see a complete example for using Infleqtion's backends, take a look at our :doc:`C++ examples <../examples/examples>`. + +Submission from Python +````````````````````````` + +The target to which quantum kernels are submitted +can be controlled with the ``cudaq::set_target()`` function. + +.. code:: python + + cudaq.set_target("infleqtion") + +By default, quantum kernel code will be submitted to Infleqtion's Sqale +simulator. + +To specify which Infleqtion QPU to use, set the :code:`machine` parameter. + +.. code:: python + + cudaq.set_target("infleqtion", machine="cq_sqale_qpu") + +where ``cq_sqale_qpu`` is an example of a physical QPU. + +To run an ideal dry-run execution of the QPU, additionally set the ``method`` flag to ``"dry-run"``. + +.. code:: python + + cudaq.set_target("infleqtion", machine="cq_sqale_qpu", method="dry-run") + +To noisily simulate the QPU instead, set the ``method`` flag to ``"noise-sim"``. + +.. code:: python + + cudaq.set_target("infleqtion", machine="cq_sqale_qpu", method="noise-sim") + +Alternatively, to emulate the Infleqtion machine locally, without submitting through the cloud, +you can also set the ``emulate`` flag to ``True``. This will emit any target +specific compiler diagnostics, before running a noise free emulation. + +.. code:: python + + cudaq.set_target("infleqtion", emulate=True) + +The number of shots for a kernel execution can be set through +the ``shots_count`` argument to ``cudaq.sample`` or ``cudaq.observe``. By default, +the ``shots_count`` is set to 1000. + +.. code:: python + + cudaq.sample(kernel, shots_count=100) + +To see a complete example for using Infleqtion's backends, take a look at our :doc:`Python examples <../examples/examples>`. +Moreover, for an end-to-end application workflow example executed on the Infleqtion QPU, take a look at the +:doc:`Anderson Impurity Model ground state solver <../applications>` notebook. IonQ ================================== diff --git a/pr-2458/_sources/using/backends/platform.rst.txt b/pr-2458/_sources/using/backends/platform.rst.txt index ad395ebc55..da019f3f65 100644 --- a/pr-2458/_sources/using/backends/platform.rst.txt +++ b/pr-2458/_sources/using/backends/platform.rst.txt @@ -96,7 +96,7 @@ QPU via the :code:`cudaq::get_state_async` (C++) or :code:`cudaq.get_state_async ./a.out .. deprecated:: 0.8 - The :code:`nvidia-mqpu` and :code:`nvidia-mqpu-fp64` targets, which are equivalent to the multi-QPU options `mgpu,fp32` and `mgpu,fp64`, respectively, of the :code:`nvidia` target, are deprecated and will be removed in a future release. + The :code:`nvidia-mqpu` and :code:`nvidia-mqpu-fp64` targets, which are equivalent to the multi-QPU options `mqpu,fp32` and `mqpu,fp64`, respectively, of the :code:`nvidia` target, are deprecated and will be removed in a future release. Parallel distribution mode ^^^^^^^^^^^^^^^^^^^^^^^^^^ diff --git a/pr-2458/_sources/using/backends/simulators.rst.txt b/pr-2458/_sources/using/backends/simulators.rst.txt index 70a94343a5..43d115f127 100644 --- a/pr-2458/_sources/using/backends/simulators.rst.txt +++ b/pr-2458/_sources/using/backends/simulators.rst.txt @@ -33,6 +33,11 @@ and multi-QPU (`mqpu` :ref:`platform `) distribution whereby each Host CPU memory can be leveraged in addition to GPU memory to accommodate the state vector (i.e., maximizing the number of qubits to be simulated). +* Trajectory simulation for noisy quantum circuits + +The :code:`nvidia` target supports noisy quantum circuit simulations using quantum trajectory method across all configurations: single GPU, multi-node multi-GPU, and with host memory. +When simulating many trajectories with small state vectors, the simulation is batched for optimal performance. + .. _cuQuantum single-GPU: @@ -151,7 +156,7 @@ To execute a program on the multi-node multi-GPU NVIDIA target, use the followin .. note:: If you installed CUDA-Q via :code:`pip`, you will need to install the necessary MPI dependencies separately; - please follow the instructions for installing dependencies in the `Project Description `__. + please follow the instructions for installing dependencies in the `Project Description `__. In addition to using MPI in the simulator, you can use it in your application code by installing `mpi4py `__, and invoking the program with the command @@ -266,6 +271,100 @@ environment variable to another integer value as shown below. nvq++ --target nvidia --target-option mgpu,fp64 program.cpp [...] -o program.x CUDAQ_MGPU_FUSE=5 mpiexec -np 2 ./program.x + +Trajectory Noisy Simulation +++++++++++++++++++++++++++++++++++ + +When a :code:`noise_model` is provided to CUDA-Q, the :code:`nvidia` target will incorporate quantum noise into the quantum circuit simulation according to the noise model specified. + + +.. tab:: Python + + .. literalinclude:: ../../snippets/python/using/backends/trajectory.py + :language: python + :start-after: [Begin Docs] + + .. code:: bash + + python3 program.py + { 00:15 01:92 10:81 11:812 } + +.. tab:: C++ + + .. literalinclude:: ../../snippets/cpp/using/backends/trajectory.cpp + :language: cpp + :start-after: [Begin Documentation] + + .. code:: bash + + nvq++ --target nvidia program.cpp [...] -o program.x + ./program.x + { 00:15 01:92 10:81 11:812 } + + +In the case of bit-string measurement sampling as in the above example, each measurement 'shot' is executed as a trajectory, whereby Kraus operators specified in the noise model are sampled. + +For observable expectation value estimation, the statistical error scales asymptotically as :math:`1/\sqrt{N_{trajectories}}`, where :math:`N_{trajectories}` is the number of trajectories. +Hence, depending on the required level of accuracy, the number of trajectories can be specified accordingly. + +.. tab:: Python + + .. literalinclude:: ../../snippets/python/using/backends/trajectory_observe.py + :language: python + :start-after: [Begin Docs] + + .. code:: bash + + python3 program.py + Noisy with 1024 trajectories = -0.810546875 + Noisy with 8192 trajectories = -0.800048828125 + +.. tab:: C++ + + .. literalinclude:: ../../snippets/cpp/using/backends/trajectory_observe.cpp + :language: cpp + :start-after: [Begin Documentation] + + .. code:: bash + + nvq++ --target nvidia program.cpp [...] -o program.x + ./program.x + Noisy with 1024 trajectories = -0.810547 + Noisy with 8192 trajectories = -0.800049 + + +The following environment variable options are applicable to the :code:`nvidia` target for trajectory noisy simulation. Any environment variables must be set +prior to setting the target. + +.. list-table:: **Additional environment variable options for trajectory simulation** + :widths: 20 30 50 + + * - Option + - Value + - Description + * - ``CUDAQ_OBSERVE_NUM_TRAJECTORIES`` + - positive integer + - The default number of trajectories for observe simulation if none was provided in the `observe` call. The default value is 1000. + * - ``CUDAQ_BATCH_SIZE`` + - positive integer or `NONE` + - The number of state vectors in the batched mode. If `NONE`, the batch size will be calculated based on the available device memory. Default is `NONE`. + * - ``CUDAQ_BATCHED_SIM_MAX_BRANCHES`` + - positive integer + - The number of trajectory branches to be tracked simultaneously in the gate fusion. Default is 16. + * - ``CUDAQ_BATCHED_SIM_MAX_QUBITS`` + - positive integer + - The max number of qubits for batching. If the qubit count in the circuit is more than this value, batched trajectory simulation will be disabled. The default value is 20. + * - ``CUDAQ_BATCHED_SIM_MIN_BATCH_SIZE`` + - positive integer + - The minimum number of trajectories for batching. If the number of trajectories is less than this value, batched trajectory simulation will be disabled. Default value is 4. + +.. note:: + + Batched trajectory simulation is only available on the single-GPU execution mode of the :code:`nvidia` target. + + If batched trajectory simulation is not activated, e.g., due to problem size, number of trajectories, or the nature of the circuit (dynamic circuits with mid-circuit measurements and conditional branching), the required number of trajectories will be executed sequentially. + + .. _OpenMP CPU-only: OpenMP CPU-only @@ -382,6 +481,8 @@ Specific aspects of the simulation can be configured by setting the following of * **`CUDA_VISIBLE_DEVICES=X`**: Makes the process only see GPU X on multi-GPU nodes. Each MPI process must only see its own dedicated GPU. For example, if you run 8 MPI processes on a DGX system with 8 GPUs, each MPI process should be assigned its own dedicated GPU via `CUDA_VISIBLE_DEVICES` when invoking `mpiexec` (or `mpirun`) commands. * **`OMP_PLACES=cores`**: Set this environment variable to improve CPU parallelization. * **`OMP_NUM_THREADS=X`**: To enable CPU parallelization, set X to `NUMBER_OF_CORES_PER_NODE/NUMBER_OF_GPUS_PER_NODE`. +* **`CUDAQ_TENSORNET_CONTROLLED_RANK=X`**: Specify the number of controlled qubits whereby the full tensor body of the controlled gate is expanded. If the number of controlled qubits is greater than this value, the gate is applied as a controlled tensor operator to the tensor network state. Default value is 1. +* **`CUDAQ_TENSORNET_OBSERVE_CONTRACT_PATH_REUSE=X`**: Set this environment variable to `TRUE` (`ON`) or `FALSE` (`OFF`) to enable or disable contraction path reuse when computing expectation values. Default is `OFF`. .. note:: @@ -389,10 +490,18 @@ Specific aspects of the simulation can be configured by setting the following of If you do not have these dependencies installed, you may encounter an error stating `Invalid simulator requested`. See the section :ref:`dependencies-and-compatibility` for more information about how to install dependencies. -.. note:: +.. note:: + + When using contraction path reuse (`CUDAQ_TENSORNET_OBSERVE_CONTRACT_PATH_REUSE=TRUE`), :code:`tensornet` backends perform a single contraction path optimization with an opaque spin operator term. This path is then used to contract all the actual terms in the spin operator, hence saving the path finding time. - Setting random seed, via :code:`cudaq::set_random_seed`, is not supported for this backend due to a limitation of the :code:`cuTensorNet` library. This will be fixed in future release once this feature becomes available. + As we use an opaque spin operator term as a placeholder for contraction path optimization, the resulting contraction path is not as optimal as if the actual spin operator is used. + For instance, if the spin operator is sparse (only acting on a few qubits), the contraction can be significantly simplified. +.. note:: + + :code:`tensornet` backends only return the overall expectation value for a :class:`cudaq.SpinOperator` when using the `cudaq::observe` method. + Term-by-term expectation values will not be available in the resulting `ObserveResult` object. + If needed, these values can be computed by calling `cudaq::observe` on individual terms instead. Matrix product state +++++++++++++++++++++++++++++++++++ @@ -436,10 +545,6 @@ Specific aspects of the simulation can be configured by defining the following e If you do not have these dependencies installed, you may encounter an error stating `Invalid simulator requested`. See the section :ref:`dependencies-and-compatibility` for more information about how to install dependencies. -.. note:: - - Setting random seed, via :code:`cudaq::set_random_seed`, is not supported for this backend due to a limitation of the :code:`cuTensorNet` library. This will be fixed in future release once this feature becomes available. - .. note:: The parallelism of Jacobi method (the default `CUDAQ_MPS_SVD_ALGO` setting) gives GPU better performance on small and medium size matrices. If you expect a large number of singular values (e.g., increasing the `CUDAQ_MPS_MAX_BOND` setting), please adjust the `CUDAQ_MPS_SVD_ALGO` setting accordingly. @@ -486,6 +591,45 @@ To execute a program on the :code:`stim` target, use the following commands: can be slower than executing Stim a single time and generating all the shots from that single execution. + +Photonics Simulators +================================== + +The :code:`orca-photonics` target provides a state vector simulator with +the :code:`Q++` library. + +The :code:`orca-photonics` target supports supports a double precision simulator that can run in multiple CPUs. + +OpenMP CPU-only +++++++++++++++++++++++++++++++++++ + +.. _qpp-cpu-photonics-backend: + +This target provides a state vector simulator based on the CPU-only, OpenMP threaded `Q++ `_ library. + +To execute a program on the :code:`orca-photonics` target, use the following commands: + +.. tab:: Python + + .. code:: bash + + python3 program.py [...] --target orca-photonics + + The target can also be defined in the application code by calling + + .. code:: python + + cudaq.set_target('orca-photonics') + + If a target is set in the application code, this target will override the :code:`--target` command line flag given during program invocation. + +.. tab:: C++ + + .. code:: bash + + nvq++ --library-mode --target orca-photonics program.cpp [...] -o program.x + + Fermioniq ================================== @@ -522,7 +666,7 @@ compute expectation values of observables. .. code:: python cudaq.set_target("fermioniq", **{ - "remote-config": remote_config_id + "remote_config": remote_config_id }) For a comprehensive list of all remote configurations, please contact Fermioniq directly. @@ -533,15 +677,15 @@ compute expectation values of observables. .. code:: python cudaq.set_target("fermioniq", **{ - "project-id": project_id + "project_id": project_id }) - To specify the bond dimension, you can pass the ``fermioniq-bond-dim`` parameter. + To specify the bond dimension, you can pass the ``bond_dim`` parameter. .. code:: python cudaq.set_target("fermioniq", **{ - "bond-dim": 5 + "bond_dim": 5 }) .. tab:: C++ diff --git a/pr-2458/_sources/using/examples/examples.rst.txt b/pr-2458/_sources/using/examples/examples.rst.txt index f62c32afd9..ef3fd40e59 100644 --- a/pr-2458/_sources/using/examples/examples.rst.txt +++ b/pr-2458/_sources/using/examples/examples.rst.txt @@ -10,9 +10,11 @@ Examples that illustrate how to use CUDA-Q for application development are avail Introduction Building Kernels Quantum Operations + Photonic Operations Measuring Kernels <../../examples/python/measuring_kernels.ipynb> Visualizing Kernels <../../examples/python/visualization.ipynb> Executing Kernels <../../examples/python/executing_kernels.ipynb> + Executing Photonic Kernels <../../examples/python/executing_photonic_kernels.ipynb> Computing Expectation Values Multi-Control Synthesis Multi-GPU Workflows diff --git a/pr-2458/_sources/using/examples/hardware_providers.rst.txt b/pr-2458/_sources/using/examples/hardware_providers.rst.txt index 96fbc559f2..6abbb8dea7 100644 --- a/pr-2458/_sources/using/examples/hardware_providers.rst.txt +++ b/pr-2458/_sources/using/examples/hardware_providers.rst.txt @@ -2,7 +2,7 @@ Using Quantum Hardware Providers ----------------------------------- CUDA-Q contains support for using a set of hardware providers (Amazon Braket, -IonQ, IQM, OQC, ORCA Computing, Quantinuum and QuEra Computing). +Infleqtion, IonQ, IQM, OQC, ORCA Computing, Quantinuum, and QuEra Computing). For more information about executing quantum kernels on different hardware backends, please take a look at :doc:`hardware <../backends/hardware>`. @@ -21,6 +21,21 @@ The following code illustrates how to run kernels on Amazon Braket's backends. .. literalinclude:: ../../targets/cpp/braket.cpp :language: cpp +Infleqtion +================================== + +The following code illustrates how to run kernels on Infleqtion's backends. + +.. tab:: Python + + .. literalinclude:: ../../targets/python/infleqtion.py + :language: python + +.. tab:: C++ + + .. literalinclude:: ../../targets/cpp/infleqtion.cpp + :language: cpp + IonQ ================================== diff --git a/pr-2458/_sources/using/examples/photonic_operations.rst.txt b/pr-2458/_sources/using/examples/photonic_operations.rst.txt new file mode 100644 index 0000000000..18bd1ffbfa --- /dev/null +++ b/pr-2458/_sources/using/examples/photonic_operations.rst.txt @@ -0,0 +1,158 @@ +Photonics 101 +====================== + +Quantum Photonic States +----------------------------- + +We define a qumode (qudit) to have the states +:math:`\ket{0}`, :math:`\ket{1}`, ... :math:`\ket{d}` in Dirac notation where: + +.. math:: \ket{0} = \begin{bmatrix} 1 & 0 & 0 & \dots & 0 \end{bmatrix} ^ \top + +.. math:: \ket{1} = \begin{bmatrix} 0 & 1 & 0 & \dots & 0 \end{bmatrix}^ \top + +.. math:: \ket{2} = \begin{bmatrix} 0 & 0 & 1 & \dots & 0 \end{bmatrix}^ \top + +.. math:: \vdots + +.. math:: \ket{d} = \begin{bmatrix} 0 & 0 & 0 & \dots & 1 \end{bmatrix}^ \top + +where the linear combinations of states or superpositions are: + +.. math:: \ket{\psi} = \alpha_0\ket{0} + \alpha_1\ket{1} + \alpha_2\ket{2} + \dots + \alpha_d\ket{d} + +where :math:`\alpha_i \in \mathbb{C}`. It is important to note that this is +still the state of one qudit; although we have :math:`d` kets, they represent a +superposition state of one qudit. + +Multiple qudits can be combined and the possible combinations of their states +used to process information. + +A two qudit system, :math:`n=2`, with three levels, :math:`d=3`, has +:math:`d^n=8` computational basis states: +:math:`\ket{00}, \ket{01}, \ket{02}, \ket{10}, \ket{11}, \ket{12}, \ket{20}, \ket{21}, \ket{22}`. + +A photonic quantum state of a :math:`n` qudit system with :math:`d` levels is +written as a sum of :math:`d^n` possible basis states where the coefficients +track the probability of the system collapsing into that state if a measurement +is applied. + +Storing the complex numbers associated with :math:`d^n` amplitudes would not be +feasible using bits and classical computations once :math:`n` and :math:`d` are +relatively large. + + +Quantum Photonics Gates +----------------------- + +We can manipulate the state of a qumode via quantum photonic gates. For +example, the create gate allows us to increase the number of photons in a +qumode up to a maximum given by the qudit level :math:`d`: + +.. math:: C \ket{0} = \ket{1} + +.. math:: \begin{bmatrix} + 0 & 0 & \dots & 0 & 0 & 0 & 0 \\ + 1 & 0 & \dots & 0 & 0 & 0 & 0 \\ + 0 & 1 & \dots & 0 & 0 & 0 & 0 \\ + & & \ddots & & & & \\ + 0 & 0 & \dots & 1 & 0 & 0 & 0 \\ + 0 & 0 & \dots & 0 & 1 & 0 & 0 \\ + 0 & 0 & \dots & 0 & 0 & 1 & 1 + \end{bmatrix} + \begin{bmatrix} 1 \\ 0 \\ 0 \\ \vdots \\ 0 \\ 0 \\ 0 \end{bmatrix} = + \begin{bmatrix} 0 \\ 1 \\ 0 \\ \vdots \\ 0 \\ 0 \\ 0 \end{bmatrix} + +.. literalinclude:: ../../snippets/python/using/examples/create_photonic_gate.py + :language: python + :start-after: [Begin Docs] + :end-before: [End Docs] + +.. parsed-literal:: + + { 1:1000 } + +The annihilate gate allows us to decrease the number of photons in a qumode, if +it is applied to a qumode where the number of photons is already at the minimum +value 0, the operation has no effect: + +.. math:: A \ket{1} = \ket{0} + +.. math:: \begin{bmatrix} + 1 & 1 & 0 & 0 & \dots & 0 & 0 \\ + 0 & 0 & 1 & 0 & \dots & 0 & 0 \\ + 0 & 0 & 0 & 1 & \dots & 0 & 0 \\ + & & & & \ddots & & \\ + 0 & 0 & 0 & 0 & \dots & 1 & 0 \\ + 0 & 0 & 0 & 0 & \dots & 0 & 1 \\ + 0 & 0 & 0 & 0 & \dots & 0 & 0 + \end{bmatrix} + \begin{bmatrix} 0 \\ 1 \\ 0 \\ \vdots \\ 0 \\ 0 \\ 0 \end{bmatrix} = + \begin{bmatrix} 1 \\ 0 \\ 0 \\ \vdots \\ 0 \\ 0 \\ 0 \end{bmatrix} + +.. literalinclude:: ../../snippets/python/using/examples/annihilate_photonic_gate.py + :language: python + :start-after: [Begin Docs] + :end-before: [End Docs] + +.. parsed-literal:: + + { 0:1000 } + +A phase shifter adds a phase :math:`\phi` on a qumode. For the annihilation +(:math:`a_1`) and creation operators (:math:`a_1^\dagger`) of a qumode, the +phase shift operator is defined by + +.. math:: + P(\phi) = \exp\left(i \phi a_1^\dagger a_1 \right) + + +Just like the single-qubit gates above, we can define multi-qudit gates to act +on multiple qumodes. + +Beam splitters act on two qumodes together and are parameterized by a single +angle :math:`\theta`, which is related to the transmission amplitude :math:`t` +by :math:`t=\cos(\theta)`. + +For the annihilation (:math:`a_1` and :math:`a_2`) and creation operators +(:math:`a_1^\dagger` and :math:`a_2^\dagger`) of two qumodes, the beam splitter +operator is defined by + +.. math:: + B(\theta) = \exp\left[i \theta (a_1^\dagger a_2 + a_1 a_2^\dagger) \right] + +As an example, the code below implements a simulation of the Hong-Ou-Mandel +effect, in which two identical photons that interfere on a balanced beam +splitter leave the beam splitter together. + +.. literalinclude:: ../../snippets/python/using/examples/beam_splitter_photonic_gate.py + :language: python + :start-after: [Begin Docs] + :end-before: [End Docs] + +.. parsed-literal:: + + { 02:491 20:509 } + + +For a full list of photonic gates supported in CUDA-Q see +:doc:`../../api/default_ops`. + +Measurements +----------------------------- + +Quantum theory is probabilistic and hence requires statistical inference +to derive observations. Prior to measurement, the state of a qumode is +all possible combinations of :math:`\alpha_0, \alpha_1, \dots, \alpha_d` +and upon measurement, wave function collapse yields either a classical +:math:`0, 1, \dots,` or :math:`d`. + +The mathematical theory devised to explain quantum phenomena tells us +that the probability of observing the qumode in the state +:math:`\ket{0}, \ket{1}, \dots, \ket{d}`, yielding a classical +:math:`0, 1, \dots,` or :math:`d`, is :math:`\lvert \alpha_0 \rvert ^2, \lvert \alpha_1 \rvert ^2, \dots,` +or :math:`\lvert \alpha_d \rvert ^2`, respectively. + +As we see in the example of the `beam_splitter` gate above, states 02 and 20 +are yielded roughly 50% of the times, providing and illustration of the +Hong-Ou-Mandel effect. diff --git a/pr-2458/_sources/using/install/data_center_install.rst.txt b/pr-2458/_sources/using/install/data_center_install.rst.txt index 8b0fb1a0d0..11a78d0876 100644 --- a/pr-2458/_sources/using/install/data_center_install.rst.txt +++ b/pr-2458/_sources/using/install/data_center_install.rst.txt @@ -356,7 +356,7 @@ copy the built `.whl` file to the host system, and install it using `pip`; e.g. .. TODO: update pypi links throughout the docs To install the necessary CUDA and MPI dependencies for some of the components, -you can either follow the instructions on `PyPI.org `__, +you can either follow the instructions on `PyPI.org `__, replacing `pip install cudaq` with the command above, or you can follow the instructions in the remaining sections of this document to customize and better optimize them for your host system. diff --git a/pr-2458/_sources/using/install/local_installation.rst.txt b/pr-2458/_sources/using/install/local_installation.rst.txt index 737ca2a336..8542a0d370 100644 --- a/pr-2458/_sources/using/install/local_installation.rst.txt +++ b/pr-2458/_sources/using/install/local_installation.rst.txt @@ -183,8 +183,8 @@ please take a look at the section on :ref:`Development with VS Code `__. -Installation instructions can be found in the `project description `__. +CUDA-Q Python wheels are available on `PyPI.org `__. +Installation instructions can be found in the `project description `__. For more information about available versions and documentation, see :doc:`../../releases`. @@ -218,7 +218,7 @@ Pre-built binaries Starting with the 0.6.0 release, we provide pre-built binaries for using CUDA-Q with C++. Support for using CUDA-Q with Python can be installed side-by-side with the pre-built binaries for C++ by following the instructions on -`PyPI.org `__. +`PyPI.org `__. The pre-built binaries work across a range of Linux operating systems listed under :ref:`dependencies-and-compatibility`. @@ -659,7 +659,7 @@ certain CUDA libraries separately to take advantage of these. Installation via PyPI ++++++++++++++++++++++++++++++++++++ -If you installed CUDA-Q via `PyPI `__, please follow the installation instructions there to install the necessary CUDA dependencies. +If you installed CUDA-Q via `PyPI `__, please follow the installation instructions there to install the necessary CUDA dependencies. Installation In Container Images ++++++++++++++++++++++++++++++++++++ diff --git a/pr-2458/_sources/using/quick_start.rst.txt b/pr-2458/_sources/using/quick_start.rst.txt index d020dbbb19..8904b3695a 100644 --- a/pr-2458/_sources/using/quick_start.rst.txt +++ b/pr-2458/_sources/using/quick_start.rst.txt @@ -20,7 +20,7 @@ Install CUDA-Q .. tab:: Python To develop CUDA-Q applications using Python, - please follow the instructions for `installing CUDA-Q `_ from PyPI. + please follow the instructions for `installing CUDA-Q `_ from PyPI. 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  • Measurements
    • +
  • Photonic Operations +
  • Measuring Kernels @@ -149,6 +155,12 @@
    • +
  • Executing Photonic Kernels +
  • Computing Expectation Values @@ -181,6 +193,7 @@
  • Using Quantum Hardware Providers
  • Divisive Clustering With Coresets Using CUDA-Q
    • @@ -322,6 +344,10 @@
  • Stim (CPU)
    • +
  • Photonics Simulators +
  • Fermioniq
  • Default Simulator
    • @@ -333,48 +359,54 @@
  • Submission from Python
    • -
  • IonQ
      -
    • Setting Credentials
      • +
    • Infleqtion
      • -
    • Anyon Technologies/Anyon Computing
        -
      • Setting Credentials
        • +
      • IonQ
        • -
      • IQM
        • -
      • IonQ
          -
        • Setting Credentials
          • +
        • Infleqtion
          • -
        • Anyon Technologies/Anyon Computing
            -
          • Setting Credentials
            • +
          • IonQ
            • -
          • IQM
            • -
          • IonQ
              -
            • Setting Credentials
              • +
            • Infleqtion
              • -
            • Anyon Technologies/Anyon Computing
                -
              • Setting Credentials
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                • Anyon Technologies/Anyon Computing
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                  • IQM
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                                                        • QuEra Computing
                                                        • NVIDIA Quantum Cloud
                                                        • Installation
                                                            @@ -616,6 +649,7 @@
                                                          • spin.y()
                                                          • spin.z()
                                                          • CuDensityMatState
                                                            • +
                                                          • InitialState
                                                          • to_cupy_array()
                                                          • SampleResult
                                                          • AsyncSampleResult
                                                            • @@ -713,30 +747,33 @@

                                                            Multi-reference Quantum Krylov Algorithm - \(H_2\) Molecule

                                                            -

                                                            The multireference selected quantum Krylov (MRSQK) algorithm is defined in this paper and was developed as a low-cost alternative to quantum phase estimation. This tutorial will demonstrate how this algorithm can be implemented in CUDA-Q and accelerated using multiple GPUs. The CUDA-Q Hadamard test tutorial might provide helpful background information for understanding this tutorial.

                                                            +

                                                            The multireference selected quantum Krylov (MRSQK) algorithm is defined in this paper and was developed as a low-cost alternative to quantum phase estimation. This tutorial will demonstrate how this algorithm can be implemented in CUDA-Q and accelerated using multiple GPUs. The CUDA-Q Hadamard test tutorial might provide helpful background information for understanding +this tutorial.

                                                            The algorithm works by preparing an initial state, and then defining this state in a smaller subspace constructed with a basis that corresponds to Trotter steps of the initial state. This subspace can be diagonalized to produce an approximate energy for the system without variational optimization of any parameters.

                                                            In the example below, the initial guess is the ground state of the diagonalized Hamiltonian for demonstration purposes. In practice one could use a number of heuristics to prepare the ground state such as Hartree Fock or CISD. A very promising ground state preparation method which can leverage quantum computers is the linear combination of unitaries (LCU). LCU would allow for the state preparation to occur completely on the quantum computer and avoid storing an inputting the exponentially large state vector.

                                                            -

                                                            Regardless of the method used for state preparation, the procedure begins by selecting a \(d\) dimensional basis of reference states \({\Phi_0 \cdots \Phi_d}\) where each is a linear combination of slater determinants.

                                                            +

                                                            Regardless of the method used for state preparation, the procedure begins by selecting a \(d\)-dimensional basis of reference states \({\Phi_0 \cdots \Phi_d},\) where each is a linear combination of Slater determinants:

                                                            -\[\ket{\Phi_I} = \sum_{\mu} d_{\mu I}\ket{\phi_{\mu}}\]
                                                            -

                                                            From this, a non-orthogonal Krylov Space \(\mathcal{K} = \{\psi_{0} \cdots \psi_{N}\}\) is constructed by applying a family of \(s\) unitary operators on each of the \(d\) reference states resulting in \(d*s = N\) elements in the Krylov space where,

                                                            +\[\ket{\Phi_I} = \sum_{\mu} d_{\mu I}\ket{\phi_{\mu}}.\] +

                                                            From this, a non-orthogonal Krylov Space \(\mathcal{K} = \{\psi_{0} \cdots \psi_{N}\}\) is constructed by applying a family of \(s\) unitary operators on each of the \(d\) reference states resulting in \(d*s = N\) elements in the Krylov space where

                                                            -\[\ket{\psi_{\alpha}} \equiv \ket{\psi_I^{(n)}} = \hat{U}_n\ket{\Phi_I}\]
                                                            +\[\ket{\psi_{\alpha}} \equiv \ket{\psi_I^{(n)}} = \hat{U}_n\ket{\Phi_I},\]

                                                            Therefore, the general quantum state that we originally set out to describe is

                                                            -\[\ket{\Psi} = \sum_{\alpha} c_{\alpha}\ket{\psi_{\alpha}} = \sum_{I=0}^d \sum_{n=0}^s c_I^{(n)}\hat{U}_n\ket{\Phi_I}\]
                                                            +\[\ket{\Psi} = \sum_{\alpha} c_{\alpha}\ket{\psi_{\alpha}} = \sum_{I=0}^d \sum_{n=0}^s c_I^{(n)}\hat{U}_n\ket{\Phi_I}.\]

                                                            The energy of this state can be obtained by solving the generalized eigenvalue problem

                                                            -\[\boldsymbol{Hc}=\boldsymbol{Sc}E\]
                                                            -

                                                            Where the elements of the overlap and Hamiltonian matrix are

                                                            +\[\boldsymbol{Hc}=\boldsymbol{Sc}E,\] +

                                                            where the elements of the overlap are

                                                            \[S_{\alpha \beta} = \braket{\psi_{\alpha}|\psi_{\beta}} = \braket{\Phi_I|\hat{U}_m^{\dagger}\hat{U}_n|\Phi_J}\]
                                                            +

                                                            and Hamiltonian matrix is

                                                            -\[H_{\alpha \beta} = \braket{\psi_{\alpha}|\hat{H}|\psi_{\beta}} = \braket{\Phi_I|\hat{U}_m^{\dagger}\hat{H}\hat{U}_n|\Phi_J}\]
                                                            -

                                                            These matrix elements are computed using a quantum computer and the Hadamard test with a circuit shown below for the case of the overlap matrix elements (The Hamiltonian matrix elements circuit would include controlled application of the Hamiltonian in the circuit). Once the matrices are constructed, the diagonalization is performed classically to produce an estimate for the ground state in question.

                                                            +\[H_{\alpha \beta} = \braket{\psi_{\alpha}|\hat{H}|\psi_{\beta}} = \braket{\Phi_I|\hat{U}_m^{\dagger}\hat{H}\hat{U}_n|\Phi_J}.\] +

                                                            The matrix elements for \(S\) are computed with the Hadamard test with a circuit shown below for the case of the overlap matrix elements.

                                                            Htest

                                                            The \(2\sigma_+\) term refers to measurement of the expectation value of this circuit with the \(X+iY\) operator.

                                                            +

                                                            The Hamiltonian matrix elements are computed with a circuit that includes controlled application of the Hamiltonian. Once the \(H\) and \(S\) matrices are constructed, the diagonalization is performed classically to produce an estimate for the ground state in question.

                                                            Setup

                                                            This cell installs the necessary packages. This application can be parallelized, so please uncomment the mgpu specification below if you would like to run on more than one GPU.

                                                            @@ -744,9 +781,9 @@

                                                            Setup 
                                                            [ ]:
                                                            -
                                                            import cudaq
-import numpy as np
-import scipy
+
                                                            import cudaq
+import numpy as np
+import scipy
 
 !pip install openfermion==1.6.1 pyscf==2.6.2 openfermionpyscf==0.5 -q
 
@@ -794,20 +831,20 @@ 
                                                            Setup
 
                                                            
 
                                                            
 
                                                            # Collect coefficients from a spin operator so they can pass to a kernel
-def termCoefficients(ham: cudaq.SpinOperator) -> list[complex]:
+def termCoefficients(ham: cudaq.SpinOperator) -> list[complex]:
     result = []
     ham.for_each_term(lambda term: result.append(term.get_coefficient()))
     return result
 
 
 # Collect Pauli words from a spin operator so they can pass to a kernel
-def termWords(ham: cudaq.SpinOperator) -> list[str]:
+def termWords(ham: cudaq.SpinOperator) -> list[str]:
     result = []
     ham.for_each_term(lambda term: result.append(term.to_string(False)))
     return result
 
 
-#Build the lists of coefficients and Pauli Words from H2 Hamiltonian
+# Build the lists of coefficients and Pauli Words from the H2 Hamiltonian
 coefficient = termCoefficients(hamiltonian)
 pauli_string = termWords(hamiltonian)
 
@@ -816,14 +853,14 @@ 
                                                            Setup
                                                            -

                                                            In the case of this example, the unitary operators that build the Krylov subspace are first-order Trotter operations at different time steps. The performance here could potentially be improved by increasing the size of the time step, using a higher order Trotter approximation, or using other sorts of approximations. The CUDA-Q kernels below define the unitary operations that construct the \(\psi\) basis. Each receives the target qubits, the time step, and components of the Hamiltonian.

                                                            +

                                                            In this example, the unitary operators that build the Krylov subspace are first-order Trotter operations at different time steps. The performance here could potentially be improved by increasing the size of the time step, using a higher order Trotter approximation, or using other sorts of approximations. The CUDA-Q kernels below define the unitary operations that construct the \(\psi\) basis. Each receives the target qubits, the time step, and components of the Hamiltonian.

                                                            [4]:
 
                                                            # Applies Unitary operation corresponding to Um
 @cudaq.kernel
-def U_m(qubits: cudaq.qview, dt: float, coefficients: list[complex],
+def U_m(qubits: cudaq.qview, dt: float, coefficients: list[complex],
         words: list[cudaq.pauli_word]):
     # Compute U_m = exp(-i m dt H)
     for i in range(len(coefficients)):
@@ -834,7 +871,7 @@ 
                                                            Setup
 
 
 @cudaq.kernel
-def U_n(qubits: cudaq.qview, dt: float, coefficients: list[complex],
+def U_n(qubits: cudaq.qview, dt: float, coefficients: list[complex],
         words: list[cudaq.pauli_word]):
     # Compute U_n = exp(-i n dt H)
     for i in range(len(coefficients)):
@@ -845,7 +882,7 @@ 
                                                            Setup
 
 
 @cudaq.kernel
-def apply_pauli(qubits: cudaq.qview, word: list[int]):
+def apply_pauli(qubits: cudaq.qview, word: list[int]):
     # Add H (Hamiltonian operator)
     for i in range(len(word)):
         if word[i] == 1:
@@ -860,7 +897,7 @@ 
                                                            Setup
 
 
 @cudaq.kernel
-def qfd_kernel(dt_alpha: float, dt_beta: float, coefficients: list[complex],
+def qfd_kernel(dt_alpha: float, dt_beta: float, coefficients: list[complex],
                words: list[cudaq.pauli_word], word_list: list[int],
                vec: list[complex]):
 
@@ -883,7 +920,7 @@ 
                                                            Setup
 
                                                            [5]:
 
                                                            
 
                                                            
-
                                                            def pauli_str(pauli_word, qubits_num):
+
                                                            def pauli_str(pauli_word, qubits_num):
 
     my_list = []
     for i in range(qubits_num):
@@ -927,9 +964,9 @@ 
                                                            Setup
 
                                                            
 
                                                            Computing the matrix elements
                                                            
 
                                                            The cell below computes the overlap matrix. This can be done in serial or in parallel, depending on the multi_gpu specification. First, an operator is built to apply the identity to the overlap matrix circuit when apply_pauli is called. Next, the wf_overlap array is constructed which will hold the matrix elements.
                                                            
-
                                                            Next, a pair of nested loops, iterate over the time steps defined by the dimension of the subspace. Each m,n combination corresponds to computation of an off-diagonal matrix element of the overlap matrix \(S\) using the Hadamard test. This is accomplished by calling the CUDA-Q observe function with the X and Y operators, along with the time steps, the components of the Hamiltonian matrix, and the initial state vector vec.
                                                            
+
                                                            Next, a pair of nested loops iterate over the time steps defined by the dimension of the subspace. Each m,n combination corresponds to computation of an off-diagonal matrix element of the overlap matrix \(S\) using the Hadamard test. This is accomplished by calling the CUDA-Q observe function with the X and Y operators, along with the time steps, the components of the Hamiltonian matrix, and the initial state vector vec.
                                                            
 
                                                            The observe function broadcasts over the two provided operators \(X\) and \(Y\) and returns a list of results. The expectation function returns the expectation values which are summed and stored in the matrix.
                                                            
-
                                                            The multi-gpu case completes the same steps, expect for observe_async is used. This allows for the \(X\) and \(Y\) observables to be evaluated at the same time on two different simulated QPUs. In this case, the results are stored in lists corresponding to the real an imaginary parts, and then accessed later with the get command to build \(S\)
                                                            
+
                                                            The multi-gpu case completes the same steps, except the observe_async command is used. This allows for the \(X\) and \(Y\) observables to be evaluated at the same time on two different simulated QPUs. In this case, the results are stored in lists corresponding to the real and imaginary parts. These are then accessed later with the get command to build \(S\).
                                                            
 
                                                            
 
                                                            [8]:
 
                                                            
@@ -1149,23 +1186,23 @@ 
                                                            Computing the matrix elements
-
                                                            Determining the ground state energy of the Subspace
                                                            
+
                                                            
+
                                                            Determining the ground state energy of the subspace
                                                            
 
                                                            The final step is to solve the generalized eigenvaulue problem with the overlap and Hamiltonian matrices constructed using the quantum computer. The procedure begins by diagonalizing \(S\) with the transform
                                                            
 
                                                            
 \[S = U\Sigma U^{\dagger}\]
                                                            
-
                                                            The eigenvectors \(v\) and eigenvalues \(s\) are used to construct a new matrix \(X'\)
                                                            
+
                                                            The eigenvectors \(v\) and eigenvalues \(s\) are used to construct a new matrix \(X':\)
                                                            
 
                                                            
-\[X' = S ^{\frac{-1}{2}} = \sum_k v_{ki} \frac{1}{\sqrt{s_k}} v_{kj}\]
                                                            
-
                                                            The \(X'\) matrix diagonalizes \(H\)
                                                            
+\[X' = S ^{\frac{-1}{2}} = \sum_k v_{ki} \frac{1}{\sqrt{s_k}} v_{kj}.\]
                                                            
+
                                                            The matrix \(X'\) diagonalizes \(H:\)
                                                            
 
                                                            
-\[X'^{\dagger}HX' = ES^{\frac{1}{2}}C\]
                                                            
-
                                                            Using the eigenvectors of \(H'\), (\(^{\frac{1}{2}}C\)), the original eigenvectors to the problem can be found by left multiplying by \(S^{\frac{-1}{2}}C\)
                                                            
+\[X'^{\dagger}HX' = ES^{\frac{1}{2}}C.\]
                                                            
+
                                                            Using the eigenvectors of \(H'\), (\(^{\frac{1}{2}}C\)), the original eigenvectors to the problem can be found by left multiplying by \(S^{\frac{-1}{2}}C.\)
                                                            
 
                                                            
 
                                                            [10]:
 
                                                            
 
                                                            
-
                                                            def eig(H, s):
+
                                                            def eig(H, s):
     #Solver for generalized eigenvalue problem
     # HC = SCE
 
@@ -1218,7 +1255,7 @@ 
                                                            Determining the ground state energy of the Subspace
 
   
                                                            
-    
                                                            © Copyright 2024, NVIDIA Corporation & Affiliates.
                                                            
+    
                                                            © Copyright 2025, NVIDIA Corporation & Affiliates.
                                                            
   
                                                            
 
   Built with                                                             Sphinx using a
diff --git a/pr-2458/applications/python/krylov.ipynb b/pr-2458/applications/python/krylov.ipynb
index 1954212c02..183a13d691 100644
--- a/pr-2458/applications/python/krylov.ipynb
+++ b/pr-2458/applications/python/krylov.ipynb
@@ -7,39 +7,45 @@
    "source": [
     "# Multi-reference Quantum Krylov Algorithm - $H_2$ Molecule\n",
     "\n",
-    "The multireference selected quantum Krylov (MRSQK) algorithm is defined in [this paper](https://arxiv.org/pdf/1911.05163) and was developed as a low-cost alternative to quantum phase estimation. This tutorial will demonstrate how this algorithm can be implemented in CUDA-Q and accelerated using multiple GPUs. The CUDA-Q Hadamard test tutorial might provide helpful background information for understanding this tutorial.\n",
+    "The multireference selected quantum Krylov (MRSQK) algorithm is defined in [this paper](https://arxiv.org/pdf/1911.05163) and was developed as a low-cost alternative to quantum phase estimation. This tutorial will demonstrate how this algorithm can be implemented in CUDA-Q and accelerated using multiple GPUs. The [CUDA-Q Hadamard test tutorial](https://nvidia.github.io/cuda-quantum/latest/applications/python/hadamard_test.html) might provide helpful background information for understanding this tutorial.\n",
     "\n",
     "The algorithm works by preparing an initial state, and then defining this state in a smaller subspace constructed with a basis that corresponds to Trotter steps of the initial state. This subspace can be diagonalized to produce an approximate energy for the system without variational optimization of any parameters.\n",
     "\n",
     "In the example below, the initial guess is the ground state of the diagonalized Hamiltonian for demonstration purposes.  In practice one could use a number of heuristics to prepare the ground state such as Hartree Fock or CISD. A very promising ground state preparation method which can leverage quantum computers is the linear combination of unitaries (LCU). LCU would allow for the state preparation to occur completely on the quantum computer and avoid storing an inputting the exponentially large state vector.\n",
     "\n",
     "\n",
-    "Regardless of the method used for state preparation, the procedure begins by selecting a $d$ dimensional basis of reference states ${\\Phi_0 \\cdots \\Phi_d}$ where each is a linear combination of slater determinants. \n",
+    "Regardless of the method used for state preparation, the procedure begins by selecting a $d$-dimensional basis of reference states ${\\Phi_0 \\cdots \\Phi_d},$ where each is a linear combination of Slater determinants: \n",
     "\n",
-    "$$ \\ket{\\Phi_I}  =  \\sum_{\\mu} d_{\\mu I}\\ket{\\phi_{\\mu}} $$\n",
+    "$$ \\ket{\\Phi_I}  =  \\sum_{\\mu} d_{\\mu I}\\ket{\\phi_{\\mu}}. $$\n",
     "\n",
     "\n",
-    "From this, a non-orthogonal Krylov Space $\\mathcal{K} = \\{\\psi_{0} \\cdots \\psi_{N}\\}$ is constructed by applying a family of $s$ unitary operators on each of the $d$ reference states resulting in $d*s = N$ elements in the Krylov space where, \n",
-    "$$ \\ket{\\psi_{\\alpha}} \\equiv \\ket{\\psi_I^{(n)}} = \\hat{U}_n\\ket{\\Phi_I} $$\n",
+    "From this, a non-orthogonal Krylov Space $\\mathcal{K} = \\{\\psi_{0} \\cdots \\psi_{N}\\}$ is constructed by applying a family of $s$ unitary operators on each of the $d$ reference states resulting in $d*s = N$ elements in the Krylov space where \n",
+    "$$ \\ket{\\psi_{\\alpha}} \\equiv \\ket{\\psi_I^{(n)}} = \\hat{U}_n\\ket{\\Phi_I}, $$\n",
     "\n",
     "Therefore, the general quantum state that we originally set out to describe is\n",
     "\n",
-    "$$ \\ket{\\Psi} = \\sum_{\\alpha} c_{\\alpha}\\ket{\\psi_{\\alpha}} = \\sum_{I=0}^d \\sum_{n=0}^s c_I^{(n)}\\hat{U}_n\\ket{\\Phi_I}  $$\n",
+    "$$ \\ket{\\Psi} = \\sum_{\\alpha} c_{\\alpha}\\ket{\\psi_{\\alpha}} = \\sum_{I=0}^d \\sum_{n=0}^s c_I^{(n)}\\hat{U}_n\\ket{\\Phi_I}.  $$\n",
     "\n",
     "The energy of this state can be obtained by solving the generalized eigenvalue problem\n",
-    "$$ \\boldsymbol{Hc}=\\boldsymbol{Sc}E $$\n",
+    "$$ \\boldsymbol{Hc}=\\boldsymbol{Sc}E, $$\n",
     "\n",
-    "Where the elements of the overlap and Hamiltonian matrix are\n",
+    "where the elements of the overlap are\n",
     "\n",
     "$$S_{\\alpha \\beta} = \\braket{\\psi_{\\alpha}|\\psi_{\\beta}} =   \\braket{\\Phi_I|\\hat{U}_m^{\\dagger}\\hat{U}_n|\\Phi_J}$$ \n",
     "\n",
-    "$$H_{\\alpha \\beta} = \\braket{\\psi_{\\alpha}|\\hat{H}|\\psi_{\\beta}} =   \\braket{\\Phi_I|\\hat{U}_m^{\\dagger}\\hat{H}\\hat{U}_n|\\Phi_J}$$\n",
+    "and Hamiltonian matrix is\n",
     "\n",
-    "These matrix elements are computed using a quantum computer and the Hadamard test with a circuit shown below for the case of the overlap matrix elements (The Hamiltonian matrix elements circuit would include controlled application of the Hamiltonian in the circuit).  Once the matrices are constructed, the diagonalization is performed classically to produce an estimate for the ground state in question.\n",
+    "$$H_{\\alpha \\beta} = \\braket{\\psi_{\\alpha}|\\hat{H}|\\psi_{\\beta}} =   \\braket{\\Phi_I|\\hat{U}_m^{\\dagger}\\hat{H}\\hat{U}_n|\\Phi_J}.$$\n",
+    "\n",
+    "The matrix elements for $S$ are computed with the Hadamard test with a circuit shown below for the case of the overlap matrix elements. \n",
     "\n",
     "![Htest](./images/krylovcircuit.png)\n",
     "\n",
-    "The $2\\sigma_+$ term refers to measurement of the expectation value of this circuit with the $X+iY$ operator. \n"
+    "The $2\\sigma_+$ term refers to measurement of the expectation value of this circuit with the $X+iY$ operator.\n",
+    "\n",
+    "The Hamiltonian matrix elements are computed with a circuit that includes controlled application of the Hamiltonian. Once the $H$ and $S$ matrices are constructed, the diagonalization is performed classically to produce an estimate for the ground state in question.\n",
+    "\n",
+    "\n"
    ]
   },
   {
@@ -140,7 +146,7 @@
     "    return result\n",
     "\n",
     "\n",
-    "#Build the lists of coefficients and Pauli Words from H2 Hamiltonian\n",
+    "# Build the lists of coefficients and Pauli Words from the H2 Hamiltonian\n",
     "coefficient = termCoefficients(hamiltonian)\n",
     "pauli_string = termWords(hamiltonian)\n",
     "\n",
@@ -153,7 +159,7 @@
    "id": "74b4c079-8837-47ae-a484-52ec5f4a160e",
    "metadata": {},
    "source": [
-    "In the case of this example, the unitary operators that build the Krylov subspace are first-order Trotter operations at different time steps. The performance here could potentially be improved by increasing the size of the time step, using a higher order Trotter approximation, or using other sorts of approximations. The CUDA-Q kernels below define the unitary operations that construct the $\\psi$ basis.  Each receives the target qubits, the time step, and components of the Hamiltonian."
+    "In this example, the unitary operators that build the Krylov subspace are first-order Trotter operations at different time steps. The performance here could potentially be improved by increasing the size of the time step, using a higher order Trotter approximation, or using other sorts of approximations. The CUDA-Q kernels below define the unitary operations that construct the $\\psi$ basis.  Each receives the target qubits, the time step, and components of the Hamiltonian."
    ]
   },
   {
@@ -300,11 +306,11 @@
     "\n",
     "The cell below computes the overlap matrix. This can be done in serial or in parallel, depending on the `multi_gpu` specification.  First, an operator is built to apply the identity to the overlap matrix circuit when `apply_pauli` is called. Next, the `wf_overlap` array is constructed which will hold the matrix elements. \n",
     "\n",
-    "Next, a pair of nested loops, iterate over the time steps defined by the dimension of the subspace.  Each m,n combination corresponds to computation of an off-diagonal matrix element of the overlap matrix $S$ using the Hadamard test.  This is accomplished by calling the CUDA-Q `observe` function with the X and Y operators, along with the time steps, the components of the Hamiltonian matrix, and the initial state vector `vec`.\n",
+    "Next, a pair of nested loops iterate over the time steps defined by the dimension of the subspace.  Each m,n combination corresponds to computation of an off-diagonal matrix element of the overlap matrix $S$ using the Hadamard test.  This is accomplished by calling the CUDA-Q `observe` function with the X and Y operators, along with the time steps, the components of the Hamiltonian matrix, and the initial state vector `vec`.\n",
     "\n",
     "The observe function broadcasts over the two provided operators $X$ and $Y$ and returns a list of results. The `expectation` function returns the expectation values which are summed and stored in the matrix.\n",
     "\n",
-    "The multi-gpu case completes the same steps, expect for `observe_async` is used. This allows for the $X$ and $Y$ observables to be evaluated at the same time on two different simulated QPUs. In this case, the results are stored in lists corresponding to the real an imaginary parts, and then accessed later with the `get` command to build $S$\n"
+    "The multi-gpu case completes the same steps, except the `observe_async` command is used. This allows for the $X$ and $Y$ observables to be evaluated at the same time on two different simulated QPUs. In this case, the results are stored in lists corresponding to the real and imaginary parts. These are then accessed later with the `get` command to build $S$.\n"
    ]
   },
   {
@@ -541,19 +547,19 @@
    "id": "1917bd58-4ce3-4e3e-9ccf-096577c0da14",
    "metadata": {},
    "source": [
-    "### Determining the ground state energy of the Subspace\n",
+    "### Determining the ground state energy of the subspace\n",
     "\n",
     "The final step is to solve the generalized eigenvaulue problem with the overlap and Hamiltonian matrices constructed using the quantum computer. The procedure begins by diagonalizing  $S$ with the transform $$S = U\\Sigma U^{\\dagger}$$\n",
     "\n",
-    "The eigenvectors $v$ and eigenvalues $s$ are used to construct a new matrix $X'$\n",
+    "The eigenvectors $v$ and eigenvalues $s$ are used to construct a new matrix $X':$\n",
     "\n",
-    "$$ X' = S ^{\\frac{-1}{2}} = \\sum_k v_{ki} \\frac{1}{\\sqrt{s_k}} v_{kj}$$\n",
+    "$$ X' = S ^{\\frac{-1}{2}} = \\sum_k v_{ki} \\frac{1}{\\sqrt{s_k}} v_{kj}.$$\n",
     "\n",
-    "The $X'$ matrix diagonalizes $H$\n",
+    "The matrix $X'$ diagonalizes $H:$\n",
     "\n",
-    "$$ X'^{\\dagger}HX' = ES^{\\frac{1}{2}}C$$\n",
+    "$$ X'^{\\dagger}HX' = ES^{\\frac{1}{2}}C.$$\n",
     "\n",
-    "Using the eigenvectors of $H'$, ($^{\\frac{1}{2}}C$), the original eigenvectors to the problem can be found by left multiplying by $S^{\\frac{-1}{2}}C$"
+    "Using the eigenvectors of $H'$, ($^{\\frac{1}{2}}C$), the original eigenvectors to the problem can be found by left multiplying by $S^{\\frac{-1}{2}}C.$"
    ]
   },
   {
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+  Anderson Impurity Model ground state solver on Infleqtion’s Sqale — NVIDIA CUDA-Q  documentation
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+  
                                                            
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+      
                                                            
+        
                                                            
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+
                                                            Anderson Impurity Model ground state solver on Infleqtion’s Sqale
                                                            
+
                                                            Ground state quantum chemistry—computing total energies of molecular configurations to within chemical accuracy—is perhaps the most highly-touted industrial application of fault-tolerant quantum computers. Strongly correlated materials, for example, are particularly interesting, and tools like dynamical mean-field theory (DMFT) allow one to account for the effect of their strong, localized electronic correlations. These DMFT models help predict material properties by approximating the system as
+a single site impurity inside a “bath” that encompasses the rest of the system. Simulating such dynamics can be a tough task using classical methods, but can be done efficiently on a quantum computer via quantum simulation.
                                                            
+
                                                            In this notebook, we showcase a workflow for preparing the ground state of the minimal single-impurity Anderson model (SIAM) using the Hamiltonian Variational Ansatz for a range of realistic parameters. As a first step towards running DMFT on a fault-tolerant quantum computer, we will use logical qubits encoded in the [[4, 2, 2]] code. Using this workflow, we will obtain the ground state energy estimates via noisy simulation, and then also execute the corresponding optimized circuits on
+Infleqtion’s gate-based neutral-atom quantum computer, making the benefits of logical qubits apparent. More details can be found in our paper.
                                                            
+
                                                            This demo notebook uses CUDA-Q (cudaq) and a CUDA-QX library, cudaq-solvers; let us first begin by importing (and installing as needed) these packages:
                                                            
+
                                                            
+
                                                            [1]:
+
                                                            
+
                                                            
+
                                                            try:
+    import cudaq_solvers as solvers
+    import cudaq
+    import matplotlib.pyplot as plt
+except ImportError:
+    print("Installing required packages...")
+    %pip install --quiet 'cudaq-solvers' 'matplotlib'
+    print("Installed `cudaq`, `cudaq-solvers`, and `matplotlib` packages.")
+    print("You may need to restart the kernel to import newly installed packages.")
+    import cudaq_solvers as solvers
+    import cudaq
+    import matplotlib.pyplot as plt
+
+from collections.abc import Mapping, Sequence
+import numpy as np
+from scipy.optimize import minimize
+import os
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            Performing logical Variational Quantum Eigensolver (VQE) with CUDA-QX
                                                            
+
                                                            To prepare our ground state quantum Anderson impurity model circuits (referred to as AIM circuits in this notebook for short), we use VQE to train an ansatz to minimize a Hamiltonian and obtain optimal angles that can be used to set the AIM circuits. As described in our paper, the associated restricted Hamiltonian for our SIAM can be reduced to,
                                                            
+
                                                            
+\[\begin{equation}
+H_{(U, V)} = U (Z_0 Z_2 - 1) / 4 + V (X_0 + X_2),
+\end{equation}\]
                                                            
+
                                                            where \(U\) is the Coulomb interaction and \(V\) the hybridization strength. In this notebook workflow, we will optimize over a 2-dimensional grid of Hamiltonian parameter values, namely \(U\in \{1, 5, 9\}\) and \(V\in \{-9, -1, 7\}\) (with all values assumed to be in units of eV), to ensure that the ansatz is generally trainable and expressive, and obtain 9 different circuit layers identified by the key \((U, V)\). We will simulate the VQE on GPU (or optionally on CPU if you
+do not have GPU access), enabled by CUDA-Q, in the absence of noise:
                                                            
+
                                                            
+
                                                            [2]:
+
                                                            
+
                                                            
+
                                                            if cudaq.num_available_gpus() == 0:
+    cudaq.set_target("qpp-cpu", option="fp64")
+else:
+    cudaq.set_target("nvidia", option="fp64")
+
                                                            
+
                                                            
+
                                                            
+
                                                            This workflow can be easily defined in CUDA-Q as shown in the cell below, using the CUDA-QX Solvers library (which accelerates quantum algorithms like the VQE):
                                                            
+
                                                            
+
                                                            [3]:
+
                                                            
+
                                                            
+
                                                            def ansatz(n_qubits: int) -> cudaq.Kernel:
+    # Create a CUDA-Q parameterized kernel
+    paramterized_ansatz, variational_angles = cudaq.make_kernel(list)
+    qubits = paramterized_ansatz.qalloc(n_qubits)
+
+    # Using |+> as the initial state:
+    paramterized_ansatz.h(qubits[0])
+    paramterized_ansatz.cx(qubits[0], qubits[1])
+
+    paramterized_ansatz.rx(variational_angles[0], qubits[0])
+    paramterized_ansatz.cx(qubits[0], qubits[1])
+    paramterized_ansatz.rz(variational_angles[1], qubits[1])
+    paramterized_ansatz.cx(qubits[0], qubits[1])
+    return paramterized_ansatz
+
+
+def run_logical_vqe(cudaq_hamiltonian: cudaq.SpinOperator) -> tuple[float, list[float]]:
+    # Set seed for easier reproduction
+    np.random.seed(42)
+
+    # Initial angles for the optimizer
+    init_angles = np.random.random(2) * 1e-1
+
+    # Obtain CUDA-Q Ansatz
+    num_qubits = cudaq_hamiltonian.get_qubit_count()
+    variational_kernel = ansatz(num_qubits)
+
+    # Perform VQE optimization
+    energy, params, _ = solvers.vqe(
+        variational_kernel,
+        cudaq_hamiltonian,
+        init_angles,
+        optimizer=minimize,
+        method="SLSQP",
+        tol=1e-10,
+    )
+    return energy, params
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            Constructing circuits in the [[4,2,2]] encoding
                                                            
+
                                                            The [[4,2,2]] code is a quantum error detection code that uses four physical qubits to encode two logical qubits. In this notebook, we will construct two variants of quantum circuits: physical (bare, unencoded) and logical (encoded). These circuits will be informed by the Hamiltonian Variational Ansatz described earlier. To measure all the terms in our Hamiltonian, we will measure the data qubits in both the \(Z\)- and \(X\)-basis, as allowed by the [[4,2,2]] logical gateset.
+Full details on the circuit constructions are outlined in our paper.
                                                            
+
                                                            Below, we create functions to build our CUDA-Q AIM circuits, both physical and logical versions. As we consider noisy simulation in this notebook, we will include some noisy gates. Here, for simplicity, we will just register a custom identity gate – to be later used as a noisy operation to model readout error:
                                                            
+
                                                            
+
                                                            [4]:
+
                                                            
+
                                                            
+
                                                            cudaq.register_operation("meas_id", np.identity(2))
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [5]:
+
                                                            
+
                                                            
+
                                                            def aim_physical_circuit(
+    angles: list[float], basis: str, *, ignore_meas_id: bool = False
+) -> cudaq.Kernel:
+    kernel = cudaq.make_kernel()
+    qubits = kernel.qalloc(2)
+
+    # Bell state prep
+    kernel.h(qubits[0])
+    kernel.cx(qubits[0], qubits[1])
+
+    # Rx Gate
+    kernel.rx(angles[0], qubits[0])
+
+    # ZZ rotation
+    kernel.cx(qubits[0], qubits[1])
+    kernel.rz(angles[1], qubits[1])
+    kernel.cx(qubits[0], qubits[1])
+
+    if basis == "z_basis":
+        if not ignore_meas_id:
+            kernel.for_loop(
+                start=0, stop=2, function=lambda q_idx: getattr(kernel, "meas_id")(qubits[q_idx])
+            )
+        kernel.mz(qubits)
+    elif basis == "x_basis":
+        kernel.h(qubits)
+        if not ignore_meas_id:
+            kernel.for_loop(
+                start=0, stop=2, function=lambda q_idx: getattr(kernel, "meas_id")(qubits[q_idx])
+            )
+        kernel.mz(qubits)
+    else:
+        raise ValueError("Unsupported basis provided:", basis)
+    return kernel
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [6]:
+
                                                            
+
                                                            
+
                                                            def aim_logical_circuit(
+    angles: list[float], basis: str, *, ignore_meas_id: bool = False
+) -> cudaq.Kernel:
+    kernel = cudaq.make_kernel()
+    qubits = kernel.qalloc(6)
+
+    kernel.for_loop(start=0, stop=3, function=lambda idx: kernel.h(qubits[idx]))
+    kernel.cx(qubits[1], qubits[4])
+    kernel.cx(qubits[2], qubits[3])
+    kernel.cx(qubits[0], qubits[1])
+    kernel.cx(qubits[0], qubits[3])
+
+    # Rx teleportation
+    kernel.rx(angles[0], qubits[0])
+
+    kernel.cx(qubits[0], qubits[1])
+    kernel.cx(qubits[0], qubits[3])
+    kernel.h(qubits[0])
+
+    if basis == "z_basis":
+        if not ignore_meas_id:
+            kernel.for_loop(
+                start=0, stop=5, function=lambda idx: getattr(kernel, "meas_id")(qubits[idx])
+            )
+        kernel.mz(qubits)
+    elif basis == "x_basis":
+        # ZZ rotation and teleportation
+        kernel.cx(qubits[3], qubits[5])
+        kernel.cx(qubits[2], qubits[5])
+        kernel.rz(angles[1], qubits[5])
+        kernel.cx(qubits[1], qubits[5])
+        kernel.cx(qubits[4], qubits[5])
+        kernel.for_loop(start=1, stop=5, function=lambda idx: kernel.h(qubits[idx]))
+        if not ignore_meas_id:
+            kernel.for_loop(
+                start=0, stop=6, function=lambda idx: getattr(kernel, "meas_id")(qubits[idx])
+            )
+        kernel.mz(qubits)
+    else:
+        raise ValueError("Unsupported basis provided:", basis)
+    return kernel
+
                                                            
+
                                                            
+
                                                            
+
                                                            With the circuit definitions above, we can now define a function that automatically runs the VQE and constructs a dictionary containing all the AIM circuits we want to submit to hardware (or noisily simulate):
                                                            
+
                                                            
+
                                                            [7]:
+
                                                            
+
                                                            
+
                                                            def generate_circuit_set(ignore_meas_id: bool = False) -> object:
+    u_vals = [1, 5, 9]
+    v_vals = [-9, -1, 7]
+    circuit_dict = {}
+    for u in u_vals:
+        for v in v_vals:
+            qubit_hamiltonian = (
+                0.25 * u * cudaq.spin.z(0) * cudaq.spin.z(1)
+                - 0.25 * u
+                + v * cudaq.spin.x(0)
+                + v * cudaq.spin.x(1)
+            )
+            _, opt_params = run_logical_vqe(qubit_hamiltonian)
+            angles = [float(angle) for angle in opt_params]
+            print(f"Computed optimal angles={angles} for U={u}, V={v}")
+
+            tmp_physical_dict = {}
+            tmp_logical_dict = {}
+            for basis in ("z_basis", "x_basis"):
+                tmp_physical_dict[basis] = aim_physical_circuit(
+                    angles, basis, ignore_meas_id=ignore_meas_id
+                )
+                tmp_logical_dict[basis] = aim_logical_circuit(
+                    angles, basis, ignore_meas_id=ignore_meas_id
+                )
+
+            circuit_dict[f"{u}:{v}"] = {
+                "physical": tmp_physical_dict,
+                "logical": tmp_logical_dict,
+            }
+    print("\nFinished building optimized circuits!")
+    return circuit_dict
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [8]:
+
                                                            
+
                                                            
+
                                                            sim_circuit_dict = generate_circuit_set()
+circuit_layers = sim_circuit_dict.keys()
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            +Computed optimal angles=[1.5846845738799267, 1.5707961678256028] for U=1, V=-9
+Computed optimal angles=[4.588033710930825, 4.712388365176642] for U=1, V=-1
+Computed optimal angles=[-1.588651490745171, 1.5707962742876598] for U=1, V=7
+Computed optimal angles=[1.64012940802256, 1.5707963354922125] for U=5, V=-9
+Computed optimal angles=[2.1293956916868737, 1.5707963294715355] for U=5, V=-1
+Computed optimal angles=[-1.6598458659836037, 1.570796331040382] for U=5, V=7
+Computed optimal angles=[1.695151467539617, 1.5707960973500679] for U=9, V=-9
+Computed optimal angles=[2.4149519241823376, 1.5707928509325972] for U=9, V=-1
+Computed optimal angles=[-1.7301462729177735, 1.570796033796985] for U=9, V=7
+
+Finished building optimized circuits!
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            Setting up submission and decoding workflow
                                                            
+
                                                            In this section, we define various helper functions that will play a role in generating the associated energies of the AIM circuits based on the circuit samples (in the different bases), as well as decode the logical circuits with post-selection informed by the [[4,2,2]] code:
                                                            
+
                                                            
+
                                                            [9]:
+
                                                            
+
                                                            
+
                                                            def _num_qubits(counts: Mapping[str, float]) -> int:
+    for key in counts:
+        if key.isdecimal():
+            return len(key)
+    return 0
+
+
+def process_counts(
+    counts: Mapping[str, float],
+    data_qubits: Sequence[int],
+    flag_qubits: Sequence[int] = (),
+) -> dict[str, float]:
+    new_data: dict[str, float] = {}
+    for key, val in counts.items():
+        if not all(key[i] == "0" for i in flag_qubits):
+            continue
+
+        new_key = "".join(key[i] for i in data_qubits)
+
+        if not set("01").issuperset(new_key):
+            continue
+
+        new_data.setdefault(new_key, 0)
+        new_data[new_key] += val
+
+    return new_data
+
+
+def decode(counts: Mapping[str, float]) -> dict[str, float]:
+    """Decode physical counts into logical counts. Should be called after `process_counts`."""
+
+    if not counts:
+        return {}
+
+    num_qubits = _num_qubits(counts)
+    assert num_qubits % 4 == 0
+
+    physical_to_logical = {
+        "0000": "00",
+        "1111": "00",
+        "0011": "01",
+        "1100": "01",
+        "0101": "10",
+        "1010": "10",
+        "0110": "11",
+        "1001": "11",
+    }
+
+    new_data: dict[str, float] = {}
+    for key, val in counts.items():
+        physical_keys = [key[i : i + 4] for i in range(0, num_qubits, 4)]
+        logical_keys = [physical_to_logical.get(physical_key) for physical_key in physical_keys]
+        if None not in logical_keys:
+            new_key = "".join(logical_keys)
+            new_data.setdefault(new_key, 0)
+            new_data[new_key] += val
+
+    return new_data
+
+
+def ev_x(counts: Mapping[str, float]) -> float:
+    ev = 0.0
+
+    for k, val in counts.items():
+        ev += val * ((-1) ** int(k[0]) + (-1) ** int(k[1]))
+
+    total = sum(counts.values())
+    ev /= total
+    return ev
+
+
+def ev_xx(counts: Mapping[str, float]) -> float:
+    ev = 0.0
+
+    for k, val in counts.items():
+        ev += val * (-1) ** k.count("1")
+
+    total = sum(counts.values())
+    ev /= total
+    return ev
+
+
+def ev_zz(counts: Mapping[str, float]) -> float:
+    ev = 0.0
+
+    for k, val in counts.items():
+        ev += val * (-1) ** k.count("1")
+
+    total = sum(counts.values())
+    ev /= total
+    return ev
+
+
+def aim_logical_energies(
+    data_ordering: object, counts_list: Sequence[dict[str, float]]
+) -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:
+    counts_data = {
+        data_ordering[i]: decode(
+            process_counts(
+                counts,
+                data_qubits=[1, 2, 3, 4],
+                flag_qubits=[0, 5],
+            )
+        )
+        for i, counts in enumerate(counts_list)
+    }
+    return _aim_energies(counts_data)
+
+
+def aim_physical_energies(
+    data_ordering: object, counts_list: Sequence[dict[str, float]]
+) -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:
+    counts_data = {
+        data_ordering[i]: process_counts(
+            counts,
+            data_qubits=[0, 1],
+        )
+        for i, counts in enumerate(counts_list)
+    }
+    return _aim_energies(counts_data)
+
+
+def _aim_energies(
+    counts_data: Mapping[tuple[int, int, str], dict[str, float]],
+) -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:
+    evxs: dict[tuple[int, int], float] = {}
+    evxxs: dict[tuple[int, int], float] = {}
+    evzzs: dict[tuple[int, int], float] = {}
+    totals: dict[tuple[int, int], float] = {}
+
+    for key, counts in counts_data.items():
+        h_params, basis = key
+        key_a, key_b = h_params.split(":")
+        u, v = int(key_a), int(key_b)
+        if basis.startswith("x"):
+            evxs[u, v] = ev_x(counts)
+            evxxs[u, v] = ev_xx(counts)
+        else:
+            evzzs[u, v] = ev_zz(counts)
+
+        totals.setdefault((u, v), 0)
+        totals[u, v] += sum(counts.values())
+
+    energies = {}
+    uncertainties = {}
+    for u, v in evxs.keys() & evzzs.keys():
+        string_key = f"{u}:{v}"
+        energies[string_key] = u * (evzzs[u, v] - 1) / 4 + v * evxs[u, v]
+
+        uncertainty_xx = 2 * v**2 * (1 + evxxs[u, v]) - u * v * evxs[u, v] / 2
+        uncertainty_zz = u**2 * (1 - evzzs[u, v]) / 2
+
+        uncertainties[string_key] = np.sqrt(
+            (uncertainty_zz + uncertainty_xx - energies[string_key] ** 2) / (totals[u, v] / 2)
+        )
+
+    return energies, uncertainties
+
+
+def _get_energy_diff(
+    bf_energies: dict[str, float],
+    physical_energies: dict[str, float],
+    logical_energies: dict[str, float],
+) -> tuple[list[float], list[float]]:
+    physical_energy_diff = []
+    logical_energy_diff = []
+
+    # Data ordering following `bf_energies` keys
+    for layer in bf_energies.keys():
+        physical_sim_energy = physical_energies[layer]
+        logical_sim_energy = logical_energies[layer]
+        true_energy = bf_energies[layer]
+        u, v = layer.split(":")
+        print(f"Layer=({u}, {v}) has brute-force energy of: {true_energy}")
+        print(f"Physical circuit of layer=({u}, {v}) got an energy of: {physical_sim_energy}")
+        print(f"Logical circuit of layer=({u}, {v}) got an energy of: {logical_sim_energy}")
+        print("-" * 72)
+
+        if logical_sim_energy < physical_sim_energy:
+            print("Logical circuit achieved the lower energy!")
+        else:
+            print("Physical circuit achieved the lower energy")
+        print("-" * 72, "\n")
+
+        physical_energy_diff.append(
+            -1 * (true_energy - physical_sim_energy)
+        )  # Multiply by -1 since negative energies
+        logical_energy_diff.append(-1 * (true_energy - logical_sim_energy))
+    return physical_energy_diff, logical_energy_diff
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [10]:
+
                                                            
+
                                                            
+
                                                            def submit_aim_circuits(
+    circuit_dict: object,
+    *,
+    folder_path: str = "future_aim_results",
+    shots_count: int = 1000,
+    noise_model: cudaq.mlir._mlir_libs._quakeDialects.cudaq_runtime.NoiseModel | None = None,
+    run_async: bool = False,
+) -> dict[str, list[dict[str, int]]] | None:
+    if run_async:
+        os.makedirs(folder_path, exist_ok=True)
+    else:
+        aim_results = {"physical": [], "logical": []}
+
+    for layer in circuit_dict.keys():
+        if run_async:
+            print(f"Posting circuits associated with layer=('{layer}')")
+        else:
+            print(f"Running circuits associated with layer=('{layer}')")
+
+        for basis in ("z_basis", "x_basis"):
+            if run_async:
+                u, v = layer.split(":")
+
+                tmp_physical_results = cudaq.sample_async(
+                    circuit_dict[layer]["physical"][basis], shots_count=shots_count
+                )
+                file = open(f"{folder_path}/physical_{basis}_job_u={u}_v={v}_result.txt", "w")
+                file.write(str(tmp_physical_results))
+                file.close()
+
+                tmp_logical_results = cudaq.sample_async(
+                    circuit_dict[layer]["logical"][basis], shots_count=shots_count
+                )
+                file = open(f"{folder_path}/logical_{basis}_job_u={u}_v={v}_result.txt", "w")
+                file.write(str(tmp_logical_results))
+                file.close()
+            else:
+                tmp_physical_results = cudaq.sample(
+                    circuit_dict[layer]["physical"][basis],
+                    shots_count=shots_count,
+                    noise_model=noise_model,
+                )
+                tmp_logical_results = cudaq.sample(
+                    circuit_dict[layer]["logical"][basis],
+                    shots_count=shots_count,
+                    noise_model=noise_model,
+                )
+                aim_results["physical"].append({k: v for k, v in tmp_physical_results.items()})
+                aim_results["logical"].append({k: v for k, v in tmp_logical_results.items()})
+    if not run_async:
+        print("\nCompleted all circuit sampling!")
+        return aim_results
+    else:
+        print("\nAll circuits submitted for async sampling!")
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [11]:
+
                                                            
+
                                                            
+
                                                            def _get_async_results(
+    layers: object, *, folder_path: str = "future_aim_results"
+) -> dict[str, list[dict[str, int]]]:
+    aim_results = {"physical": [], "logical": []}
+    for layer in layers:
+        print(f"Retrieving all circuits counts associated with layer=('{layer}')")
+        u, v = layer.split(":")
+        for basis in ("z_basis", "x_basis"):
+            file = open(f"{folder_path}/physical_{basis}_job_u={u}_v={v}_result.txt", "r")
+            tmp_physical_results = cudaq.AsyncSampleResult(str(file.read()))
+            physical_counts = tmp_physical_results.get()
+
+            file = open(f"{folder_path}/logical_{basis}_job_u={u}_v={v}_result.txt", "r")
+            tmp_logical_results = cudaq.AsyncSampleResult(str(file.read()))
+            logical_counts = tmp_logical_results.get()
+
+            aim_results["physical"].append({k: v for k, v in physical_counts.items()})
+            aim_results["logical"].append({k: v for k, v in logical_counts.items()})
+
+    print("\nObtained all circuit samples!")
+    return aim_results
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            Running a CUDA-Q noisy simulation
                                                            
+
                                                            In this section, we will first explore the performance of the physical and logical circuits under the influence of a device noise model. This will help us predict experimental results, as well as understand the dominant error sources at play. Such a simulation can be achieved via CUDA-Q’s density matrix simulator:
                                                            
+
                                                            
+
                                                            [12]:
+
                                                            
+
                                                            
+
                                                            cudaq.reset_target()
+cudaq.set_target("density-matrix-cpu")
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [13]:
+
                                                            
+
                                                            
+
                                                            def get_device_noise(
+    depolar_prob_1q: float,
+    depolar_prob_2q: float,
+    *,
+    readout_error_prob: float | None = None,
+    custom_gates: list[str] | None = None,
+) -> cudaq.mlir._mlir_libs._quakeDialects.cudaq_runtime.NoiseModel:
+    noise = cudaq.NoiseModel()
+    depolar_noise = cudaq.DepolarizationChannel(depolar_prob_1q)
+
+    noisy_ops = ["z", "s", "x", "h", "rx", "rz"]
+    for op in noisy_ops:
+        noise.add_all_qubit_channel(op, depolar_noise)
+
+    if custom_gates:
+        custom_depolar_channel = cudaq.DepolarizationChannel(depolar_prob_1q)
+        for op in custom_gates:
+            noise.add_all_qubit_channel(op, custom_depolar_channel)
+
+    # Two qubit depolarization error
+    p_0 = 1 - depolar_prob_2q
+    p_1 = np.sqrt((1 - p_0**2) / 3)
+
+    k0 = np.array(
+        [[p_0, 0.0, 0.0, 0.0], [0.0, p_0, 0.0, 0.0], [0.0, 0.0, p_0, 0.0], [0.0, 0.0, 0.0, p_0]],
+        dtype=np.complex128,
+    )
+    k1 = np.array(
+        [[0.0, 0.0, p_1, 0.0], [0.0, 0.0, 0.0, p_1], [p_1, 0.0, 0.0, 0.0], [0.0, p_1, 0.0, 0.0]],
+        dtype=np.complex128,
+    )
+    k2 = np.array(
+        [
+            [0.0, 0.0, -1j * p_1, 0.0],
+            [0.0, 0.0, 0.0, -1j * p_1],
+            [1j * p_1, 0.0, 0.0, 0.0],
+            [0.0, 1j * p_1, 0.0, 0.0],
+        ],
+        dtype=np.complex128,
+    )
+    k3 = np.array(
+        [[p_1, 0.0, 0.0, 0.0], [0.0, p_1, 0.0, 0.0], [0.0, 0.0, -p_1, 0.0], [0.0, 0.0, 0.0, -p_1]],
+        dtype=np.complex128,
+    )
+    kraus_channel = cudaq.KrausChannel([k0, k1, k2, k3])
+
+    noise.add_all_qubit_channel("cz", kraus_channel)
+    noise.add_all_qubit_channel("cx", kraus_channel)
+
+    if readout_error_prob is not None:
+        # Readout error modeled with a Bit flip channel on identity before measurement
+        bit_flip = cudaq.BitFlipChannel(readout_error_prob)
+        noise.add_all_qubit_channel("meas_id", bit_flip)
+    return noise
+
                                                            
+
                                                            
+
                                                            
+
                                                            Finally, with our example noise model defined above, we can synchronously & noisily sample all of our AIM circuits by passing noise_model=cudaq_noise_model to the workflow containing function submit_aim_circuits():
                                                            
+
                                                            
+
                                                            [14]:
+
                                                            
+
                                                            
+
                                                            # Example parameters that can model execution on hardware at the high, simulation, level:
+# Take single-qubit gate depolarization rate: ~0.2% or better (fidelity ≥99.8%)
+# Take two-qubit gate depolarization rate: ~1–2% (fidelity ~98–99%)
+cudaq_noise_model = get_device_noise(0.002, 0.02, readout_error_prob=0.02)
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [15]:
+
                                                            
+
                                                            
+
                                                            aim_sim_data = submit_aim_circuits(sim_circuit_dict, noise_model=cudaq_noise_model)
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            +Running circuits associated with layer=('1:-9')
+Running circuits associated with layer=('1:-1')
+Running circuits associated with layer=('1:7')
+Running circuits associated with layer=('5:-9')
+Running circuits associated with layer=('5:-1')
+Running circuits associated with layer=('5:7')
+Running circuits associated with layer=('9:-9')
+Running circuits associated with layer=('9:-1')
+Running circuits associated with layer=('9:7')
+
+Completed all circuit sampling!
+
                                                            
+
                                                            
+
                                                            
+
                                                            [16]:
+
                                                            
+
                                                            
+
                                                            data_ordering = []
+for key in circuit_layers:
+    for basis in ("z_basis", "x_basis"):
+        data_ordering.append((key, basis))
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [17]:
+
                                                            
+
                                                            
+
                                                            sim_physical_energies, sim_physical_uncertainties = aim_physical_energies(
+    data_ordering, aim_sim_data["physical"]
+)
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [18]:
+
                                                            
+
                                                            
+
                                                            sim_logical_energies, sim_logical_uncertainties = aim_logical_energies(
+    data_ordering, aim_sim_data["logical"]
+)
+
                                                            
+
                                                            
+
                                                            
+
                                                            To analyze our simulated energy results in the above cells, we will compare them to the brute-force computed exact ground state energies for the AIM Hamiltonian. For simplicity, these are already stored in the dictionary bf_energies below:
                                                            
+
                                                            
+
                                                            [19]:
+
                                                            
+
                                                            
+
                                                            bf_energies = {
+    "1:-9": -18.251736027394713,
+    "1:-1": -2.265564437074638,
+    "1:7": -14.252231964940428,
+    "5:-9": -19.293350575766127,
+    "5:-1": -3.608495283014149,
+    "5:7": -15.305692796870582,
+    "9:-9": -20.39007993367173,
+    "9:-1": -5.260398644698076,
+    "9:7": -16.429650912487233,
+}
+
                                                            
+
                                                            
+
                                                            
+
                                                            With the above metric, we can assess the performance of the logical circuits against the physical circuits by considering how far away the respective energies are from the brute-force expected energies. The cell below computes these energy deviations:
                                                            
+
                                                            
+
                                                            [20]:
+
                                                            
+
                                                            
+
                                                            sim_physical_energy_diff, sim_logical_energy_diff = _get_energy_diff(
+    bf_energies, sim_physical_energies, sim_logical_energies
+)
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            +Layer=(1, -9) has brute-force energy of: -18.251736027394713
+Physical circuit of layer=(1, -9) got an energy of: -15.929
+Logical circuit of layer=(1, -9) got an energy of: -17.46016175277361
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(1, -1) has brute-force energy of: -2.265564437074638
+Physical circuit of layer=(1, -1) got an energy of: -1.97
+Logical circuit of layer=(1, -1) got an energy of: -2.176531948420889
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(1, 7) has brute-force energy of: -14.252231964940428
+Physical circuit of layer=(1, 7) got an energy of: -12.268
+Logical circuit of layer=(1, 7) got an energy of: -13.26321740664324
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(5, -9) has brute-force energy of: -19.293350575766127
+Physical circuit of layer=(5, -9) got an energy of: -16.8495
+Logical circuit of layer=(5, -9) got an energy of: -18.46681284816878
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(5, -1) has brute-force energy of: -3.608495283014149
+Physical circuit of layer=(5, -1) got an energy of: -3.1965000000000003
+Logical circuit of layer=(5, -1) got an energy of: -3.4531715120183297
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(5, 7) has brute-force energy of: -15.305692796870582
+Physical circuit of layer=(5, 7) got an energy of: -13.336
+Logical circuit of layer=(5, 7) got an energy of: -14.341784541550897
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(9, -9) has brute-force energy of: -20.39007993367173
+Physical circuit of layer=(9, -9) got an energy of: -17.802
+Logical circuit of layer=(9, -9) got an energy of: -19.339249509416753
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(9, -1) has brute-force energy of: -5.260398644698076
+Physical circuit of layer=(9, -1) got an energy of: -4.8580000000000005
+Logical circuit of layer=(9, -1) got an energy of: -5.1227150992242025
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(9, 7) has brute-force energy of: -16.429650912487233
+Physical circuit of layer=(9, 7) got an energy of: -14.3635
+Logical circuit of layer=(9, 7) got an energy of: -15.448422736181264
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+
                                                            
+
                                                            
+
                                                            Both physical and logical circuits were subject to the same noise model, but the [[4,2,2]] provides additional information that can help overcome some errors. Visualizing the computed energy differences from the above the cell, our noisy simulation provides a preview of the benefits logical qubits can offer:
                                                            
+
                                                            
+
                                                            [21]:
+
                                                            
+
                                                            
+
                                                            fig, ax = plt.subplots(figsize=(11, 7), dpi=200)
+
+layer_labels = [(int(key.split(":")[0]), int(key.split(":")[1])) for key in bf_energies.keys()]
+plot_labels = [str(item) for item in layer_labels]
+
+plt.errorbar(
+    plot_labels,
+    sim_physical_energy_diff,
+    yerr=sim_physical_uncertainties.values(),
+    ecolor=(20 / 255.0, 26 / 255.0, 94 / 255.0),
+    color=(20 / 255.0, 26 / 255.0, 94 / 255.0),
+    capsize=4,
+    elinewidth=1.5,
+    fmt="o",
+    markersize=8,
+    markeredgewidth=1,
+    label="Physical",
+)
+
+plt.errorbar(
+    plot_labels,
+    sim_logical_energy_diff,
+    yerr=sim_logical_uncertainties.values(),
+    color=(0, 177 / 255.0, 152 / 255.0),
+    ecolor=(0, 177 / 255.0, 152 / 255.0),
+    capsize=4,
+    elinewidth=1.5,
+    fmt="o",
+    markersize=8,
+    markeredgewidth=1,
+    label="Logical",
+)
+
+ax.set_xlabel("Hamiltonian Parameters (U, V)", fontsize=18)
+ax.set_ylabel("Energy above true ground state (in eV)", fontsize=18)
+ax.set_title("CUDA-Q AIM Circuits Simulation (lower is better)", fontsize=20)
+ax.legend(loc="upper right", fontsize=18.5)
+plt.xticks(fontsize=16)
+plt.yticks(fontsize=16)
+
+ax.axhline(y=0, color="black", linestyle="--", linewidth=2)
+plt.ylim(
+    top=max(sim_physical_energy_diff) + max(sim_physical_uncertainties.values()) + 0.2, bottom=-0.2
+)
+plt.tight_layout()
+plt.show()
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+../../_images/applications_python_logical_aim_sqale_38_0.png
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            Running logical AIM on Infleqtion’s hardware
                                                            
+
                                                            The entire workflow we’ve seen thus far can be seamlessly executed on real quantum hardware as well. CUDA-Q has integration with Infleqtion’s gate-based neutral atom quantum computer, Sqale, allowing execution of CUDA-Q kernels on neutral-atom hardware via Infleqtion’s cross-platform Superstaq compiler API that performs low-level compilation and optimization under the hood. Indeed, the AIM research results seen in our
+paper were obtained via this complete end-to-end workflow.
                                                            
+
                                                            To do so, users can obtain a Superstaq API key from superstaq.infleqtion.com to gain access to Infleqtion’s neutral-atom simulator, with pre-registration open for access to Infleqtion’s neutral atom QPU.
                                                            
+
                                                            As a tutorial, let us reproduce the workflow we’ve run so far but on Infleqtion’s QPU. We begin with the same GPU-enhanced VQE to generate the AIM circuits:
                                                            
+
                                                            
+
                                                            [22]:
+
                                                            
+
                                                            
+
                                                            cudaq.reset_target()
+
+if cudaq.num_available_gpus() == 0:
+    cudaq.set_target("qpp-cpu", option="fp64")
+else:
+    cudaq.set_target("nvidia", option="fp64")
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [23]:
+
                                                            
+
                                                            
+
                                                            device_circuit_dict = generate_circuit_set(
+    ignore_meas_id=True
+)  # Setting `ignore_meas_id=True` drops the noisy-identity gate from earlier
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            +Computed optimal angles=[1.5846845738799267, 1.5707961678256028] for U=1, V=-9
+Computed optimal angles=[4.588033710930825, 4.712388365176642] for U=1, V=-1
+Computed optimal angles=[-1.588651490745171, 1.5707962742876598] for U=1, V=7
+Computed optimal angles=[1.64012940802256, 1.5707963354922125] for U=5, V=-9
+Computed optimal angles=[2.1293956916868737, 1.5707963294715355] for U=5, V=-1
+Computed optimal angles=[-1.6598458659836037, 1.570796331040382] for U=5, V=7
+Computed optimal angles=[1.695151467539617, 1.5707960973500679] for U=9, V=-9
+Computed optimal angles=[2.4149519241823376, 1.5707928509325972] for U=9, V=-1
+Computed optimal angles=[-1.7301462945564499, 1.570796044872433] for U=9, V=7
+
+Finished building optimized circuits!
+
                                                            
+
                                                            
+
                                                            And now, we change backends! Before selecting an Infleqtion machine in CUDA-Q, we must first set our Superstaq API key, like so:
                                                            
+
                                                            
+
                                                            [24]:
+
                                                            
+
                                                            
+
                                                            # os.environ['SUPERSTAQ_API_KEY'] = "api_key"
+
                                                            
+
                                                            
+
                                                            
+
                                                            Next, we declare the type of execution we would like on Infleqtion’s machine based on the keyword options specified:
                                                            
+
                                                            
+
                                                            [25]:
+
                                                            
+
                                                            
+
                                                            cudaq.reset_target()
+
+# Set the following to run on Infleqtion's Sqale QPU:
+cudaq.set_target("infleqtion", machine="cq_sqale_qpu")
+
+# Set the following to run an ideal dry-run on Infleqtion's Sqale QPU:
+# cudaq.set_target("infleqtion", machine="cq_sqale_qpu", method="dry-run")
+
+# Set the following to run a device-realistic noisy simulation of Infleqtion's Sqale QPU:
+# cudaq.set_target("infleqtion", machine="cq_sqale_qpu", method="noise-sim")
+
+# Set the following to run a local, ideal emulation:
+# cudaq.set_target("infleqtion", emulate=True)
+
                                                            
+
                                                            
+
                                                            
+
                                                            With that, we’re all set! That simple change instructs our AIM circuits to execute on Infleqtion’s QPU (or simulator). Due to the general queue wait time of running on hardware, we optionally recommend enabling the run_async=True flag to asynchronously sample the circuits. This will allow the cell to be executed and not wait synchronously until all the jobs are complete, allowing other classical code to be run in the meantime. When using run_async, an optional directory to store the job
+information can be specified with folder_path (this will be important to later retrieve the job results from the same directory)
                                                            
+
                                                            
+
                                                            [26]:
+
                                                            
+
                                                            
+
                                                            submit_aim_circuits(
+    device_circuit_dict, folder_path="hardware_aim_future_results", shots_count=1000, run_async=True
+)
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            +Posting circuits associated with layer=('1:-9')
+Posting circuits associated with layer=('1:-1')
+Posting circuits associated with layer=('1:7')
+Posting circuits associated with layer=('5:-9')
+Posting circuits associated with layer=('5:-1')
+Posting circuits associated with layer=('5:7')
+Posting circuits associated with layer=('9:-9')
+Posting circuits associated with layer=('9:-1')
+Posting circuits associated with layer=('9:7')
+
+All circuits submitted for async sampling!
+
                                                            
+
                                                            
+
                                                            With the above cell execution, all the circuits will post to execute on QPU. We can then return at a later time to retrieve the job results with the cell below:
                                                            
+
                                                            
+
                                                            [27]:
+
                                                            
+
                                                            
+
                                                            aim_device_data = _get_async_results(circuit_layers, folder_path="hardware_aim_future_results")
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            +Retrieving all circuits counts associated with layer=('1:-9')
+Retrieving all circuits counts associated with layer=('1:-1')
+Retrieving all circuits counts associated with layer=('1:7')
+Retrieving all circuits counts associated with layer=('5:-9')
+Retrieving all circuits counts associated with layer=('5:-1')
+Retrieving all circuits counts associated with layer=('5:7')
+Retrieving all circuits counts associated with layer=('9:-9')
+Retrieving all circuits counts associated with layer=('9:-1')
+Retrieving all circuits counts associated with layer=('9:7')
+
+Obtained all circuit samples!
+
                                                            
+
                                                            
+
                                                            
+
                                                            [28]:
+
                                                            
+
                                                            
+
                                                            physical_energies, physical_uncertainties = aim_physical_energies(
+    data_ordering, aim_device_data["physical"]
+)
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [29]:
+
                                                            
+
                                                            
+
                                                            logical_energies, logical_uncertainties = aim_logical_energies(
+    data_ordering, aim_device_data["logical"]
+)
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            [30]:
+
                                                            
+
                                                            
+
                                                            physical_energy_diff, logical_energy_diff = _get_energy_diff(
+    bf_energies, physical_energies, logical_energies
+)
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            +Layer=(1, -9) has brute-force energy of: -18.251736027394713
+Physical circuit of layer=(1, -9) got an energy of: -17.626499999999997
+Logical circuit of layer=(1, -9) got an energy of: -17.69666562801761
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(1, -1) has brute-force energy of: -2.265564437074638
+Physical circuit of layer=(1, -1) got an energy of: -2.1415
+Logical circuit of layer=(1, -1) got an energy of: -2.2032104443266585
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(1, 7) has brute-force energy of: -14.252231964940428
+Physical circuit of layer=(1, 7) got an energy of: -12.9955
+Logical circuit of layer=(1, 7) got an energy of: -13.76919450035401
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(5, -9) has brute-force energy of: -19.293350575766127
+Physical circuit of layer=(5, -9) got an energy of: -18.331
+Logical circuit of layer=(5, -9) got an energy of: -18.85730052910377
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(5, -1) has brute-force energy of: -3.608495283014149
+Physical circuit of layer=(5, -1) got an energy of: -3.476
+Logical circuit of layer=(5, -1) got an energy of: -3.5425689231532203
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(5, 7) has brute-force energy of: -15.305692796870582
+Physical circuit of layer=(5, 7) got an energy of: -14.043500000000002
+Logical circuit of layer=(5, 7) got an energy of: -14.795918428433312
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(9, -9) has brute-force energy of: -20.39007993367173
+Physical circuit of layer=(9, -9) got an energy of: -19.4715
+Logical circuit of layer=(9, -9) got an energy of: -19.96524696701215
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(9, -1) has brute-force energy of: -5.260398644698076
+Physical circuit of layer=(9, -1) got an energy of: -4.973
+Logical circuit of layer=(9, -1) got an energy of: -5.207315773582224
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+Layer=(9, 7) has brute-force energy of: -16.429650912487233
+Physical circuit of layer=(9, 7) got an energy of: -15.182
+Logical circuit of layer=(9, 7) got an energy of: -16.241375689575516
+------------------------------------------------------------------------
+Logical circuit achieved the lower energy!
+------------------------------------------------------------------------
+
+
                                                            
+
                                                            
+
                                                            As before, we use the same metric of comparing against the true ground state energies; however, this time, both the physical and logical circuits are fully exposed to real hardware noise. Yet, we expect the use of logical qubits afforded to us by the [[4,2,2]] code to achieve energies closer to the true ground state than the bare physical circuits (up to a certain error threshold). And indeed they do! Visually, we can plot the energy deviations of both the physical and logical circuits from
+the cell above and observe that the logical circuits are able to outperform the physical circuits by obtaining much lower energies, demonstrating the power of error detection and the beginning possibilities of fault-tolerant quantum computation:
                                                            
+
                                                            
+
                                                            [31]:
+
                                                            
+
                                                            
+
                                                            fig, ax = plt.subplots(figsize=(11, 7), dpi=200)
+
+plt.errorbar(
+    plot_labels,
+    physical_energy_diff,
+    yerr=physical_uncertainties.values(),
+    ecolor=(20 / 255.0, 26 / 255.0, 94 / 255.0),
+    color=(20 / 255.0, 26 / 255.0, 94 / 255.0),
+    capsize=4,
+    elinewidth=1.5,
+    fmt="o",
+    markersize=8,
+    markeredgewidth=1,
+    label="Physical",
+)
+plt.errorbar(
+    plot_labels,
+    logical_energy_diff,
+    yerr=logical_uncertainties.values(),
+    color=(0, 177 / 255.0, 152 / 255.0),
+    ecolor=(0, 177 / 255.0, 152 / 255.0),
+    capsize=4,
+    elinewidth=1.5,
+    fmt="o",
+    markersize=8,
+    markeredgewidth=1,
+    label="Logical",
+)
+
+ax.set_xlabel("Hamiltonian Parameters (U, V)", fontsize=18)
+ax.set_ylabel("Energy above true ground state (in eV)", fontsize=18)
+ax.set_title("CUDA-Q AIM Infleqtion Hardware Execution (lower is better)", fontsize=20)
+ax.legend(loc="upper left", fontsize=18.5)
+plt.xticks(fontsize=16)
+plt.yticks(fontsize=16)
+
+ax.axhline(y=0, color="black", linestyle="--", linewidth=2)
+plt.ylim(top=max(physical_energy_diff) + max(physical_uncertainties.values()) + 0.2, bottom=-0.2)
+plt.tight_layout()
+plt.show()
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+../../_images/applications_python_logical_aim_sqale_56_0.png
+
                                                            
+
                                                            
+
                                                            
+
                                                            
+
+
+           
                                                            
+          
                                                            
+          
+        
                                                            
+      
                                                            
+    
                                                            
+  
                                                            
+    
+
+  
+  
+
+
+
\ No newline at end of file
diff --git a/pr-2458/applications/python/logical_aim_sqale.ipynb b/pr-2458/applications/python/logical_aim_sqale.ipynb
new file mode 100644
index 0000000000..f51bd10294
--- /dev/null
+++ b/pr-2458/applications/python/logical_aim_sqale.ipynb
@@ -0,0 +1,1356 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Anderson Impurity Model ground state solver on Infleqtion's Sqale"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Ground state quantum chemistry—computing total energies of molecular configurations to within chemical accuracy—is perhaps the most highly-touted industrial application of fault-tolerant quantum computers. Strongly correlated materials, for example, are particularly interesting, and tools like dynamical mean-field theory (DMFT) allow one to account for the effect of their strong, localized electronic correlations. These DMFT models help predict material properties by approximating the system as a single site impurity inside a “bath” that encompasses the rest of the system. Simulating such dynamics can be a tough task using classical methods, but can be done efficiently on a quantum computer via quantum simulation.\n",
+    "\n",
+    "In this notebook, we showcase a workflow for preparing the ground state of the minimal single-impurity Anderson model (SIAM) using the Hamiltonian Variational Ansatz for a range of realistic parameters. As a first step towards running DMFT on a fault-tolerant quantum computer, we will use logical qubits encoded in the `[[4, 2, 2]]` code. Using this workflow, we will obtain the ground state energy estimates via noisy simulation, and then also execute the corresponding optimized circuits on Infleqtion's gate-based neutral-atom quantum computer, making the benefits of logical qubits apparent. More details can be found in our [paper](https://arxiv.org/abs/2412.07670)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This demo notebook uses CUDA-Q (`cudaq`) and a CUDA-QX library, `cudaq-solvers`; let us first begin by importing (and installing as needed) these packages:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "try:\n",
+    "    import cudaq_solvers as solvers\n",
+    "    import cudaq\n",
+    "    import matplotlib.pyplot as plt\n",
+    "except ImportError:\n",
+    "    print(\"Installing required packages...\")\n",
+    "    %pip install --quiet 'cudaq-solvers' 'matplotlib'\n",
+    "    print(\"Installed `cudaq`, `cudaq-solvers`, and `matplotlib` packages.\")\n",
+    "    print(\"You may need to restart the kernel to import newly installed packages.\")\n",
+    "    import cudaq_solvers as solvers\n",
+    "    import cudaq\n",
+    "    import matplotlib.pyplot as plt\n",
+    "\n",
+    "from collections.abc import Mapping, Sequence\n",
+    "import numpy as np\n",
+    "from scipy.optimize import minimize\n",
+    "import os"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Performing logical Variational Quantum Eigensolver (VQE) with CUDA-QX"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To prepare our ground state quantum Anderson impurity model circuits (referred to as AIM circuits in this notebook for short), we use VQE to train an ansatz to minimize a Hamiltonian and obtain optimal angles that can be used to set the AIM circuits. As described in our [paper](https://arxiv.org/abs/2412.07670), the associated restricted Hamiltonian for our SIAM can be reduced to,\n",
+    "$$  \n",
+    "\\begin{equation}\n",
+    "H_{(U, V)} = U (Z_0 Z_2 - 1) / 4 + V (X_0 + X_2),\n",
+    "\\end{equation}\n",
+    "$$\n",
+    "where $U$ is the Coulomb interaction and $V$ the hybridization strength. In this notebook workflow, we will optimize over a 2-dimensional grid of Hamiltonian parameter values, namely $U\\in \\{1, 5, 9\\}$ and $V\\in \\{-9, -1, 7\\}$ (with all values assumed to be in units of eV), to ensure that the ansatz is generally trainable and expressive, and obtain 9 different circuit layers identified by the key $(U, V)$. We will simulate the VQE on GPU (or optionally on CPU if you do not have GPU access), enabled by CUDA-Q, in the absence of noise:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "if cudaq.num_available_gpus() == 0:\n",
+    "    cudaq.set_target(\"qpp-cpu\", option=\"fp64\")\n",
+    "else:\n",
+    "    cudaq.set_target(\"nvidia\", option=\"fp64\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This workflow can be easily defined in CUDA-Q as shown in the cell below, using the CUDA-QX Solvers library (which accelerates quantum algorithms like the VQE):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def ansatz(n_qubits: int) -> cudaq.Kernel:\n",
+    "    # Create a CUDA-Q parameterized kernel\n",
+    "    paramterized_ansatz, variational_angles = cudaq.make_kernel(list)\n",
+    "    qubits = paramterized_ansatz.qalloc(n_qubits)\n",
+    "\n",
+    "    # Using |+> as the initial state:\n",
+    "    paramterized_ansatz.h(qubits[0])\n",
+    "    paramterized_ansatz.cx(qubits[0], qubits[1])\n",
+    "\n",
+    "    paramterized_ansatz.rx(variational_angles[0], qubits[0])\n",
+    "    paramterized_ansatz.cx(qubits[0], qubits[1])\n",
+    "    paramterized_ansatz.rz(variational_angles[1], qubits[1])\n",
+    "    paramterized_ansatz.cx(qubits[0], qubits[1])\n",
+    "    return paramterized_ansatz\n",
+    "\n",
+    "\n",
+    "def run_logical_vqe(cudaq_hamiltonian: cudaq.SpinOperator) -> tuple[float, list[float]]:\n",
+    "    # Set seed for easier reproduction\n",
+    "    np.random.seed(42)\n",
+    "\n",
+    "    # Initial angles for the optimizer\n",
+    "    init_angles = np.random.random(2) * 1e-1\n",
+    "\n",
+    "    # Obtain CUDA-Q Ansatz\n",
+    "    num_qubits = cudaq_hamiltonian.get_qubit_count()\n",
+    "    variational_kernel = ansatz(num_qubits)\n",
+    "\n",
+    "    # Perform VQE optimization\n",
+    "    energy, params, _ = solvers.vqe(\n",
+    "        variational_kernel,\n",
+    "        cudaq_hamiltonian,\n",
+    "        init_angles,\n",
+    "        optimizer=minimize,\n",
+    "        method=\"SLSQP\",\n",
+    "        tol=1e-10,\n",
+    "    )\n",
+    "    return energy, params"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Constructing circuits in the `[[4,2,2]]` encoding"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The `[[4,2,2]]` code is a quantum error detection code that uses four physical qubits to encode two logical qubits. In this notebook, we will construct two variants of quantum circuits: physical (bare, unencoded) and logical (encoded). These circuits will be informed by the Hamiltonian Variational Ansatz described earlier. To measure all the terms in our Hamiltonian, we will measure the data qubits in both the $Z$- and $X$-basis, as allowed by the `[[4,2,2]]` logical gateset. Full details on the circuit constructions are outlined in our [paper](https://arxiv.org/abs/2412.07670)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Below, we create functions to build our CUDA-Q AIM circuits, both physical and logical versions. As we consider noisy simulation in this notebook, we will include some noisy gates. Here, for simplicity, we will just register a custom identity gate -- to be later used as a noisy operation to model readout error: "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cudaq.register_operation(\"meas_id\", np.identity(2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def aim_physical_circuit(\n",
+    "    angles: list[float], basis: str, *, ignore_meas_id: bool = False\n",
+    ") -> cudaq.Kernel:\n",
+    "    kernel = cudaq.make_kernel()\n",
+    "    qubits = kernel.qalloc(2)\n",
+    "\n",
+    "    # Bell state prep\n",
+    "    kernel.h(qubits[0])\n",
+    "    kernel.cx(qubits[0], qubits[1])\n",
+    "\n",
+    "    # Rx Gate\n",
+    "    kernel.rx(angles[0], qubits[0])\n",
+    "\n",
+    "    # ZZ rotation\n",
+    "    kernel.cx(qubits[0], qubits[1])\n",
+    "    kernel.rz(angles[1], qubits[1])\n",
+    "    kernel.cx(qubits[0], qubits[1])\n",
+    "\n",
+    "    if basis == \"z_basis\":\n",
+    "        if not ignore_meas_id:\n",
+    "            kernel.for_loop(\n",
+    "                start=0, stop=2, function=lambda q_idx: getattr(kernel, \"meas_id\")(qubits[q_idx])\n",
+    "            )\n",
+    "        kernel.mz(qubits)\n",
+    "    elif basis == \"x_basis\":\n",
+    "        kernel.h(qubits)\n",
+    "        if not ignore_meas_id:\n",
+    "            kernel.for_loop(\n",
+    "                start=0, stop=2, function=lambda q_idx: getattr(kernel, \"meas_id\")(qubits[q_idx])\n",
+    "            )\n",
+    "        kernel.mz(qubits)\n",
+    "    else:\n",
+    "        raise ValueError(\"Unsupported basis provided:\", basis)\n",
+    "    return kernel"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def aim_logical_circuit(\n",
+    "    angles: list[float], basis: str, *, ignore_meas_id: bool = False\n",
+    ") -> cudaq.Kernel:\n",
+    "    kernel = cudaq.make_kernel()\n",
+    "    qubits = kernel.qalloc(6)\n",
+    "\n",
+    "    kernel.for_loop(start=0, stop=3, function=lambda idx: kernel.h(qubits[idx]))\n",
+    "    kernel.cx(qubits[1], qubits[4])\n",
+    "    kernel.cx(qubits[2], qubits[3])\n",
+    "    kernel.cx(qubits[0], qubits[1])\n",
+    "    kernel.cx(qubits[0], qubits[3])\n",
+    "\n",
+    "    # Rx teleportation\n",
+    "    kernel.rx(angles[0], qubits[0])\n",
+    "\n",
+    "    kernel.cx(qubits[0], qubits[1])\n",
+    "    kernel.cx(qubits[0], qubits[3])\n",
+    "    kernel.h(qubits[0])\n",
+    "\n",
+    "    if basis == \"z_basis\":\n",
+    "        if not ignore_meas_id:\n",
+    "            kernel.for_loop(\n",
+    "                start=0, stop=5, function=lambda idx: getattr(kernel, \"meas_id\")(qubits[idx])\n",
+    "            )\n",
+    "        kernel.mz(qubits)\n",
+    "    elif basis == \"x_basis\":\n",
+    "        # ZZ rotation and teleportation\n",
+    "        kernel.cx(qubits[3], qubits[5])\n",
+    "        kernel.cx(qubits[2], qubits[5])\n",
+    "        kernel.rz(angles[1], qubits[5])\n",
+    "        kernel.cx(qubits[1], qubits[5])\n",
+    "        kernel.cx(qubits[4], qubits[5])\n",
+    "        kernel.for_loop(start=1, stop=5, function=lambda idx: kernel.h(qubits[idx]))\n",
+    "        if not ignore_meas_id:\n",
+    "            kernel.for_loop(\n",
+    "                start=0, stop=6, function=lambda idx: getattr(kernel, \"meas_id\")(qubits[idx])\n",
+    "            )\n",
+    "        kernel.mz(qubits)\n",
+    "    else:\n",
+    "        raise ValueError(\"Unsupported basis provided:\", basis)\n",
+    "    return kernel"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "With the circuit definitions above, we can now define a function that automatically runs the VQE and constructs a dictionary containing all the AIM circuits we want to submit to hardware (or noisily simulate):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def generate_circuit_set(ignore_meas_id: bool = False) -> object:\n",
+    "    u_vals = [1, 5, 9]\n",
+    "    v_vals = [-9, -1, 7]\n",
+    "    circuit_dict = {}\n",
+    "    for u in u_vals:\n",
+    "        for v in v_vals:\n",
+    "            qubit_hamiltonian = (\n",
+    "                0.25 * u * cudaq.spin.z(0) * cudaq.spin.z(1)\n",
+    "                - 0.25 * u\n",
+    "                + v * cudaq.spin.x(0)\n",
+    "                + v * cudaq.spin.x(1)\n",
+    "            )\n",
+    "            _, opt_params = run_logical_vqe(qubit_hamiltonian)\n",
+    "            angles = [float(angle) for angle in opt_params]\n",
+    "            print(f\"Computed optimal angles={angles} for U={u}, V={v}\")\n",
+    "\n",
+    "            tmp_physical_dict = {}\n",
+    "            tmp_logical_dict = {}\n",
+    "            for basis in (\"z_basis\", \"x_basis\"):\n",
+    "                tmp_physical_dict[basis] = aim_physical_circuit(\n",
+    "                    angles, basis, ignore_meas_id=ignore_meas_id\n",
+    "                )\n",
+    "                tmp_logical_dict[basis] = aim_logical_circuit(\n",
+    "                    angles, basis, ignore_meas_id=ignore_meas_id\n",
+    "                )\n",
+    "\n",
+    "            circuit_dict[f\"{u}:{v}\"] = {\n",
+    "                \"physical\": tmp_physical_dict,\n",
+    "                \"logical\": tmp_logical_dict,\n",
+    "            }\n",
+    "    print(\"\\nFinished building optimized circuits!\")\n",
+    "    return circuit_dict"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Computed optimal angles=[1.5846845738799267, 1.5707961678256028] for U=1, V=-9\n",
+      "Computed optimal angles=[4.588033710930825, 4.712388365176642] for U=1, V=-1\n",
+      "Computed optimal angles=[-1.588651490745171, 1.5707962742876598] for U=1, V=7\n",
+      "Computed optimal angles=[1.64012940802256, 1.5707963354922125] for U=5, V=-9\n",
+      "Computed optimal angles=[2.1293956916868737, 1.5707963294715355] for U=5, V=-1\n",
+      "Computed optimal angles=[-1.6598458659836037, 1.570796331040382] for U=5, V=7\n",
+      "Computed optimal angles=[1.695151467539617, 1.5707960973500679] for U=9, V=-9\n",
+      "Computed optimal angles=[2.4149519241823376, 1.5707928509325972] for U=9, V=-1\n",
+      "Computed optimal angles=[-1.7301462729177735, 1.570796033796985] for U=9, V=7\n",
+      "\n",
+      "Finished building optimized circuits!\n"
+     ]
+    }
+   ],
+   "source": [
+    "sim_circuit_dict = generate_circuit_set()\n",
+    "circuit_layers = sim_circuit_dict.keys()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Setting up submission and decoding workflow "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this section, we define various helper functions that will play a role in generating the associated energies of the AIM circuits based on the circuit samples (in the different bases), as well as decode the logical circuits with post-selection informed by the `[[4,2,2]]` code:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def _num_qubits(counts: Mapping[str, float]) -> int:\n",
+    "    for key in counts:\n",
+    "        if key.isdecimal():\n",
+    "            return len(key)\n",
+    "    return 0\n",
+    "\n",
+    "\n",
+    "def process_counts(\n",
+    "    counts: Mapping[str, float],\n",
+    "    data_qubits: Sequence[int],\n",
+    "    flag_qubits: Sequence[int] = (),\n",
+    ") -> dict[str, float]:\n",
+    "    new_data: dict[str, float] = {}\n",
+    "    for key, val in counts.items():\n",
+    "        if not all(key[i] == \"0\" for i in flag_qubits):\n",
+    "            continue\n",
+    "\n",
+    "        new_key = \"\".join(key[i] for i in data_qubits)\n",
+    "\n",
+    "        if not set(\"01\").issuperset(new_key):\n",
+    "            continue\n",
+    "\n",
+    "        new_data.setdefault(new_key, 0)\n",
+    "        new_data[new_key] += val\n",
+    "\n",
+    "    return new_data\n",
+    "\n",
+    "\n",
+    "def decode(counts: Mapping[str, float]) -> dict[str, float]:\n",
+    "    \"\"\"Decode physical counts into logical counts. Should be called after `process_counts`.\"\"\"\n",
+    "\n",
+    "    if not counts:\n",
+    "        return {}\n",
+    "\n",
+    "    num_qubits = _num_qubits(counts)\n",
+    "    assert num_qubits % 4 == 0\n",
+    "\n",
+    "    physical_to_logical = {\n",
+    "        \"0000\": \"00\",\n",
+    "        \"1111\": \"00\",\n",
+    "        \"0011\": \"01\",\n",
+    "        \"1100\": \"01\",\n",
+    "        \"0101\": \"10\",\n",
+    "        \"1010\": \"10\",\n",
+    "        \"0110\": \"11\",\n",
+    "        \"1001\": \"11\",\n",
+    "    }\n",
+    "\n",
+    "    new_data: dict[str, float] = {}\n",
+    "    for key, val in counts.items():\n",
+    "        physical_keys = [key[i : i + 4] for i in range(0, num_qubits, 4)]\n",
+    "        logical_keys = [physical_to_logical.get(physical_key) for physical_key in physical_keys]\n",
+    "        if None not in logical_keys:\n",
+    "            new_key = \"\".join(logical_keys)\n",
+    "            new_data.setdefault(new_key, 0)\n",
+    "            new_data[new_key] += val\n",
+    "\n",
+    "    return new_data\n",
+    "\n",
+    "\n",
+    "def ev_x(counts: Mapping[str, float]) -> float:\n",
+    "    ev = 0.0\n",
+    "\n",
+    "    for k, val in counts.items():\n",
+    "        ev += val * ((-1) ** int(k[0]) + (-1) ** int(k[1]))\n",
+    "\n",
+    "    total = sum(counts.values())\n",
+    "    ev /= total\n",
+    "    return ev\n",
+    "\n",
+    "\n",
+    "def ev_xx(counts: Mapping[str, float]) -> float:\n",
+    "    ev = 0.0\n",
+    "\n",
+    "    for k, val in counts.items():\n",
+    "        ev += val * (-1) ** k.count(\"1\")\n",
+    "\n",
+    "    total = sum(counts.values())\n",
+    "    ev /= total\n",
+    "    return ev\n",
+    "\n",
+    "\n",
+    "def ev_zz(counts: Mapping[str, float]) -> float:\n",
+    "    ev = 0.0\n",
+    "\n",
+    "    for k, val in counts.items():\n",
+    "        ev += val * (-1) ** k.count(\"1\")\n",
+    "\n",
+    "    total = sum(counts.values())\n",
+    "    ev /= total\n",
+    "    return ev\n",
+    "\n",
+    "\n",
+    "def aim_logical_energies(\n",
+    "    data_ordering: object, counts_list: Sequence[dict[str, float]]\n",
+    ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n",
+    "    counts_data = {\n",
+    "        data_ordering[i]: decode(\n",
+    "            process_counts(\n",
+    "                counts,\n",
+    "                data_qubits=[1, 2, 3, 4],\n",
+    "                flag_qubits=[0, 5],\n",
+    "            )\n",
+    "        )\n",
+    "        for i, counts in enumerate(counts_list)\n",
+    "    }\n",
+    "    return _aim_energies(counts_data)\n",
+    "\n",
+    "\n",
+    "def aim_physical_energies(\n",
+    "    data_ordering: object, counts_list: Sequence[dict[str, float]]\n",
+    ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n",
+    "    counts_data = {\n",
+    "        data_ordering[i]: process_counts(\n",
+    "            counts,\n",
+    "            data_qubits=[0, 1],\n",
+    "        )\n",
+    "        for i, counts in enumerate(counts_list)\n",
+    "    }\n",
+    "    return _aim_energies(counts_data)\n",
+    "\n",
+    "\n",
+    "def _aim_energies(\n",
+    "    counts_data: Mapping[tuple[int, int, str], dict[str, float]],\n",
+    ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n",
+    "    evxs: dict[tuple[int, int], float] = {}\n",
+    "    evxxs: dict[tuple[int, int], float] = {}\n",
+    "    evzzs: dict[tuple[int, int], float] = {}\n",
+    "    totals: dict[tuple[int, int], float] = {}\n",
+    "\n",
+    "    for key, counts in counts_data.items():\n",
+    "        h_params, basis = key\n",
+    "        key_a, key_b = h_params.split(\":\")\n",
+    "        u, v = int(key_a), int(key_b)\n",
+    "        if basis.startswith(\"x\"):\n",
+    "            evxs[u, v] = ev_x(counts)\n",
+    "            evxxs[u, v] = ev_xx(counts)\n",
+    "        else:\n",
+    "            evzzs[u, v] = ev_zz(counts)\n",
+    "\n",
+    "        totals.setdefault((u, v), 0)\n",
+    "        totals[u, v] += sum(counts.values())\n",
+    "\n",
+    "    energies = {}\n",
+    "    uncertainties = {}\n",
+    "    for u, v in evxs.keys() & evzzs.keys():\n",
+    "        string_key = f\"{u}:{v}\"\n",
+    "        energies[string_key] = u * (evzzs[u, v] - 1) / 4 + v * evxs[u, v]\n",
+    "\n",
+    "        uncertainty_xx = 2 * v**2 * (1 + evxxs[u, v]) - u * v * evxs[u, v] / 2\n",
+    "        uncertainty_zz = u**2 * (1 - evzzs[u, v]) / 2\n",
+    "\n",
+    "        uncertainties[string_key] = np.sqrt(\n",
+    "            (uncertainty_zz + uncertainty_xx - energies[string_key] ** 2) / (totals[u, v] / 2)\n",
+    "        )\n",
+    "\n",
+    "    return energies, uncertainties\n",
+    "\n",
+    "\n",
+    "def _get_energy_diff(\n",
+    "    bf_energies: dict[str, float],\n",
+    "    physical_energies: dict[str, float],\n",
+    "    logical_energies: dict[str, float],\n",
+    ") -> tuple[list[float], list[float]]:\n",
+    "    physical_energy_diff = []\n",
+    "    logical_energy_diff = []\n",
+    "\n",
+    "    # Data ordering following `bf_energies` keys\n",
+    "    for layer in bf_energies.keys():\n",
+    "        physical_sim_energy = physical_energies[layer]\n",
+    "        logical_sim_energy = logical_energies[layer]\n",
+    "        true_energy = bf_energies[layer]\n",
+    "        u, v = layer.split(\":\")\n",
+    "        print(f\"Layer=({u}, {v}) has brute-force energy of: {true_energy}\")\n",
+    "        print(f\"Physical circuit of layer=({u}, {v}) got an energy of: {physical_sim_energy}\")\n",
+    "        print(f\"Logical circuit of layer=({u}, {v}) got an energy of: {logical_sim_energy}\")\n",
+    "        print(\"-\" * 72)\n",
+    "\n",
+    "        if logical_sim_energy < physical_sim_energy:\n",
+    "            print(\"Logical circuit achieved the lower energy!\")\n",
+    "        else:\n",
+    "            print(\"Physical circuit achieved the lower energy\")\n",
+    "        print(\"-\" * 72, \"\\n\")\n",
+    "\n",
+    "        physical_energy_diff.append(\n",
+    "            -1 * (true_energy - physical_sim_energy)\n",
+    "        )  # Multiply by -1 since negative energies\n",
+    "        logical_energy_diff.append(-1 * (true_energy - logical_sim_energy))\n",
+    "    return physical_energy_diff, logical_energy_diff"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def submit_aim_circuits(\n",
+    "    circuit_dict: object,\n",
+    "    *,\n",
+    "    folder_path: str = \"future_aim_results\",\n",
+    "    shots_count: int = 1000,\n",
+    "    noise_model: cudaq.mlir._mlir_libs._quakeDialects.cudaq_runtime.NoiseModel | None = None,\n",
+    "    run_async: bool = False,\n",
+    ") -> dict[str, list[dict[str, int]]] | None:\n",
+    "    if run_async:\n",
+    "        os.makedirs(folder_path, exist_ok=True)\n",
+    "    else:\n",
+    "        aim_results = {\"physical\": [], \"logical\": []}\n",
+    "\n",
+    "    for layer in circuit_dict.keys():\n",
+    "        if run_async:\n",
+    "            print(f\"Posting circuits associated with layer=('{layer}')\")\n",
+    "        else:\n",
+    "            print(f\"Running circuits associated with layer=('{layer}')\")\n",
+    "\n",
+    "        for basis in (\"z_basis\", \"x_basis\"):\n",
+    "            if run_async:\n",
+    "                u, v = layer.split(\":\")\n",
+    "\n",
+    "                tmp_physical_results = cudaq.sample_async(\n",
+    "                    circuit_dict[layer][\"physical\"][basis], shots_count=shots_count\n",
+    "                )\n",
+    "                file = open(f\"{folder_path}/physical_{basis}_job_u={u}_v={v}_result.txt\", \"w\")\n",
+    "                file.write(str(tmp_physical_results))\n",
+    "                file.close()\n",
+    "\n",
+    "                tmp_logical_results = cudaq.sample_async(\n",
+    "                    circuit_dict[layer][\"logical\"][basis], shots_count=shots_count\n",
+    "                )\n",
+    "                file = open(f\"{folder_path}/logical_{basis}_job_u={u}_v={v}_result.txt\", \"w\")\n",
+    "                file.write(str(tmp_logical_results))\n",
+    "                file.close()\n",
+    "            else:\n",
+    "                tmp_physical_results = cudaq.sample(\n",
+    "                    circuit_dict[layer][\"physical\"][basis],\n",
+    "                    shots_count=shots_count,\n",
+    "                    noise_model=noise_model,\n",
+    "                )\n",
+    "                tmp_logical_results = cudaq.sample(\n",
+    "                    circuit_dict[layer][\"logical\"][basis],\n",
+    "                    shots_count=shots_count,\n",
+    "                    noise_model=noise_model,\n",
+    "                )\n",
+    "                aim_results[\"physical\"].append({k: v for k, v in tmp_physical_results.items()})\n",
+    "                aim_results[\"logical\"].append({k: v for k, v in tmp_logical_results.items()})\n",
+    "    if not run_async:\n",
+    "        print(\"\\nCompleted all circuit sampling!\")\n",
+    "        return aim_results\n",
+    "    else:\n",
+    "        print(\"\\nAll circuits submitted for async sampling!\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def _get_async_results(\n",
+    "    layers: object, *, folder_path: str = \"future_aim_results\"\n",
+    ") -> dict[str, list[dict[str, int]]]:\n",
+    "    aim_results = {\"physical\": [], \"logical\": []}\n",
+    "    for layer in layers:\n",
+    "        print(f\"Retrieving all circuits counts associated with layer=('{layer}')\")\n",
+    "        u, v = layer.split(\":\")\n",
+    "        for basis in (\"z_basis\", \"x_basis\"):\n",
+    "            file = open(f\"{folder_path}/physical_{basis}_job_u={u}_v={v}_result.txt\", \"r\")\n",
+    "            tmp_physical_results = cudaq.AsyncSampleResult(str(file.read()))\n",
+    "            physical_counts = tmp_physical_results.get()\n",
+    "\n",
+    "            file = open(f\"{folder_path}/logical_{basis}_job_u={u}_v={v}_result.txt\", \"r\")\n",
+    "            tmp_logical_results = cudaq.AsyncSampleResult(str(file.read()))\n",
+    "            logical_counts = tmp_logical_results.get()\n",
+    "\n",
+    "            aim_results[\"physical\"].append({k: v for k, v in physical_counts.items()})\n",
+    "            aim_results[\"logical\"].append({k: v for k, v in logical_counts.items()})\n",
+    "\n",
+    "    print(\"\\nObtained all circuit samples!\")\n",
+    "    return aim_results"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Running a CUDA-Q noisy simulation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this section, we will first explore the performance of the physical and logical circuits under the influence of a device noise model. This will help us predict experimental results, as well as understand the dominant error sources at play. Such a simulation can be achieved via CUDA-Q's density matrix simulator: "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cudaq.reset_target()\n",
+    "cudaq.set_target(\"density-matrix-cpu\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_device_noise(\n",
+    "    depolar_prob_1q: float,\n",
+    "    depolar_prob_2q: float,\n",
+    "    *,\n",
+    "    readout_error_prob: float | None = None,\n",
+    "    custom_gates: list[str] | None = None,\n",
+    ") -> cudaq.mlir._mlir_libs._quakeDialects.cudaq_runtime.NoiseModel:\n",
+    "    noise = cudaq.NoiseModel()\n",
+    "    depolar_noise = cudaq.DepolarizationChannel(depolar_prob_1q)\n",
+    "\n",
+    "    noisy_ops = [\"z\", \"s\", \"x\", \"h\", \"rx\", \"rz\"]\n",
+    "    for op in noisy_ops:\n",
+    "        noise.add_all_qubit_channel(op, depolar_noise)\n",
+    "\n",
+    "    if custom_gates:\n",
+    "        custom_depolar_channel = cudaq.DepolarizationChannel(depolar_prob_1q)\n",
+    "        for op in custom_gates:\n",
+    "            noise.add_all_qubit_channel(op, custom_depolar_channel)\n",
+    "\n",
+    "    # Two qubit depolarization error\n",
+    "    p_0 = 1 - depolar_prob_2q\n",
+    "    p_1 = np.sqrt((1 - p_0**2) / 3)\n",
+    "\n",
+    "    k0 = np.array(\n",
+    "        [[p_0, 0.0, 0.0, 0.0], [0.0, p_0, 0.0, 0.0], [0.0, 0.0, p_0, 0.0], [0.0, 0.0, 0.0, p_0]],\n",
+    "        dtype=np.complex128,\n",
+    "    )\n",
+    "    k1 = np.array(\n",
+    "        [[0.0, 0.0, p_1, 0.0], [0.0, 0.0, 0.0, p_1], [p_1, 0.0, 0.0, 0.0], [0.0, p_1, 0.0, 0.0]],\n",
+    "        dtype=np.complex128,\n",
+    "    )\n",
+    "    k2 = np.array(\n",
+    "        [\n",
+    "            [0.0, 0.0, -1j * p_1, 0.0],\n",
+    "            [0.0, 0.0, 0.0, -1j * p_1],\n",
+    "            [1j * p_1, 0.0, 0.0, 0.0],\n",
+    "            [0.0, 1j * p_1, 0.0, 0.0],\n",
+    "        ],\n",
+    "        dtype=np.complex128,\n",
+    "    )\n",
+    "    k3 = np.array(\n",
+    "        [[p_1, 0.0, 0.0, 0.0], [0.0, p_1, 0.0, 0.0], [0.0, 0.0, -p_1, 0.0], [0.0, 0.0, 0.0, -p_1]],\n",
+    "        dtype=np.complex128,\n",
+    "    )\n",
+    "    kraus_channel = cudaq.KrausChannel([k0, k1, k2, k3])\n",
+    "\n",
+    "    noise.add_all_qubit_channel(\"cz\", kraus_channel)\n",
+    "    noise.add_all_qubit_channel(\"cx\", kraus_channel)\n",
+    "\n",
+    "    if readout_error_prob is not None:\n",
+    "        # Readout error modeled with a Bit flip channel on identity before measurement\n",
+    "        bit_flip = cudaq.BitFlipChannel(readout_error_prob)\n",
+    "        noise.add_all_qubit_channel(\"meas_id\", bit_flip)\n",
+    "    return noise"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Finally, with our example noise model defined above, we can synchronously & noisily sample all of our AIM circuits by passing `noise_model=cudaq_noise_model` to the workflow containing function `submit_aim_circuits()`:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Example parameters that can model execution on hardware at the high, simulation, level:\n",
+    "# Take single-qubit gate depolarization rate: ~0.2% or better (fidelity ≥99.8%)\n",
+    "# Take two-qubit gate depolarization rate: ~1–2% (fidelity ~98–99%)\n",
+    "cudaq_noise_model = get_device_noise(0.002, 0.02, readout_error_prob=0.02)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Running circuits associated with layer=('1:-9')\n",
+      "Running circuits associated with layer=('1:-1')\n",
+      "Running circuits associated with layer=('1:7')\n",
+      "Running circuits associated with layer=('5:-9')\n",
+      "Running circuits associated with layer=('5:-1')\n",
+      "Running circuits associated with layer=('5:7')\n",
+      "Running circuits associated with layer=('9:-9')\n",
+      "Running circuits associated with layer=('9:-1')\n",
+      "Running circuits associated with layer=('9:7')\n",
+      "\n",
+      "Completed all circuit sampling!\n"
+     ]
+    }
+   ],
+   "source": [
+    "aim_sim_data = submit_aim_circuits(sim_circuit_dict, noise_model=cudaq_noise_model)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "data_ordering = []\n",
+    "for key in circuit_layers:\n",
+    "    for basis in (\"z_basis\", \"x_basis\"):\n",
+    "        data_ordering.append((key, basis))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sim_physical_energies, sim_physical_uncertainties = aim_physical_energies(\n",
+    "    data_ordering, aim_sim_data[\"physical\"]\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sim_logical_energies, sim_logical_uncertainties = aim_logical_energies(\n",
+    "    data_ordering, aim_sim_data[\"logical\"]\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To analyze our simulated energy results in the above cells, we will compare them to the brute-force computed exact ground state energies for the AIM Hamiltonian. For simplicity, these are already stored in the dictionary `bf_energies` below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "bf_energies = {\n",
+    "    \"1:-9\": -18.251736027394713,\n",
+    "    \"1:-1\": -2.265564437074638,\n",
+    "    \"1:7\": -14.252231964940428,\n",
+    "    \"5:-9\": -19.293350575766127,\n",
+    "    \"5:-1\": -3.608495283014149,\n",
+    "    \"5:7\": -15.305692796870582,\n",
+    "    \"9:-9\": -20.39007993367173,\n",
+    "    \"9:-1\": -5.260398644698076,\n",
+    "    \"9:7\": -16.429650912487233,\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "With the above metric, we can assess the performance of the logical circuits against the physical circuits by considering how far away the respective energies are from the brute-force expected energies. The cell below computes these energy deviations:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Layer=(1, -9) has brute-force energy of: -18.251736027394713\n",
+      "Physical circuit of layer=(1, -9) got an energy of: -15.929\n",
+      "Logical circuit of layer=(1, -9) got an energy of: -17.46016175277361\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(1, -1) has brute-force energy of: -2.265564437074638\n",
+      "Physical circuit of layer=(1, -1) got an energy of: -1.97\n",
+      "Logical circuit of layer=(1, -1) got an energy of: -2.176531948420889\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(1, 7) has brute-force energy of: -14.252231964940428\n",
+      "Physical circuit of layer=(1, 7) got an energy of: -12.268\n",
+      "Logical circuit of layer=(1, 7) got an energy of: -13.26321740664324\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(5, -9) has brute-force energy of: -19.293350575766127\n",
+      "Physical circuit of layer=(5, -9) got an energy of: -16.8495\n",
+      "Logical circuit of layer=(5, -9) got an energy of: -18.46681284816878\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(5, -1) has brute-force energy of: -3.608495283014149\n",
+      "Physical circuit of layer=(5, -1) got an energy of: -3.1965000000000003\n",
+      "Logical circuit of layer=(5, -1) got an energy of: -3.4531715120183297\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(5, 7) has brute-force energy of: -15.305692796870582\n",
+      "Physical circuit of layer=(5, 7) got an energy of: -13.336\n",
+      "Logical circuit of layer=(5, 7) got an energy of: -14.341784541550897\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(9, -9) has brute-force energy of: -20.39007993367173\n",
+      "Physical circuit of layer=(9, -9) got an energy of: -17.802\n",
+      "Logical circuit of layer=(9, -9) got an energy of: -19.339249509416753\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(9, -1) has brute-force energy of: -5.260398644698076\n",
+      "Physical circuit of layer=(9, -1) got an energy of: -4.8580000000000005\n",
+      "Logical circuit of layer=(9, -1) got an energy of: -5.1227150992242025\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(9, 7) has brute-force energy of: -16.429650912487233\n",
+      "Physical circuit of layer=(9, 7) got an energy of: -14.3635\n",
+      "Logical circuit of layer=(9, 7) got an energy of: -15.448422736181264\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "sim_physical_energy_diff, sim_logical_energy_diff = _get_energy_diff(\n",
+    "    bf_energies, sim_physical_energies, sim_logical_energies\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Both physical and logical circuits were subject to the same noise model, but the `[[4,2,2]]` provides additional information that can help overcome some errors. Visualizing the computed energy differences from the above the cell, our noisy simulation provides a preview of the benefits logical qubits can offer:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "
                                                            "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(figsize=(11, 7), dpi=200)\n",
+    "\n",
+    "layer_labels = [(int(key.split(\":\")[0]), int(key.split(\":\")[1])) for key in bf_energies.keys()]\n",
+    "plot_labels = [str(item) for item in layer_labels]\n",
+    "\n",
+    "plt.errorbar(\n",
+    "    plot_labels,\n",
+    "    sim_physical_energy_diff,\n",
+    "    yerr=sim_physical_uncertainties.values(),\n",
+    "    ecolor=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
+    "    color=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
+    "    capsize=4,\n",
+    "    elinewidth=1.5,\n",
+    "    fmt=\"o\",\n",
+    "    markersize=8,\n",
+    "    markeredgewidth=1,\n",
+    "    label=\"Physical\",\n",
+    ")\n",
+    "\n",
+    "plt.errorbar(\n",
+    "    plot_labels,\n",
+    "    sim_logical_energy_diff,\n",
+    "    yerr=sim_logical_uncertainties.values(),\n",
+    "    color=(0, 177 / 255.0, 152 / 255.0),\n",
+    "    ecolor=(0, 177 / 255.0, 152 / 255.0),\n",
+    "    capsize=4,\n",
+    "    elinewidth=1.5,\n",
+    "    fmt=\"o\",\n",
+    "    markersize=8,\n",
+    "    markeredgewidth=1,\n",
+    "    label=\"Logical\",\n",
+    ")\n",
+    "\n",
+    "ax.set_xlabel(\"Hamiltonian Parameters (U, V)\", fontsize=18)\n",
+    "ax.set_ylabel(\"Energy above true ground state (in eV)\", fontsize=18)\n",
+    "ax.set_title(\"CUDA-Q AIM Circuits Simulation (lower is better)\", fontsize=20)\n",
+    "ax.legend(loc=\"upper right\", fontsize=18.5)\n",
+    "plt.xticks(fontsize=16)\n",
+    "plt.yticks(fontsize=16)\n",
+    "\n",
+    "ax.axhline(y=0, color=\"black\", linestyle=\"--\", linewidth=2)\n",
+    "plt.ylim(\n",
+    "    top=max(sim_physical_energy_diff) + max(sim_physical_uncertainties.values()) + 0.2, bottom=-0.2\n",
+    ")\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Running logical AIM on Infleqtion's hardware "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The entire workflow we've seen thus far can be seamlessly executed on real quantum hardware as well. CUDA-Q has integration with Infleqtion's gate-based neutral atom quantum computer, [Sqale](https://arxiv.org/html/2408.08288v2), allowing execution of CUDA-Q kernels on neutral-atom hardware via Infleqtion’s cross-platform Superstaq compiler API that performs low-level compilation and optimization under the hood. Indeed, the AIM research results seen in [our paper](https://arxiv.org/abs/2412.07670) were obtained via this complete end-to-end workflow.\n",
+    "\n",
+    "To do so, users can obtain a Superstaq API key from [superstaq.infleqtion.com](https://superstaq.infleqtion.com/) to gain access to Infleqtion's neutral-atom simulator, with [pre-registration](https://www.infleqtion.com/sqale-preregistration) open for access to Infleqtion’s neutral atom QPU."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As a tutorial, let us reproduce the workflow we've run so far but on Infleqtion's QPU. We begin with the same GPU-enhanced VQE to generate the AIM circuits:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cudaq.reset_target()\n",
+    "\n",
+    "if cudaq.num_available_gpus() == 0:\n",
+    "    cudaq.set_target(\"qpp-cpu\", option=\"fp64\")\n",
+    "else:\n",
+    "    cudaq.set_target(\"nvidia\", option=\"fp64\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Computed optimal angles=[1.5846845738799267, 1.5707961678256028] for U=1, V=-9\n",
+      "Computed optimal angles=[4.588033710930825, 4.712388365176642] for U=1, V=-1\n",
+      "Computed optimal angles=[-1.588651490745171, 1.5707962742876598] for U=1, V=7\n",
+      "Computed optimal angles=[1.64012940802256, 1.5707963354922125] for U=5, V=-9\n",
+      "Computed optimal angles=[2.1293956916868737, 1.5707963294715355] for U=5, V=-1\n",
+      "Computed optimal angles=[-1.6598458659836037, 1.570796331040382] for U=5, V=7\n",
+      "Computed optimal angles=[1.695151467539617, 1.5707960973500679] for U=9, V=-9\n",
+      "Computed optimal angles=[2.4149519241823376, 1.5707928509325972] for U=9, V=-1\n",
+      "Computed optimal angles=[-1.7301462945564499, 1.570796044872433] for U=9, V=7\n",
+      "\n",
+      "Finished building optimized circuits!\n"
+     ]
+    }
+   ],
+   "source": [
+    "device_circuit_dict = generate_circuit_set(\n",
+    "    ignore_meas_id=True\n",
+    ")  # Setting `ignore_meas_id=True` drops the noisy-identity gate from earlier"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "And now, we change backends! Before selecting an Infleqtion machine in CUDA-Q, we must first set our Superstaq API key, like so:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# os.environ['SUPERSTAQ_API_KEY'] = \"api_key\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Next, we declare the type of execution we would like on Infleqtion's machine based on the keyword options specified:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cudaq.reset_target()\n",
+    "\n",
+    "# Set the following to run on Infleqtion's Sqale QPU:\n",
+    "cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\")\n",
+    "\n",
+    "# Set the following to run an ideal dry-run on Infleqtion's Sqale QPU:\n",
+    "# cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\", method=\"dry-run\")\n",
+    "\n",
+    "# Set the following to run a device-realistic noisy simulation of Infleqtion's Sqale QPU:\n",
+    "# cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\", method=\"noise-sim\")\n",
+    "\n",
+    "# Set the following to run a local, ideal emulation:\n",
+    "# cudaq.set_target(\"infleqtion\", emulate=True)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "With that, we're all set! That simple change instructs our AIM circuits to execute on Infleqtion's QPU (or simulator). Due to the general queue wait time of running on hardware, we optionally recommend enabling the `run_async=True` flag to asynchronously sample the circuits. This will allow the cell to be executed and not wait synchronously until all the jobs are complete, allowing other classical code to be run in the meantime. When using `run_async`, an optional directory to store the job information can be specified with `folder_path` (this will be important to later retrieve the job results from the same directory)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Posting circuits associated with layer=('1:-9')\n",
+      "Posting circuits associated with layer=('1:-1')\n",
+      "Posting circuits associated with layer=('1:7')\n",
+      "Posting circuits associated with layer=('5:-9')\n",
+      "Posting circuits associated with layer=('5:-1')\n",
+      "Posting circuits associated with layer=('5:7')\n",
+      "Posting circuits associated with layer=('9:-9')\n",
+      "Posting circuits associated with layer=('9:-1')\n",
+      "Posting circuits associated with layer=('9:7')\n",
+      "\n",
+      "All circuits submitted for async sampling!\n"
+     ]
+    }
+   ],
+   "source": [
+    "submit_aim_circuits(\n",
+    "    device_circuit_dict, folder_path=\"hardware_aim_future_results\", shots_count=1000, run_async=True\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "With the above cell execution, all the circuits will post to execute on QPU. We can then return at a later time to retrieve the job results with the cell below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Retrieving all circuits counts associated with layer=('1:-9')\n",
+      "Retrieving all circuits counts associated with layer=('1:-1')\n",
+      "Retrieving all circuits counts associated with layer=('1:7')\n",
+      "Retrieving all circuits counts associated with layer=('5:-9')\n",
+      "Retrieving all circuits counts associated with layer=('5:-1')\n",
+      "Retrieving all circuits counts associated with layer=('5:7')\n",
+      "Retrieving all circuits counts associated with layer=('9:-9')\n",
+      "Retrieving all circuits counts associated with layer=('9:-1')\n",
+      "Retrieving all circuits counts associated with layer=('9:7')\n",
+      "\n",
+      "Obtained all circuit samples!\n"
+     ]
+    }
+   ],
+   "source": [
+    "aim_device_data = _get_async_results(circuit_layers, folder_path=\"hardware_aim_future_results\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "physical_energies, physical_uncertainties = aim_physical_energies(\n",
+    "    data_ordering, aim_device_data[\"physical\"]\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "logical_energies, logical_uncertainties = aim_logical_energies(\n",
+    "    data_ordering, aim_device_data[\"logical\"]\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Layer=(1, -9) has brute-force energy of: -18.251736027394713\n",
+      "Physical circuit of layer=(1, -9) got an energy of: -17.626499999999997\n",
+      "Logical circuit of layer=(1, -9) got an energy of: -17.69666562801761\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(1, -1) has brute-force energy of: -2.265564437074638\n",
+      "Physical circuit of layer=(1, -1) got an energy of: -2.1415\n",
+      "Logical circuit of layer=(1, -1) got an energy of: -2.2032104443266585\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(1, 7) has brute-force energy of: -14.252231964940428\n",
+      "Physical circuit of layer=(1, 7) got an energy of: -12.9955\n",
+      "Logical circuit of layer=(1, 7) got an energy of: -13.76919450035401\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(5, -9) has brute-force energy of: -19.293350575766127\n",
+      "Physical circuit of layer=(5, -9) got an energy of: -18.331\n",
+      "Logical circuit of layer=(5, -9) got an energy of: -18.85730052910377\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(5, -1) has brute-force energy of: -3.608495283014149\n",
+      "Physical circuit of layer=(5, -1) got an energy of: -3.476\n",
+      "Logical circuit of layer=(5, -1) got an energy of: -3.5425689231532203\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(5, 7) has brute-force energy of: -15.305692796870582\n",
+      "Physical circuit of layer=(5, 7) got an energy of: -14.043500000000002\n",
+      "Logical circuit of layer=(5, 7) got an energy of: -14.795918428433312\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(9, -9) has brute-force energy of: -20.39007993367173\n",
+      "Physical circuit of layer=(9, -9) got an energy of: -19.4715\n",
+      "Logical circuit of layer=(9, -9) got an energy of: -19.96524696701215\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(9, -1) has brute-force energy of: -5.260398644698076\n",
+      "Physical circuit of layer=(9, -1) got an energy of: -4.973\n",
+      "Logical circuit of layer=(9, -1) got an energy of: -5.207315773582224\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n",
+      "Layer=(9, 7) has brute-force energy of: -16.429650912487233\n",
+      "Physical circuit of layer=(9, 7) got an energy of: -15.182\n",
+      "Logical circuit of layer=(9, 7) got an energy of: -16.241375689575516\n",
+      "------------------------------------------------------------------------\n",
+      "Logical circuit achieved the lower energy!\n",
+      "------------------------------------------------------------------------ \n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "physical_energy_diff, logical_energy_diff = _get_energy_diff(\n",
+    "    bf_energies, physical_energies, logical_energies\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As before, we use the same metric of comparing against the true ground state energies; however, this time, both the physical and logical circuits are fully exposed to real hardware noise. Yet, we expect the use of logical qubits afforded to us by the `[[4,2,2]]` code to achieve energies closer to the true ground state than the bare physical circuits (up to a certain error threshold). And indeed they do! Visually, we can plot the energy deviations of both the physical and logical circuits from the cell above and observe that the logical circuits are able to outperform the physical circuits by obtaining much lower energies, demonstrating the power of error detection and the beginning possibilities of fault-tolerant quantum computation: "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "
                                                            "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(figsize=(11, 7), dpi=200)\n",
+    "\n",
+    "plt.errorbar(\n",
+    "    plot_labels,\n",
+    "    physical_energy_diff,\n",
+    "    yerr=physical_uncertainties.values(),\n",
+    "    ecolor=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
+    "    color=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
+    "    capsize=4,\n",
+    "    elinewidth=1.5,\n",
+    "    fmt=\"o\",\n",
+    "    markersize=8,\n",
+    "    markeredgewidth=1,\n",
+    "    label=\"Physical\",\n",
+    ")\n",
+    "plt.errorbar(\n",
+    "    plot_labels,\n",
+    "    logical_energy_diff,\n",
+    "    yerr=logical_uncertainties.values(),\n",
+    "    color=(0, 177 / 255.0, 152 / 255.0),\n",
+    "    ecolor=(0, 177 / 255.0, 152 / 255.0),\n",
+    "    capsize=4,\n",
+    "    elinewidth=1.5,\n",
+    "    fmt=\"o\",\n",
+    "    markersize=8,\n",
+    "    markeredgewidth=1,\n",
+    "    label=\"Logical\",\n",
+    ")\n",
+    "\n",
+    "ax.set_xlabel(\"Hamiltonian Parameters (U, V)\", fontsize=18)\n",
+    "ax.set_ylabel(\"Energy above true ground state (in eV)\", fontsize=18)\n",
+    "ax.set_title(\"CUDA-Q AIM Infleqtion Hardware Execution (lower is better)\", fontsize=20)\n",
+    "ax.legend(loc=\"upper left\", fontsize=18.5)\n",
+    "plt.xticks(fontsize=16)\n",
+    "plt.yticks(fontsize=16)\n",
+    "\n",
+    "ax.axhline(y=0, color=\"black\", linestyle=\"--\", linewidth=2)\n",
+    "plt.ylim(top=max(physical_energy_diff) + max(physical_uncertainties.values()) + 0.2, bottom=-0.2)\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.16"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/pr-2458/applications/python/qaoa.html b/pr-2458/applications/python/qaoa.html
index 21af2719cf..ab8eb8c8a6 100644
--- a/pr-2458/applications/python/qaoa.html
+++ b/pr-2458/applications/python/qaoa.html
@@ -131,6 +131,12 @@
 
                                                          • Measurements
                                                            •

                                                          • +
                                                        • Photonic Operations +
                                                        • Measuring Kernels @@ -152,6 +158,12 @@
                                                        • +
                                                      • Executing Photonic Kernels +
                                                      • Computing Expectation Values @@ -184,6 +196,7 @@
                                                      • Using Quantum Hardware Providers
                                                      • Divisive Clustering With Coresets Using CUDA-Q
                                                        • @@ -325,6 +347,10 @@
                                                      • Stim (CPU)
                                                      • +
                                                    • Photonics Simulators +
                                                    • Fermioniq
                                                    • Default Simulator
                                                    @@ -336,48 +362,54 @@
                                                  • Submission from Python
                                                  • -
                                                • IonQ
                                                    -
                                                  • Setting Credentials
                                                    • +
                                                  • Infleqtion
                                                    • -
                                                  • Anyon Technologies/Anyon Computing
                                                      -
                                                    • Setting Credentials
                                                      • +
                                                    • IonQ
                                                      • -
                                                    • IQM
                                                      • -
                                                    • IonQ
                                                        -
                                                      • Setting Credentials
                                                        • +
                                                      • Infleqtion
                                                        • -
                                                      • Anyon Technologies/Anyon Computing
                                                          -
                                                        • Setting Credentials
                                                          • +
                                                        • IonQ
                                                          • -
                                                        • IQM
                                                          • -
                                                        • IonQ
                                                            -
                                                          • Setting Credentials
                                                            • +
                                                          • Infleqtion
                                                            • -
                                                          • Anyon Technologies/Anyon Computing
                                                              -
                                                            • Setting Credentials
                                                              • +
                                                            • IonQ
                                                              • -
                                                            • IQM
                                                              • -
                                                            • IonQ
                                                                -
                                                              • Setting Credentials
                                                                • +
                                                              • Infleqtion
                                                                • -
                                                              • Anyon Technologies/Anyon Computing
                                                                  -
                                                                • Setting Credentials
                                                                  • +
                                                                • IonQ
                                                                  • -
                                                                • IQM
                                                                  • -
                                                                • IonQ
                                                                    -
                                                                  • Setting Credentials
                                                                    • +
                                                                  • Infleqtion
                                                                    • -
                                                                  • Anyon Technologies/Anyon Computing
                                                                    • -
                                                                  • IonQ
                                                                      -
                                                                    • Setting Credentials
                                                                      • +
                                                                    • Infleqtion
                                                                      • -
                                                                    • Anyon Technologies/Anyon Computing
                                                                        -
                                                                      • Setting Credentials
                                                                        • +
                                                                      • IonQ
                                                                        • -
                                                                      • IQM
                                                                        • -
                                                                      • IonQ
                                                                          -
                                                                        • Setting Credentials
                                                                          • +
                                                                        • Infleqtion
                                                                          • -
                                                                        • Anyon Technologies/Anyon Computing
                                                                            -
                                                                          • Setting Credentials
                                                                            • +
                                                                          • IonQ
                                                                            • -
                                                                          • IQM
                                                                            • -
                                                                          • IonQ
                                                                              -
                                                                            • Setting Credentials
                                                                              • +
                                                                            • Infleqtion
                                                                              • -
                                                                            • Anyon Technologies/Anyon Computing
                                                                                -
                                                                              • Setting Credentials
                                                                                • +
                                                                              • IonQ
                                                                                • -
                                                                              • IQM
                                                                                • -
                                                                              • IonQ
                                                                                  -
                                                                                • Setting Credentials
                                                                                  • +
                                                                                • Infleqtion
                                                                                  • -
                                                                                • Anyon Technologies/Anyon Computing
                                                                                  • -
                                                                                • IonQ
                                                                                    -
                                                                                  • Setting Credentials
                                                                                    • +
                                                                                  • Infleqtion
                                                                                    • -
                                                                                  • Anyon Technologies/Anyon Computing
                                                                                    • -
                                                                                  • IonQ
                                                                                      -
                                                                                    • Setting Credentials
                                                                                      • +
                                                                                    • Infleqtion
                                                                                      • -
                                                                                    • Anyon Technologies/Anyon Computing
                                                                                      • -
                                                                                    • IonQ
                                                                                        -
                                                                                      • Setting Credentials
                                                                                        • +
                                                                                      • Infleqtion
                                                                                        • -
                                                                                      • Anyon Technologies/Anyon Computing
                                                                                        • -
                                                                                      • IonQ
                                                                                          -
                                                                                        • Setting Credentials
                                                                                          • +
                                                                                        • Infleqtion
                                                                                          • -
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                                                                                                                              @@ -825,7 +863,7 @@

                                                                                                                              CUDA-Q
                                                                                                                              -

                                                                                                                              © Copyright 2024, NVIDIA Corporation & Affiliates.

                                                                                                                              +

                                                                                                                              © Copyright 2025, NVIDIA Corporation & Affiliates.

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                                                                                                                            • Measurements

                                                                                                                            • +
                                                                                                                          • Photonic Operations +
                                                                                                                          • Measuring Kernels @@ -153,6 +159,12 @@
                                                                                                                          • +
                                                                                                                        • Executing Photonic Kernels +
                                                                                                                        • Computing Expectation Values @@ -185,6 +197,7 @@
                                                                                                                        • Using Quantum Hardware Providers
                                                                                                                        • Divisive Clustering With Coresets Using CUDA-Q
                                                                                                                          • @@ -326,6 +348,10 @@
                                                                                                                        • Stim (CPU)
                                                                                                                        • +
                                                                                                                      • Photonics Simulators +
                                                                                                                      • Fermioniq
                                                                                                                      • Default Simulator
                                                                                                                      @@ -337,48 +363,54 @@
                                                                                                                    • Submission from Python
                                                                                                                    • -
                                                                                                                  • IonQ
                                                                                                                      -
                                                                                                                    • Setting Credentials
                                                                                                                      • +
                                                                                                                    • Infleqtion
                                                                                                                      • -
                                                                                                                    • Anyon Technologies/Anyon Computing
                                                                                                                        -
                                                                                                                      • Setting Credentials
                                                                                                                        • +
                                                                                                                      • IonQ
                                                                                                                        • -
                                                                                                                      • IQM
                                                                                                                        • -
                                                                                                                      • IonQ
                                                                                                                          -
                                                                                                                        • Setting Credentials
                                                                                                                          • +
                                                                                                                        • Infleqtion
                                                                                                                          • -
                                                                                                                        • Anyon Technologies/Anyon Computing
                                                                                                                            -
                                                                                                                          • Setting Credentials
                                                                                                                            • +
                                                                                                                          • IonQ
                                                                                                                            • -
                                                                                                                          • IQM
                                                                                                                              -
                                                                                                                            • Setting Credentials
                                                                                                                              • +
                                                                                                                            • Anyon Technologies/Anyon Computing
                                                                                                                              • -
                                                                                                                            • OQC
                                                                                                                                +
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                                                                                                                              • ORCA Computing
                                                                                                                                  +
                                                                                                                                • OQC
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                                                                                                                                • Quantinuum
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                                                                                                                                    -
                                                                                                                                  • Setting Credentials
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                                                                                                                                  • Infleqtion
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                                                                                                                                  • Anyon Technologies/Anyon Computing
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                                                                                                                                    • Setting Credentials
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                                                                                                                                    • IonQ
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                                                                                                                                    • IQM
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                                                                                                                                      • Setting Credentials
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                                                                                                                                      • Anyon Technologies/Anyon Computing
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                                                                                                                                      • OQC
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                                                                                                                                        • IQM
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                                                                                                                                        • ORCA Computing
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                                                                                                                                          • OQC
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                                                                                                                                          • Quantinuum
                                                                                                                                              -
                                                                                                                                            • Setting Credentials
                                                                                                                                              • +
                                                                                                                                            • ORCA Computing
                                                                                                                                              • -
                                                                                                                                            • QuEra Computing
                                                                                                                                            • NVIDIA Quantum Cloud
                                                                                                                                            • Installation
                                                                                                                                                @@ -613,6 +646,7 @@
                                                                                                                                              • spin.y()
                                                                                                                                              • spin.z()
                                                                                                                                              • CuDensityMatState
                                                                                                                                                • +
                                                                                                                                              • InitialState
                                                                                                                                              • to_cupy_array()
                                                                                                                                              • SampleResult
                                                                                                                                              • AsyncSampleResult
                                                                                                                                                • @@ -723,7 +757,7 @@
                                                                                                                                                -

                                                                                                                                                © Copyright 2024, NVIDIA Corporation & Affiliates.

                                                                                                                                                +

                                                                                                                                                © Copyright 2025, NVIDIA Corporation & Affiliates.

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54, 56, 60, 64, 65, 71, 80], "appli": [1, 2, 3, 5, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 25, 26, 33, 36, 37, 40, 44, 47, 52, 53, 56, 60, 63, 64, 65, 67, 68, 71], "0": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 31, 33, 35, 36, 37, 40, 41, 42, 43, 45, 47, 49, 50, 51, 52, 53, 54, 56, 58, 60, 62, 63, 64, 65, 66, 67, 68, 71, 72, 74, 76, 78, 79, 80], "1": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 50, 51, 52, 53, 54, 56, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 71, 72, 74, 78, 79, 80], "rotat": [1, 3, 9, 10, 13, 14, 17, 18, 25, 29, 40, 41, 56, 62, 71], "\u03c0": 1, "about": [1, 2, 3, 7, 9, 17, 18, 19, 20, 21, 29, 31, 33, 47, 50, 51, 52, 53, 54, 57, 58, 63, 66, 72, 74, 76, 77, 78, 79, 80], "axi": [1, 11, 20, 21, 29], "enabl": [1, 2, 3, 5, 9, 14, 23, 32, 33, 35, 37, 38, 40, 42, 43, 44, 45, 49, 50, 51, 53, 54, 57, 58, 62, 63, 66, 68, 71, 72, 74, 78, 79], "one": [1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 18, 19, 20, 22, 23, 29, 31, 33, 35, 36, 38, 40, 43, 47, 50, 51, 52, 53, 54, 59, 60, 62, 63, 65, 66, 67, 68, 70, 71, 72, 74, 78, 79, 80], "superposit": [1, 5, 7, 13, 29, 33, 36, 45, 53, 56, 58, 67], "comput": [1, 2, 3, 4, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 20, 21, 22, 23, 25, 27, 29, 30, 32, 33, 35, 36, 37, 43, 45, 47, 52, 53, 54, 57, 58, 61, 66, 71, 72, 76, 78, 79], "basi": [1, 2, 3, 4, 10, 12, 14, 17, 20, 22, 23, 24, 25, 45, 52, 53, 67], "sqrt": [1, 3, 5, 7, 10, 12, 14, 15, 17, 25, 29, 36, 50, 63, 67, 79], "2": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 47, 50, 51, 52, 53, 54, 58, 60, 62, 63, 65, 66, 67, 68, 72, 74, 76, 78, 79, 80], "an": [1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35, 37, 38, 40, 41, 43, 44, 45, 47, 48, 50, 51, 52, 53, 54, 56, 58, 60, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 79, 80], "arbitrari": [1, 2, 3, 20, 50, 51, 65, 78], "\u03bb": 1, "exp": [1, 2, 12, 18, 36, 41, 50], "i\u03bb": 1, "math": [1, 4, 7, 18, 52], "pi": [1, 8, 9, 11, 13, 14, 16, 18, 19, 21, 22, 27, 29, 36, 37, 42, 44, 50, 51, 52, 63], "std": [1, 2, 3, 33, 35, 36, 37, 40, 41, 43, 44, 45, 52, 53, 58, 63, 64, 66, 70, 71, 76, 78], "number": [1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, 23, 26, 27, 29, 33, 36, 41, 43, 45, 47, 50, 51, 52, 53, 54, 56, 58, 62, 63, 64, 65, 66, 67, 68, 71, 74, 79], "\u03b8": 1, "co": [1, 14, 19, 29, 50], "isin": 1, "sin": [1, 14, 29], "its": [1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 25, 31, 32, 33, 43, 45, 47, 48, 52, 53, 54, 58, 60, 63, 64, 67, 68, 71, 72, 74, 78, 79, 80], "4": [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 31, 33, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 51, 52, 53, 54, 60, 63, 66, 68, 72, 74, 78, 80], "i\u03c0": 1, "two": [1, 2, 3, 4, 7, 8, 9, 10, 12, 13, 15, 16, 17, 18, 19, 20, 22, 25, 27, 29, 38, 47, 50, 51, 53, 54, 58, 60, 62, 63, 65, 67, 74, 78], "qubit_1": [1, 7, 13, 60], "qubit_2": [1, 15], "univers": [1, 2, 9, 15, 20, 52, 67], "three": [1, 10, 17, 18, 20, 22, 38, 51, 52, 62], "paramet": [1, 2, 3, 6, 8, 9, 11, 12, 13, 16, 18, 20, 21, 23, 33, 37, 40, 45, 50, 51, 52, 54, 56, 60, 62, 63, 64, 66, 71, 72], "euler": [1, 50], "angl": [1, 2, 3, 6, 10, 14, 17, 18, 27, 29, 36, 37, 40, 53, 56, 62, 63], "theta": [1, 8, 9, 10, 11, 13, 14, 21, 22, 25, 27, 29, 33, 35, 36, 52, 53, 60, 62], "phi": [1, 3, 4, 10, 33, 35, 51, 63, 68], "\u03c6": 1, "lambda": [1, 2, 8, 9, 12, 13, 17, 18, 19, 22, 27, 33, 36, 37, 42, 50, 63, 65, 66, 68], "i\u03c6": 1, "np": [1, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 29, 36, 37, 42, 44, 50, 51, 53, 54, 60, 63, 66, 72], "m_pi": [1, 36, 44, 63], "m_pi_2": [1, 36, 37, 52], "adj": [1, 40, 60], "method": [1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 17, 18, 19, 20, 21, 22, 26, 27, 33, 35, 40, 45, 50, 51, 53, 54, 58, 60, 64], "ani": [1, 2, 3, 9, 12, 13, 18, 19, 20, 22, 23, 25, 27, 29, 33, 37, 39, 40, 42, 44, 45, 50, 51, 52, 54, 56, 58, 59, 60, 63, 64, 65, 71, 72, 74, 78, 79], "alloc": [1, 2, 3, 6, 13, 20, 33, 35, 36, 37, 38, 45, 53, 54, 56, 58, 64, 65, 71], "now": [1, 4, 5, 7, 9, 10, 13, 14, 15, 18, 20, 21, 22, 31, 47, 58, 63, 64, 65, 66, 74, 79, 80], "again": [1, 5, 22, 23, 33, 47, 74, 76], "initi": [1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 14, 15, 18, 19, 21, 22, 27, 33, 50, 51, 53, 60, 63, 66, 67, 72, 74], "ctrl": [1, 2, 5, 7, 13, 16, 18, 23, 27, 29, 33, 35, 36, 40, 52, 53, 56, 60, 62, 63, 64, 65, 67, 68, 74, 79], "condit": [1, 2, 14, 15, 20, 25, 33, 34, 35, 37, 38, 54, 57, 67, 68], "more": [1, 2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 17, 18, 20, 22, 26, 29, 31, 35, 38, 40, 41, 47, 51, 52, 53, 54, 57, 58, 60, 63, 66, 67, 72, 74, 76, 78, 79, 80], "wikipedia": [1, 50], "entri": [1, 3, 12, 33, 37, 53, 60, 63, 68, 74, 78], "ctrl_1": 1, "ctrl_2": 1, "00": [1, 4, 9, 15, 23, 25, 27, 58, 66, 67, 78, 79], "11": [1, 3, 4, 9, 11, 15, 16, 17, 19, 20, 22, 23, 25, 27, 29, 33, 58, 66, 67, 68, 72, 74, 78, 79], "onli": [1, 2, 3, 5, 9, 15, 17, 18, 20, 22, 23, 24, 29, 33, 37, 38, 42, 45, 47, 50, 51, 52, 53, 57, 63, 67, 68, 70, 72, 74, 78, 79], "both": [1, 3, 4, 5, 7, 11, 18, 38, 47, 51, 53, 54, 67, 72, 74, 76], "000": [1, 14, 15, 17, 18, 52, 58], "111": [1, 9, 14, 15, 17, 18], "follow": [1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 20, 22, 23, 24, 26, 27, 29, 31, 33, 35, 37, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 56, 58, 59, 60, 62, 63, 64, 68, 70, 71, 72, 74, 75, 76, 78, 79, 80], "common": [1, 3, 9, 10, 17, 18, 20, 21, 22, 33, 37, 40, 41, 68, 72], "convent": [1, 8, 11, 13, 23], "all": [1, 2, 3, 9, 15, 16, 17, 18, 19, 20, 22, 23, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 45, 47, 51, 52, 53, 54, 58, 60, 62, 63, 66, 67, 68, 72, 74, 75, 76, 78, 79, 80], "howev": [1, 4, 9, 14, 15, 17, 20, 22, 23, 47, 50, 51, 53, 78], "behavior": [1, 2, 3, 9, 22, 54], "chang": [1, 2, 5, 9, 14, 18, 28, 31, 33, 37, 50, 58, 74, 79, 80], "instead": [1, 2, 4, 9, 25, 39, 42, 53, 54, 58, 72, 74, 78], "when": [1, 2, 3, 9, 12, 13, 17, 18, 20, 33, 38, 45, 47, 52, 53, 54, 58, 62, 63, 64, 68, 71, 72, 74, 78, 79], "negat": [1, 2, 3, 40, 44, 45], "polar": [1, 40, 44, 54], "syntax": [1, 9, 31, 32, 37, 38, 40, 42, 51, 60, 63, 76, 80], "preced": [1, 40, 51], "01": [1, 4, 7, 15, 20, 25, 27, 67], "10": [1, 4, 7, 9, 10, 11, 12, 13, 15, 16, 17, 19, 20, 22, 25, 27, 29, 33, 36, 37, 54, 58, 60, 63, 64, 66, 67, 68, 72, 74, 76], "notat": [1, 15, 67], "context": [1, 2, 11, 38, 53, 54, 71], "valid": [1, 2, 3, 30, 37, 51, 54, 60, 63, 72, 74, 78], "either": [1, 7, 11, 13, 18, 38, 51, 53, 54, 63, 67, 72, 74, 79], "similarli": [1, 7, 22, 53, 59, 67], "condition": 1, "respect": [1, 2, 3, 4, 8, 13, 18, 22, 27, 33, 50, 51, 53, 58, 62, 66, 67, 72, 74, 79], "e": [1, 2, 3, 4, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 21, 26, 29, 32, 33, 34, 36, 37, 38, 39, 40, 41, 47, 50, 51, 52, 53, 54, 63, 68, 71, 72, 74, 78, 79], "project": [1, 54, 71, 72, 74, 75, 78], "onto": [1, 67], "eigenvector": [1, 2, 10, 12], "non": [1, 2, 3, 8, 10, 12, 17, 18, 33, 37, 38, 45, 53, 54, 58, 62, 64], "linear": [1, 5, 9, 11, 12, 14, 21, 25, 52, 58, 63, 67], "avail": [1, 2, 3, 8, 9, 10, 20, 22, 27, 30, 31, 32, 33, 37, 38, 40, 43, 44, 45, 46, 49, 51, 52, 53, 54, 57, 58, 60, 61, 62, 63, 68, 72, 74, 79, 80], "first": [1, 2, 3, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 25, 27, 29, 30, 33, 45, 51, 52, 53, 54, 55, 60, 62, 63, 64, 65, 68, 74, 79], "api": [1, 23, 26, 29, 30, 33, 35, 39, 40, 43, 45, 50, 51, 52, 53, 54, 58, 60, 64, 71, 72, 74, 76, 78], "regist": [1, 2, 3, 5, 10, 14, 18, 21, 24, 33, 36, 38, 45, 51, 53, 60, 63, 64, 65, 68, 71], "outsid": [1, 9, 74, 78], "Then": [1, 17, 20, 24, 51, 63, 70, 71], "within": [1, 2, 3, 21, 33, 37, 39, 41, 45, 51, 53, 54, 57, 58, 60, 63, 64, 67, 70, 72, 74, 75, 76, 78, 79], "like": [1, 2, 3, 4, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20, 21, 22, 23, 27, 28, 31, 33, 37, 45, 51, 53, 58, 60, 63, 64, 66, 67, 68, 72, 74, 75, 78, 79, 80], "built": [1, 2, 4, 6, 9, 12, 14, 22, 23, 25, 31, 51, 54, 57, 58, 72, 78, 79, 80], "abov": [1, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 20, 22, 23, 33, 35, 40, 50, 51, 52, 53, 54, 58, 60, 62, 63, 65, 67, 68, 71, 72, 74, 76, 78, 79], "level": [1, 2, 3, 22, 28, 31, 32, 33, 38, 40, 50, 52, 53, 54, 68, 71, 75, 80], "register_oper": [1, 60], "accept": [1, 2, 3, 22, 23, 56, 72, 74, 79], "identifi": [1, 2, 3, 4, 13, 18, 20, 72, 74], "string": [1, 2, 3, 5, 18, 26, 29, 33, 35, 36, 43, 50, 54, 58, 64, 68, 74, 78], "numpi": [1, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 29, 36, 50, 60, 63, 66, 72], "arrai": [1, 2, 3, 4, 7, 10, 12, 14, 15, 16, 17, 20, 23, 25, 27, 45, 47, 50, 51, 53, 54, 60, 63, 64, 66, 68], "complex": [1, 2, 3, 4, 8, 12, 15, 19, 25, 41, 47, 50, 53, 58, 60, 66, 67, 78], "A": [1, 2, 3, 4, 7, 8, 9, 10, 12, 13, 15, 16, 17, 18, 19, 21, 27, 28, 29, 33, 36, 37, 40, 47, 50, 51, 58, 60, 63, 65, 66, 67, 70, 71, 72, 74], "1d": [1, 2], "interpret": [1, 8, 57, 63, 72], "row": [1, 2, 3, 29, 60], "major": [1, 72], "import": [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 36, 41, 50, 51, 52, 53, 54, 56, 58, 60, 62, 63, 64, 66, 67, 68, 72, 78, 79], "custom_h": 1, "custom_x": [1, 60], "def": [1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 33, 36, 37, 42, 44, 50, 52, 53, 56, 58, 60, 62, 63, 64, 65, 66, 67, 74, 79], "bell": [1, 15, 33, 78], "sampl": [1, 2, 3, 5, 7, 8, 9, 13, 16, 17, 18, 20, 25, 35, 51, 52, 53, 54, 55, 57, 60, 63, 64, 65, 66, 67, 71, 74, 78, 79], "dump": [1, 2, 3, 25, 33, 36, 52, 53, 58, 63, 64, 66, 78, 79], "macro": [1, 71], "cudaq_register_oper": 1, "uniqu": [1, 2, 3, 9, 13, 17, 20, 33, 38, 40, 45, 53, 76], "name": [1, 2, 3, 9, 13, 15, 18, 33, 35, 40, 43, 49, 50, 51, 52, 53, 54, 62, 66, 67, 68, 71, 72, 74, 75, 78, 79], "represent": [1, 2, 3, 14, 15, 20, 23, 29, 33, 37, 47, 50, 54, 68, 70, 71], "includ": [1, 2, 3, 4, 12, 13, 16, 22, 31, 33, 36, 45, 50, 52, 56, 57, 58, 60, 62, 63, 64, 65, 68, 70, 71, 72, 74, 76, 78, 79, 80], "m_sqrt1_2": 1, "__qpu__": [1, 2, 33, 36, 37, 44, 52, 53, 56, 58, 62, 63, 64, 65, 68, 78, 79], "void": [1, 2, 3, 33, 35, 36, 37, 40, 41, 43, 44, 45, 56, 58, 63, 65, 68, 70, 71, 76, 78, 79], "bell_pair": [1, 2, 3], "r": [1, 4, 17, 18, 40, 45, 51, 52, 53, 54, 62, 63, 68, 74], "int": [1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 33, 36, 37, 44, 45, 50, 52, 53, 56, 58, 60, 62, 63, 64, 65, 66, 68, 71, 72, 76, 78, 79], "main": [1, 4, 5, 9, 18, 20, 31, 33, 36, 47, 52, 58, 62, 63, 64, 65, 68, 72, 74, 76, 78, 79, 80], "auto": [1, 2, 33, 35, 36, 37, 41, 44, 45, 52, 53, 54, 56, 58, 62, 63, 64, 65, 68, 70, 78, 79], "count": [1, 2, 3, 5, 8, 9, 10, 12, 13, 17, 18, 23, 33, 35, 36, 45, 51, 52, 53, 54, 58, 63, 64, 65, 66, 68, 71], "bit": [1, 2, 3, 4, 5, 7, 15, 16, 17, 18, 23, 25, 33, 36, 38, 45, 47, 53, 54, 63, 64, 65, 67, 71], "printf": [1, 33, 36, 45, 53, 62, 64, 65, 72], "n": [1, 2, 4, 5, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 22, 33, 35, 36, 37, 40, 41, 44, 52, 53, 58, 60, 62, 63, 64, 65, 66, 67, 68, 72, 76, 79], "data": [1, 2, 8, 11, 12, 13, 14, 21, 30, 33, 37, 39, 41, 47, 53, 54, 62, 64, 65, 68, 71, 73, 74, 76, 78], "multi": [1, 4, 14, 15, 23, 29, 30, 31, 32, 35, 38, 40, 44, 49, 50, 51, 52, 58, 60, 61, 62, 67, 71, 72, 78, 79, 80], "msb": 1, "order": [1, 2, 3, 4, 9, 12, 13, 15, 29, 33, 41, 50, 51, 54, 58, 62], "big": [1, 8, 16, 23], "endian": [1, 16, 23], "show": [1, 8, 9, 11, 13, 14, 15, 17, 20, 21, 22, 29, 50, 53, 60, 62, 63, 72, 74], "differ": [1, 2, 3, 7, 9, 10, 11, 12, 14, 15, 17, 18, 22, 23, 27, 29, 47, 51, 52, 53, 57, 58, 63, 66, 72, 74, 76, 79], "test": [1, 9, 11, 12, 16, 17, 18, 22, 30, 35, 66, 72, 74], "cnot": [1, 5, 9, 40, 56, 60, 67, 78], "my_cnot": 1, "print": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 29, 33, 36, 45, 50, 52, 53, 58, 60, 62, 63, 64, 65, 66, 67, 68, 72, 78, 79], "500": [1, 22, 67, 79], "exact": [1, 9, 10, 16, 20, 54], "random": [1, 2, 3, 4, 5, 8, 9, 13, 15, 16, 17, 18, 20, 21, 22, 27, 29, 53, 54, 66], "construct": [1, 2, 8, 9, 10, 12, 16, 17, 19, 22, 27, 29, 30, 33, 34, 35, 37, 45, 47, 50, 53, 56, 57, 58, 60, 61, 64, 68], "second": [1, 2, 3, 4, 7, 8, 9, 12, 13, 17, 19, 45, 50, 52, 54, 58, 60, 63], "1j": [1, 12], "xy": [1, 29], "kron": [1, 17], "my_xi": 1, "custom_xy_test": 1, "undo": 1, "prior": [1, 54, 63, 67, 72, 74, 79], "1000": [1, 3, 9, 11, 16, 17, 20, 23, 25, 33, 51, 58, 64, 66, 67, 79], "mycnot": 1, "myxi": 1, "hardwar": [1, 9, 14, 18, 20, 23, 30, 31, 49, 54, 58, 61, 78, 80], "synthes": [1, 3, 20, 40, 44, 68], "current": [1, 2, 3, 9, 29, 31, 33, 43, 51, 53, 54, 71, 74, 78, 80], "orca": [1, 2, 49], "which": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 25, 27, 29, 31, 33, 35, 38, 41, 45, 47, 50, 51, 53, 54, 60, 62, 63, 64, 66, 67, 68, 71, 72, 74, 75, 78, 80], "doe": [1, 2, 3, 7, 9, 14, 15, 20, 29, 31, 33, 37, 45, 50, 52, 53, 72, 74, 76, 78, 79, 80], "increment": [1, 2, 66], "qumod": 1, "up": [1, 2, 3, 7, 9, 13, 14, 16, 20, 29, 35, 41, 50, 51, 54, 57, 62, 63, 66, 68, 71, 74], "maximum": [1, 3, 8, 9, 20, 54], "valu": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 27, 29, 30, 33, 35, 37, 41, 45, 47, 50, 52, 53, 54, 58, 61, 63, 66, 67, 68, 72, 78, 79], "repres": [1, 2, 3, 4, 7, 8, 9, 13, 14, 15, 20, 25, 29, 33, 47, 50, 51, 54, 63, 67, 68], "If": [1, 2, 3, 5, 7, 9, 11, 14, 15, 16, 17, 18, 19, 23, 24, 29, 33, 47, 50, 51, 52, 54, 58, 63, 66, 67, 72, 74, 78, 79], "where": [1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 28, 29, 32, 38, 40, 41, 45, 47, 50, 51, 54, 58, 60, 63, 66, 67, 71, 72, 74, 76, 79], "alreadi": [1, 2, 3, 18, 29, 72, 74, 79], "ha": [1, 2, 3, 4, 5, 7, 9, 13, 15, 16, 17, 18, 20, 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"left": [1, 2, 4, 5, 7, 10, 12, 13, 14, 15, 23, 63, 71, 74], "right": [1, 4, 10, 13, 14], "17": [1, 9, 15, 16, 17, 20, 29, 60, 68, 76], "beam": [1, 51, 63], "splitter": [1, 51, 63], "act": [1, 2, 3, 6, 7, 9, 13, 26, 47, 50, 67], "togeth": [1, 17, 30, 54, 68, 79], "parameter": [1, 2, 3, 8, 9, 10, 13, 19, 21, 22, 33, 35, 37, 40, 50, 52, 57, 60, 62, 64, 66], "relat": [1, 2, 9, 13, 18, 20, 68], "reflect": [1, 36, 54], "a_2": [1, 18], "b": [1, 9, 22, 27, 33, 60, 63], "_": [1, 4, 7, 11, 17, 18, 20, 29, 50], "rang": [1, 2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 29, 31, 36, 37, 44, 45, 50, 52, 53, 56, 60, 66, 74, 79, 80], "34": [1, 9, 17], "return": [1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 27, 29, 33, 35, 36, 37, 40, 45, 47, 50, 52, 53, 54, 58, 62, 63, 64, 66, 68, 70, 71, 72, 76, 78], "result": [1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 27, 28, 33, 34, 35, 36, 38, 47, 50, 51, 52, 53, 54, 58, 60, 62, 63, 64, 65, 66, 67, 68, 71, 74, 78, 79], "input": [1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 20, 22, 26, 27, 33, 35, 36, 37, 44, 45, 53, 58, 60, 62, 63, 66], "class": [2, 3, 4, 9, 11, 20, 33, 35, 37, 41, 43, 45, 53, 54, 70, 71], "spin_op": [2, 8, 26, 33, 36, 40, 52, 53, 58, 62], "gener": [2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 17, 18, 21, 23, 26, 29, 33, 35, 36, 37, 38, 40, 41, 44, 46, 51, 52, 54, 57, 62, 63, 64, 65, 67, 68, 70, 74, 78], "sum": [2, 3, 4, 11, 12, 13, 16, 17, 20, 26, 41, 45, 63, 67], "tensor": [2, 3, 11, 17, 26, 31, 41, 52, 53, 71, 80], "product": [2, 3, 5, 17, 26, 30, 31, 41, 52, 79, 80], "expos": [2, 3, 9, 33, 35, 41, 43, 47, 53, 71], "typic": [2, 20, 33, 45, 52, 56, 57, 62, 68, 75, 76], "algebra": [2, 41, 62, 67], "programm": [2, 3, 33, 34, 35, 37, 38, 40, 42, 43, 45, 51, 53, 64], "defin": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 32, 33, 34, 35, 36, 37, 41, 42, 43, 44, 45, 50, 52, 53, 54, 56, 57, 58, 60, 62, 63, 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18, 20, 38, 50, 53, 58, 67], "spars": 2, "function": [2, 3, 5, 6, 7, 8, 11, 12, 13, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 31, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 56, 57, 58, 62, 64, 66, 68, 71, 76, 78, 80], "pair": [2, 3, 8, 12, 13, 15, 16, 37, 43, 47, 74], "const": [2, 33, 35, 36, 37, 40, 41, 43, 45, 52, 63, 70, 71, 76, 78], "termdata": 2, "constructor": [2, 3], "take": [2, 3, 4, 5, 7, 9, 12, 13, 14, 16, 17, 19, 22, 27, 28, 31, 33, 35, 36, 37, 40, 41, 42, 43, 44, 45, 47, 51, 54, 57, 58, 60, 62, 63, 64, 65, 66, 68, 72, 74, 79, 80], "coeffici": [2, 3, 8, 12, 19, 26, 50, 67], "constant": [2, 7, 19, 45, 47, 68], "id": [2, 3, 33, 43, 45, 51, 53, 54, 72, 74], "coeff": 2, "qubit": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 33, 35, 36, 37, 38, 41, 43, 44, 47, 50, 51, 52, 53, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 67, 68, 71, 74, 79], "unordered_map": [2, 33], "_term": 2, "full": [2, 3, 4, 18, 28, 31, 52, 53, 54, 66, 67, 68, 70, 72, 74, 75, 80], "composit": [2, 50], "spin": [2, 3, 4, 6, 8, 9, 10, 11, 12, 13, 19, 22, 23, 25, 27, 33, 36, 41, 47, 50, 52, 53, 58, 62, 63, 66, 68], "op": [2, 3, 12, 19, 47, 62, 68], "map": [2, 3, 5, 8, 9, 17, 20, 22, 25, 33, 45, 50, 68, 74], "individu": [2, 3, 38, 45, 53, 60], "bsf": 2, "from": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 25, 26, 27, 29, 31, 33, 34, 36, 37, 38, 41, 45, 47, 50, 52, 53, 54, 57, 58, 60, 62, 63, 66, 68, 71, 74, 75, 76, 79, 80], "creat": [2, 3, 5, 8, 9, 13, 14, 15, 17, 18, 20, 21, 25, 29, 30, 33, 35, 41, 44, 50, 51, 52, 53, 57, 58, 63, 64, 66, 68, 69, 71, 72, 74, 75, 76, 78, 79], "ident": [2, 12, 13, 17, 18, 20, 47, 50, 62], "numqubit": [2, 36], "given": [2, 3, 4, 7, 8, 9, 10, 13, 17, 18, 19, 20, 22, 23, 33, 45, 50, 51, 53, 54, 58, 62, 71], "o": [2, 9, 10, 14, 22, 36, 51, 52, 53, 54, 62, 63, 64, 65, 68, 72, 74, 76, 78, 79], "copi": [2, 15, 20, 29, 45, 47, 72, 74], "data_rep": 2, "serial": [2, 3, 12], "encod": [2, 3, 5, 9, 13, 18, 20, 33, 41, 53, 64, 67, 71], "via": [2, 3, 4, 5, 7, 11, 15, 20, 23, 25, 30, 32, 33, 35, 38, 40, 42, 44, 45, 47, 50, 51, 53, 54, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "real": [2, 8, 10, 12, 14, 16, 19, 20, 29, 57], "imaginari": [2, 4, 12], "part": [2, 3, 4, 12, 16, 18, 22, 33, 45, 68, 70, 72, 74], "append": [2, 3, 6, 8, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 27, 29, 37, 51, 53, 54, 60, 63, 66], "larg": [2, 4, 5, 12, 17, 22, 28, 40, 53, 54, 57, 67], "end": [2, 3, 4, 7, 10, 14, 15, 16, 17, 19, 20, 23, 25, 29, 33, 45, 51, 53, 54, 58, 60, 63, 67, 72, 74], "total": [2, 3, 4, 8, 9, 11, 12, 14, 20, 22, 52, 53, 54, 58, 63, 66, 74], "destructor": 2, "iter": [2, 3, 4, 9, 12, 18, 20, 22, 23, 26, 27, 33, 45], "begin": [2, 3, 4, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21, 23, 25, 29, 33, 45, 56, 63, 64, 67], "start": [2, 3, 4, 6, 14, 15, 18, 20, 23, 30, 31, 40, 45, 51, 53, 58, 60, 63, 68, 70, 76, 80], "equal": [2, 10, 20, 23, 29, 47, 53, 54, 58, 67], "v": [2, 3, 4, 8, 10, 12, 13, 18, 33, 36, 37, 42, 47, 52, 66, 68, 72], "noexcept": [2, 40], "subtract": 2, "multipli": [2, 12, 18], "true": [2, 3, 4, 5, 9, 11, 12, 15, 16, 17, 18, 20, 22, 27, 33, 37, 50, 51, 66, 72, 74, 79], "here": [2, 3, 4, 5, 7, 8, 9, 10, 12, 14, 17, 18, 20, 21, 22, 23, 25, 26, 30, 31, 33, 35, 36, 37, 40, 42, 50, 51, 52, 53, 60, 62, 63, 64, 65, 68, 70, 72, 74, 78, 79, 80], "consid": [2, 4, 5, 7, 9, 16, 17, 18, 19, 20, 36, 38, 47, 52, 53, 68, 74], "num_qubit": [2, 3, 19, 41, 52], "num_term": [2, 41], "get_coeffici": [2, 8, 12, 19, 41], "get": [2, 3, 10, 12, 14, 16, 17, 18, 20, 22, 25, 27, 29, 31, 33, 35, 36, 45, 51, 52, 53, 58, 62, 63, 66, 71, 72, 76, 79, 80], "throw": [2, 29], "except": [2, 3, 9, 12, 20, 29, 78], "get_raw_data": 2, "is_ident": [2, 41], "standard": [2, 3, 10, 20, 22, 27, 32, 33, 34, 35, 37, 40, 46, 53, 56, 57, 68, 70, 72, 74, 76, 78], "out": [2, 3, 7, 8, 9, 11, 12, 13, 14, 15, 18, 20, 22, 25, 27, 31, 33, 38, 45, 47, 53, 54, 58, 59, 60, 62, 63, 71, 74, 75, 78, 80], "to_str": [2, 8, 12, 19, 58], "printcoeffici": 2, "getdatarepresent": 2, "getdatatupl": 2, "fulli": [2, 3, 9, 11, 20, 31, 32, 51, 53, 64, 68, 72, 74, 78, 80], "distribute_term": 2, "numchunk": 2, "distribut": [2, 10, 16, 17, 20, 22, 23, 25, 31, 38, 52, 54, 58, 62, 64, 72, 78, 79, 80], "chunk": [2, 38], "for_each_term": [2, 8, 12, 19, 41], "give": [2, 13, 14, 17, 23, 31, 33, 48, 53, 54, 72, 74, 80], "functor": 2, "reduct": 2, "captur": [2, 13, 18, 22, 29, 31, 37, 50, 60, 80], "variabl": [2, 9, 12, 13, 15, 18, 22, 28, 31, 37, 38, 50, 51, 52, 53, 59, 63, 66, 72, 74, 79, 80], "for_each_pauli": [2, 41], "thrown": [2, 78], "than": [2, 3, 12, 13, 14, 15, 16, 18, 19, 22, 23, 24, 29, 40, 47, 52, 54, 58, 60, 67, 72, 74, 78], "user": [2, 3, 4, 5, 8, 9, 17, 20, 28, 31, 33, 35, 36, 38, 39, 42, 45, 50, 51, 52, 53, 54, 63, 66, 68, 71, 72, 74, 80], "should": [2, 3, 14, 18, 19, 22, 32, 33, 38, 40, 41, 43, 45, 51, 53, 54, 58, 71, 72, 74, 78, 79], "pass": [2, 3, 8, 9, 11, 12, 16, 19, 22, 29, 30, 33, 37, 38, 41, 45, 51, 53, 54, 60, 63, 65, 68, 69, 74, 78], "index": [2, 3, 5, 9, 11, 12, 16, 41, 43, 45, 47, 50, 53, 54, 71], "complex_matrix": 2, "to_matrix": [2, 10, 12, 50], "dens": 2, "to_sparse_matrix": 2, "col": 2, "static": [2, 3, 33, 40, 45, 50, 68, 72, 78], "nterm": 2, "unsign": 2, "seed": [2, 3, 4, 8, 9, 13, 17, 20, 21, 22, 29, 54, 66], "random_devic": 2, "specifi": [2, 3, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 23, 24, 26, 27, 29, 33, 36, 37, 38, 40, 41, 42, 43, 45, 50, 51, 52, 53, 54, 58, 60, 63, 64, 66, 68, 71, 72, 74], "overrid": [2, 33, 54, 70, 72], "repeat": [2, 16, 17, 18, 22, 33], "from_word": 2, "pauliword": 2, "word": [2, 3, 8, 12, 18, 19], "g": [2, 3, 9, 13, 18, 19, 20, 26, 32, 33, 34, 37, 38, 39, 40, 41, 47, 50, 51, 52, 53, 54, 63, 68, 71, 72, 74, 75, 78, 79], "xyx": 2, "3rd": 2, "typenam": [2, 33, 35, 36, 37, 40, 44, 45, 76, 78], "qualifiedspinop": 2, "struct": [2, 33, 35, 36, 37, 40, 44, 52, 53, 62, 63, 64, 65, 68, 70, 78], "constexpr": [2, 35, 45, 52], "dyn": [2, 45], "qudit": [2, 34, 38, 40], "system": [2, 3, 4, 9, 12, 15, 19, 21, 22, 23, 28, 33, 38, 43, 45, 47, 50, 51, 53, 54, 57, 58, 62, 63, 66, 67, 70, 72, 75, 76, 78, 79], "inlin": [2, 33, 68], "new": [2, 3, 4, 7, 8, 9, 12, 14, 20, 30, 31, 33, 35, 47, 57, 68, 69, 72, 74, 78, 79, 80], "enable_if_t": 2, "qreg": [2, 3, 12, 13, 52], "contain": [2, 3, 4, 9, 10, 13, 17, 20, 30, 31, 33, 38, 40, 43, 47, 52, 54, 57, 58, 62, 63, 68, 71, 72, 78, 79, 80], "dynam": [2, 30, 35, 37, 38, 45, 51, 56, 57, 68, 78], "time": [2, 3, 4, 9, 10, 12, 13, 14, 16, 17, 18, 19, 22, 23, 24, 25, 29, 30, 32, 33, 36, 38, 45, 46, 51, 52, 53, 54, 58, 63, 64, 66, 67, 68, 72, 74, 79], "By": [2, 9, 10, 22, 28, 33, 40, 50, 51, 52, 53, 54, 58, 63, 76], "value_typ": 2, "indic": [2, 3, 4, 8, 20, 37, 40, 41, 45, 50, 71], "underli": [2, 3, 9, 22, 33, 43, 45, 51, 53, 71], "interfac": [2, 3, 45, 54, 71, 72, 74, 76], "idx": [2, 3, 11, 18, 20, 45, 50, 53], "qspan": 2, "front": [2, 36, 44, 45, 65], "back": [2, 20, 36, 45, 47, 53, 63, 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33, 62], "encapsul": [2, 11, 33, 45, 53, 78], "observ": [2, 3, 4, 6, 8, 9, 10, 11, 12, 13, 17, 19, 21, 22, 25, 27, 36, 50, 51, 53, 54, 55, 57, 62, 64, 65, 66, 67, 71, 79], "call": [2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 14, 18, 20, 21, 22, 23, 25, 27, 29, 35, 36, 37, 40, 44, 50, 53, 54, 57, 58, 60, 63, 64, 65, 66, 67, 68, 71, 72, 74, 76], "measur": [2, 3, 5, 7, 9, 10, 11, 12, 14, 15, 17, 22, 23, 25, 30, 33, 34, 36, 37, 38, 40, 47, 50, 51, 53, 54, 56, 57, 58, 61, 63, 64, 68, 71, 79], "execut": [2, 4, 9, 14, 20, 29, 30, 31, 32, 33, 35, 37, 38, 43, 44, 50, 51, 53, 54, 57, 58, 59, 61, 62, 63, 64, 66, 68, 71, 74, 75, 76, 78, 79, 80], "ansatz": [2, 4, 6, 9, 13, 21, 22, 33, 36, 52, 53, 62], "circuit": [2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 27, 32, 33, 37, 38, 41, 42, 46, 47, 51, 52, 53, 54, 57, 58, 60, 62, 63, 68, 70], "global": [2, 3, 9, 13, 20, 33, 37, 52, 58, 63, 72], "expect": [2, 3, 4, 6, 8, 9, 10, 11, 12, 13, 17, 19, 20, 21, 22, 23, 25, 27, 30, 33, 50, 52, 53, 54, 58, 61, 66, 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"quantinuum": [51, 63], "quera": [51, 63], "nvidia": [52, 53], "cloud": [52, 74], "select": 52, "multipl": [52, 62, 66], "qpu": 52, "asynchron": 52, "faq": 52, "processor": [53, 62, 66], "mqpu": 53, "distribut": [53, 74], "mode": [53, 54], "remot": [53, 74], "support": [53, 54, 72, 74], "argument": 53, "serial": 53, "access": [53, 74], "vector": 54, "featur": 54, "environ": 54, "variabl": 54, "option": 54, "node": 54, "addit": [54, 74], "openmp": 54, "cpu": 54, "onli": 54, "product": 54, "clifford": 54, "stim": 54, "fermioniq": 54, "default": 54, "build": [56, 60, 72], "your": [56, 58, 70, 79], "first": [56, 58], "what": 57, "i": 57, "troubleshoot": 59, "debug": 59, "verbos": 59, "output": 59, "expect": 62, "valu": 62, "across": [62, 66], "provid": 63, "workflow": 66, "avail": 66, "batch": 66, "term": 66, "101": 67, "work": 68, "ir": 68, "extend": [69, 71], "own": 70, "pass": 70, "new": 71, "circuitsimul": 71, "requir": [71, 74], "subtyp": 71, "method": 71, "overrid": 71, "let": 71, "see": 71, "thi": 71, "sourc": 72, "prerequisit": 72, "toolchain": [72, 78], "host": [72, 74], "runtim": 72, "guid": 73, "docker": 74, "singular": 74, "wheel": 74, "pre": 74, "binari": [74, 78], "develop": 74, "v": 74, "connect": 74, "tunnel": 74, "ssh": 74, "dgx": 74, "jupyterlab": 74, "tool": [74, 77], "pypi": 74, "In": 74, "imag": 74, "updat": 74, "compat": 74, "system": 74, "next": 74, "step": 74, "cmake": 75, "project": 76, "other": 77, "softwar": 77, "call": 78, "interfac": 78, "between": 78, "differ": 78, "valid": 79, "version": 80}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 8, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "nbsphinx": 4, "sphinx": 57}, "alltitles": {"Quantum Operators": [[41, "quantum-operators"]], "cudaq::spin_op": [[41, "cudaq-spin-op"]], "Quantum Types": [[45, "quantum-types"]], "cudaq::qudit": [[45, "cudaq-qudit-levels"]], "cudaq::qubit": [[45, "cudaq-qubit"]], "Quantum Containers": [[45, "quantum-containers"]], "cudaq::qview": [[45, "cudaq-qview-levels-2"]], "cudaq::qvector": [[45, "cudaq-qvector-levels-2"]], "cudaq::qarray": [[45, "cudaq-qarray-n-levels-2"]], "cudaq::qspan (Deprecated. Use cudaq::qview instead.)": [[45, "cudaq-qspan-n-levels-deprecated-use-cudaq-qview-levels-instead"]], "cudaq::qreg (Deprecated. Use cudaq::qvector instead.)": [[45, "cudaq-qreg-n-levels-deprecated-use-cudaq-qvector-levels-instead"]], "Common Quantum Programming Patterns": [[42, "common-quantum-programming-patterns"]], "Compute-Action-Uncompute": [[42, "compute-action-uncompute"]], "CUDA-Q Backends": [[49, "cuda-q-backends"]], "Backend Targets": [[49, null]], "Specifications": [[46, "specifications"]], "Sub-circuit Synthesis": [[44, "sub-circuit-synthesis"]], "Quantum Platform": [[43, "quantum-platform"]], "Quantum Intrinsic Operations": [[40, "quantum-intrinsic-operations"]], "Operations on cudaq::qubit": [[40, "operations-on-cudaq-qubit"]], "CUDA-Q Applications": [[48, "cuda-q-applications"]], "Quake Dialect": [[47, "quake-dialect"]], "General Introduction": [[47, "general-introduction"]], "Motivation": [[47, "motivation"]], "CUDA-Q": [[30, "cuda-q"], [32, null]], "Contents": [[30, null], [73, null], [55, null]], "Machine Model": [[38, "machine-model"]], "Example Programs": [[36, "example-programs"]], "Hello World - Simple Bell State": [[36, "hello-world-simple-bell-state"]], "GHZ State Preparation and Sampling": [[36, "ghz-state-preparation-and-sampling"]], "Quantum Phase Estimation": [[36, "quantum-phase-estimation"]], "Deuteron Binding Energy Parameter Sweep": [[36, "deuteron-binding-energy-parameter-sweep"]], "Grover\u2019s Algorithm": [[36, "grover-s-algorithm"]], "Iterative Phase Estimation": [[36, "iterative-phase-estimation"]], "Control Flow": [[34, "control-flow"]], "Just-in-Time Kernel Creation": [[35, "just-in-time-kernel-creation"]], "Quantum Kernels": [[37, "quantum-kernels"]], "Namespace and Standard": [[39, "namespace-and-standard"]], "CUDA-Q Releases": [[31, "cuda-q-releases"]], "Language Specification": [[32, "language-specification"]], "Quantum Algorithmic Primitives": [[33, "quantum-algorithmic-primitives"]], "cudaq::sample": [[33, "cudaq-sample"]], "cudaq::observe": [[33, "cudaq-observe"]], "cudaq::optimizer (deprecated, functionality moved to CUDA-Q libraries)": [[33, "cudaq-optimizer-deprecated-functionality-moved-to-cuda-q-libraries"]], "cudaq::gradient (deprecated, functionality moved to CUDA-Q libraries)": [[33, "cudaq-gradient-deprecated-functionality-moved-to-cuda-q-libraries"]], "Working with the CUDA-Q IR": [[68, "working-with-the-cuda-q-ir"]], "Using Quantum Hardware Providers": [[63, "using-quantum-hardware-providers"]], "Amazon Braket": [[63, "amazon-braket"], [51, "amazon-braket"]], "IonQ": [[63, "ionq"], [51, "ionq"]], "IQM": [[63, "iqm"], [51, "iqm"]], "OQC": [[63, "oqc"], [51, "oqc"]], "ORCA Computing": [[63, "orca-computing"], [51, "orca-computing"]], "Quantinuum": [[63, "quantinuum"], [51, "quantinuum"]], "QuEra Computing": [[63, "quera-computing"], [51, "quera-computing"]], "Building Kernels": [[60, "building-kernels"]], "Computing Expectation Values": [[62, "computing-expectation-values"]], "Parallelizing across Multiple Processors": [[62, "parallelizing-across-multiple-processors"]], "CUDA-Q by Example": [[61, "cuda-q-by-example"]], "Multi-GPU Workflows": [[66, "multi-gpu-workflows"]], "Available Targets": [[66, "available-targets"]], "Parallelization across Multiple Processors": [[66, "parallelization-across-multiple-processors"]], "Batching Hamiltonian Terms": [[66, "batching-hamiltonian-terms"]], "Circuit Batching": [[66, "circuit-batching"]], "Multi-control Synthesis": [[65, "multi-control-synthesis"]], "Quantum Computing 101": [[67, "quantum-computing-101"]], "Quantum States": [[67, "quantum-states"]], "Quantum Gates": [[67, "quantum-gates"]], "Measurements": [[67, "measurements"], [24, "Measurements"]], "Introduction": [[64, "introduction"], [74, "introduction"]], "Extending CUDA-Q": [[69, "extending-cuda-q"]], "CUDA-Q Versions": [[80, "cuda-q-versions"]], "Quick Start": [[79, "quick-start"], [52, "quick-start"], [50, "quick-start"]], "Install CUDA-Q": [[79, "install-cuda-q"]], "Validate your Installation": [[79, "validate-your-installation"]], "Extending CUDA-Q with a new Simulator": [[71, "extending-cuda-q-with-a-new-simulator"]], "CircuitSimulator": [[71, "circuitsimulator"]], "Required Circuit Simulator Subtype Method Overrides": [[71, "id1"]], "Let\u2019s see this in action": [[71, "let-s-see-this-in-action"]], "Create your own CUDA-Q Compiler Pass": [[70, "create-your-own-cuda-q-compiler-pass"]], "Using CUDA and CUDA-Q in a Project": [[76, "using-cuda-and-cuda-q-in-a-project"]], "CUDA-Q and CMake": [[75, "cuda-q-and-cmake"]], "Installation from Source": [[72, "installation-from-source"]], "Prerequisites": [[72, "prerequisites"]], "Build Dependencies": [[72, "build-dependencies"]], "CUDA": [[72, "cuda"]], "Toolchain": [[72, "toolchain"]], "Building CUDA-Q": [[72, "building-cuda-q"]], "Python Support": [[72, "python-support"]], "C++ Support": [[72, "c-support"]], "Installation on the Host": [[72, "installation-on-the-host"]], "CUDA Runtime Libraries": [[72, "cuda-runtime-libraries"]], "MPI": [[72, "mpi"]], "Integration with other Software Tools": [[77, "integration-with-other-software-tools"]], "Integrating with Third-Party Libraries": [[78, "integrating-with-third-party-libraries"]], "Calling a CUDA-Q library from C++": [[78, "calling-a-cuda-q-library-from-c"]], "Calling an C++ library from CUDA-Q": [[78, "calling-an-c-library-from-cuda-q"]], "Interfacing between binaries compiled with a different toolchains": [[78, "interfacing-between-binaries-compiled-with-a-different-toolchains"]], "Installation Guide": [[73, "installation-guide"]], "Local Installation": [[74, "local-installation"]], "Docker": [[74, "docker"]], "Singularity": [[74, "singularity"]], "Python wheels": [[74, "python-wheels"]], "Pre-built binaries": [[74, "pre-built-binaries"]], "Development with VS Code": [[74, "development-with-vs-code"]], "Using a Docker container": [[74, "using-a-docker-container"]], "Using a Singularity container": [[74, "using-a-singularity-container"]], "Connecting to a Remote Host": [[74, "connecting-to-a-remote-host"]], "Developing with Remote Tunnels": [[74, "developing-with-remote-tunnels"]], "Remote Access via SSH": [[74, "remote-access-via-ssh"]], "DGX Cloud": [[74, "dgx-cloud"]], "Get Started": [[74, "get-started"]], "Use JupyterLab": [[74, "use-jupyterlab"]], "Use VS Code": [[74, "use-vs-code"]], "Additional CUDA Tools": [[74, "additional-cuda-tools"]], "Installation via PyPI": [[74, "installation-via-pypi"]], "Installation In Container Images": [[74, "installation-in-container-images"]], "Installing Pre-built Binaries": [[74, "installing-pre-built-binaries"]], "Distributed Computing with MPI": [[74, "distributed-computing-with-mpi"]], "Updating CUDA-Q": [[74, "updating-cuda-q"]], "Dependencies and Compatibility": [[74, "dependencies-and-compatibility"]], "Supported Systems": [[74, "id10"]], "Requirements for GPU Simulation": [[74, "id11"]], "Next Steps": [[74, "next-steps"]], "NVIDIA Quantum Cloud": [[52, "nvidia-quantum-cloud"]], "Simulator Backend Selection": [[52, "simulator-backend-selection"]], "Multiple GPUs": [[52, "multiple-gpus"]], "Simulator Backends": [[52, "id1"]], "Multiple QPUs Asynchronous Execution": [[52, "multiple-qpus-asynchronous-execution"]], "FAQ": [[52, "faq"]], "CUDA-Q Basics": [[55, "cuda-q-basics"]], "CUDA-Q Hardware Backends": [[51, "cuda-q-hardware-backends"]], "Setting Credentials": [[51, "setting-credentials"], [51, "ionq-backend"], [51, "anyon-backend"], [51, "id7"], [51, "id10"], [51, "id13"], [51, "quantinuum-backend"], [51, "quera-backend"]], "Submission from C++": [[51, "submission-from-c"], [51, "id2"], [51, "id5"], [51, "id8"], [51, "id11"], [51, "id14"], [51, "id17"], [51, "id20"]], "Submission from Python": [[51, "submission-from-python"], [51, "id3"], [51, "id6"], [51, "id9"], [51, "id12"], [51, "id15"], [51, "id18"], [51, "id21"]], "Anyon Technologies/Anyon Computing": [[51, "anyon-technologies-anyon-computing"]], "What is a CUDA-Q kernel?": [[57, "what-is-a-cuda-q-kernel"]], "CUDA-Q Dynamics": [[50, "cuda-q-dynamics"]], "Operator": [[50, "operator"]], "Builtin Operators": [[50, "id1"]], "Time-Dependent Dynamics": [[50, "time-dependent-dynamics"]], "Numerical Integrators": [[50, "numerical-integrators"], [50, "id2"]], "Building your first CUDA-Q Program": [[56, "building-your-first-cuda-q-program"]], "CUDA-Q Simulation Backends": [[54, "cuda-q-simulation-backends"]], "State Vector Simulators": [[54, "state-vector-simulators"]], "Features": [[54, "features"]], "Single-GPU": [[54, "single-gpu"]], "Environment variable options supported in single-GPU mode": [[54, "id4"]], "Multi-node multi-GPU": [[54, "multi-node-multi-gpu"], [54, "id2"]], "Additional environment variable options for multi-node multi-GPU mode": [[54, "id5"]], "OpenMP CPU-only": [[54, "openmp-cpu-only"]], "Tensor Network Simulators": [[54, "tensor-network-simulators"]], "Matrix product state": [[54, "matrix-product-state"]], "Clifford-Only Simulator": [[54, "clifford-only-simulator"]], "Stim (CPU)": [[54, "stim-cpu"]], "Fermioniq": [[54, "fermioniq"]], "Default Simulator": [[54, "default-simulator"]], "Running your first CUDA-Q Program": [[58, "running-your-first-cuda-q-program"]], "Sample": [[58, "sample"], [23, "Sample"]], "Observe": [[58, "observe"], [23, "Observe"]], "Running on a GPU": [[58, "running-on-a-gpu"]], "Multi-Processor Platforms": [[53, "multi-processor-platforms"]], "NVIDIA MQPU Platform": [[53, "nvidia-mqpu-platform"]], "Parallel distribution mode": [[53, "parallel-distribution-mode"]], "Remote MQPU Platform": [[53, "remote-mqpu-platform"]], "Supported Kernel Arguments": [[53, "supported-kernel-arguments"]], "Kernel argument serialization": [[53, "id4"]], "Accessing Simulated Quantum State": [[53, "accessing-simulated-quantum-state"]], "Troubleshooting": [[59, "troubleshooting"]], "Debugging and Verbose Simulation Output": [[59, "debugging-and-verbose-simulation-output"]], "Visualization": [[29, "Visualization"]], "Qubit Visualization": [[29, "Qubit-Visualization"]], "Kernel Visualization": [[29, "Kernel-Visualization"]], "Compiling Unitaries Using Diffusion Models": [[20, "Compiling-Unitaries-Using-Diffusion-Models"]], "Diffusion model pipeline": [[20, "Diffusion-model-pipeline"]], "Setup and compilation": [[20, "Setup-and-compilation"]], "Load model": [[20, "Load-model"]], "Unitary compilation": [[20, "Unitary-compilation"]], "Convert tensors to CUDA-Q": [[20, "Convert-tensors-to-CUDA-Q"]], "Evaluate generated circuits": [[20, "Evaluate-generated-circuits"]], "Simulate kernels": [[20, "Simulate-kernels"]], "Compare unitaries": [[20, "Compare-unitaries"]], "Choosing the circuit you need": [[20, "Choosing-the-circuit-you-need"]], "Variational Quantum Eigensolver": [[21, "Variational-Quantum-Eigensolver"]], "Using CUDA-Q Optimizers": [[21, "Using-CUDA-Q-Optimizers"]], "Integration with Third-Party Optimizers": [[21, "Integration-with-Third-Party-Optimizers"]], "Optimizing Performance": [[28, "Optimizing-Performance"]], "Gate Fusion": [[28, "Gate-Fusion"]], "VQE with gradients, active spaces, and gate fusion": [[22, "VQE-with-gradients,-active-spaces,-and-gate-fusion"]], "The Basics of VQE": [[22, "The-Basics-of-VQE"]], "Installing/Loading Relevant Packages": [[22, "Installing/Loading-Relevant-Packages"]], "Implementing VQE in CUDA-Q": [[22, "Implementing-VQE-in-CUDA-Q"]], "Parallel Parameter Shift Gradients": [[22, "Parallel-Parameter-Shift-Gradients"], [27, "Parallel-Parameter-Shift-Gradients"]], "Using an Active Space": [[22, "Using-an-Active-Space"]], "Gate Fusion for Larger Circuits": [[22, "Gate-Fusion-for-Larger-Circuits"]], "Midcircuit Measurement and Conditional Logic": [[24, "Midcircuit-Measurement-and-Conditional-Logic"]], "Noisy Simulation": [[25, "Noisy-Simulation"], [3, "noisy-simulation"]], "Operators": [[26, "Operators"], [2, "operators"]], "Constructing Spin Operators": [[26, "Constructing-Spin-Operators"]], "Pauli Words and Exponentiating Pauli Words": [[26, "Pauli-Words-and-Exponentiating-Pauli-Words"]], "Optimizers and Gradients": [[27, "Optimizers-and-Gradients"]], "Built in CUDA-Q Optimizers and Gradients": [[27, "Built-in-CUDA-Q-Optimizers-and-Gradients"]], "Third-Party Optimizers": [[27, "Third-Party-Optimizers"]], "Executing Quantum Circuits": [[23, "Executing-Quantum-Circuits"]], "Get state": [[23, "Get-state"]], "Parallelization Techniques": [[23, "Parallelization-Techniques"]], "Observe Async": [[23, "Observe-Async"]], "Sample Async": [[23, "Sample-Async"]], "Get State Async": [[23, "Get-State-Async"]], "Computing Magnetization With The Suzuki-Trotter Approximation": [[19, "Computing-Magnetization-With-The-Suzuki-Trotter-Approximation"]], "Problem Setup": [[19, "Problem-Setup"]], "Running the Simulation": [[19, "Running-the-Simulation"]], "Multi-reference Quantum Krylov Algorithm - H_2 Molecule": [[12, "Multi-reference-Quantum-Krylov-Algorithm---H_2-Molecule"]], "Setup": [[12, "Setup"]], "Computing the matrix elements": [[12, "Computing-the-matrix-elements"]], "Determining the ground state energy of the Subspace": [[12, "Determining-the-ground-state-energy-of-the-Subspace"]], "Factoring Integers With Shor\u2019s Algorithm": [[18, "Factoring-Integers-With-Shor's-Algorithm"]], "Shor\u2019s algorithm": [[18, "Shor's-algorithm"]], "Solving the order-finding problem classically": [[18, "Solving-the-order-finding-problem-classically"]], "Solving the order-finding problem with a quantum algorithm": [[18, "Solving-the-order-finding-problem-with-a-quantum-algorithm"]], "Inverse quantum Fourier transform": [[18, "Inverse-quantum-Fourier-transform"]], "Quantum kernels for modular exponentiation": [[18, "Quantum-kernels-for-modular-exponentiation"]], "The case N = 21 and a = 5:": [[18, "The-case-N-=-21-and-a-=-5:"]], "The case N = 21 and a = 4:": [[18, "The-case-N-=-21-and-a-=-4:"]], "Determining the order from the measurement results of the phase kernel": [[18, "Determining-the-order-from-the-measurement-results-of-the-phase-kernel"]], "Postscript": [[18, "Postscript"]], "Hybrid Quantum Neural Networks": [[11, "Hybrid-Quantum-Neural-Networks"]], "Quantum Volume": [[16, "Quantum-Volume"]], "Max-Cut with QAOA": [[13, "Max-Cut-with-QAOA"]], "Using the Hadamard Test to Determine Quantum Krylov Subspace Decomposition Matrix Elements": [[10, "Using-the-Hadamard-Test-to-Determine-Quantum-Krylov-Subspace-Decomposition-Matrix-Elements"]], "Numerical result as a reference:": [[10, "Numerical-result-as-a-reference:"]], "Using Sample to perform the Hadamard test": [[10, "Using-Sample-to-perform-the-Hadamard-test"]], "Multi-GPU evaluation of QKSD matrix elements using the Hadamard Test": [[10, "Multi-GPU-evaluation-of-QKSD-matrix-elements-using-the-Hadamard-Test"]], "Classically Diagonalize the Subspace Matrix": [[10, "Classically-Diagonalize-the-Subspace-Matrix"]], "Quantum Fourier Transform": [[14, "Quantum-Fourier-Transform"]], "Quantum Fourier Transform revisited": [[14, "Quantum-Fourier-Transform-revisited"]], "Readout Error Mitigation": [[17, "Readout-Error-Mitigation"]], "Inverse confusion matrix from single-qubit noise model": [[17, "Inverse-confusion-matrix-from-single-qubit-noise-model"]], "Inverse confusion matrix from k local confusion matrices": [[17, "Inverse-confusion-matrix-from-k-local-confusion-matrices"]], "Inverse of full confusion matrix": [[17, "Inverse-of-full-confusion-matrix"]], "Quantum Teleporation": [[15, "Quantum-Teleporation"]], "Teleportation explained": [[15, "Teleportation-explained"]], "Deutsch\u2019s Algorithm": [[7, "Deutsch's-Algorithm"]], "XOR \\oplus": [[7, "XOR-\\oplus"]], "Quantum oracles": [[7, "Quantum-oracles"]], "Phase oracle": [[7, "Phase-oracle"]], "Quantum parallelism": [[7, "Quantum-parallelism"]], "Deutschs\u2019 Algorithm:": [[7, "Deutschs'-Algorithm:"]], "Divisive Clustering With Coresets Using CUDA-Q": [[9, "Divisive-Clustering-With-Coresets-Using-CUDA-Q"]], "Data preprocessing": [[9, "Data-preprocessing"]], "Quantum functions": [[9, "Quantum-functions"]], "Divisive Clustering Function": [[9, 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33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 52, 54, 55, 56, 58, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 77, 78, 79, 82, 83], "python": [0, 1, 2, 9, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 46, 47, 50, 52, 54, 55, 56, 58, 60, 61, 62, 63, 64, 65, 66, 67, 74, 81, 82, 83], "quantum": [0, 3, 8, 14, 18, 20, 21, 23, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 40, 46, 48, 49, 51, 52, 53, 56, 58, 59, 60, 62, 63, 64, 66, 68, 71, 74, 75, 77, 78, 79, 81, 82, 83], "oper": [0, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 44, 46, 47, 48, 49, 53, 54, 56, 58, 60, 62, 63, 64, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 82, 83], "cuda": [1, 6, 7, 10, 11, 12, 14, 15, 17, 20, 24, 25, 27, 30, 31, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 54, 55, 61, 62, 64, 65, 66, 67, 68, 69, 70, 80], "q": [1, 6, 7, 10, 11, 12, 14, 15, 17, 18, 19, 20, 24, 25, 26, 27, 28, 30, 31, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 54, 55, 61, 62, 64, 65, 66, 67, 68, 69, 70, 80], "provid": [1, 2, 3, 4, 7, 8, 9, 10, 12, 13, 15, 18, 19, 20, 21, 22, 27, 28, 29, 32, 34, 35, 37, 40, 42, 43, 45, 46, 47, 49, 52, 53, 54, 55, 56, 59, 63, 64, 66, 67, 69, 71, 73, 74, 75, 77, 78, 81], "default": [1, 2, 3, 20, 23, 24, 26, 31, 35, 39, 42, 47, 52, 53, 54, 55, 60, 65, 66, 71, 74, 75, 77, 79, 81, 82], "set": [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 17, 18, 21, 23, 24, 30, 31, 32, 35, 37, 39, 42, 49, 52, 54, 55, 56, 58, 60, 65, 75, 77, 81, 82], "These": [1, 2, 8, 12, 13, 14, 17, 19, 21, 23, 27, 29, 34, 39, 42, 46, 47, 49, 51, 54, 55, 56, 71, 75, 77], "can": [1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 54, 55, 56, 58, 59, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83], "us": [1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 26, 27, 28, 29, 31, 32, 33, 35, 36, 37, 38, 39, 42, 43, 45, 46, 49, 52, 53, 54, 55, 56, 58, 59, 60, 62, 63, 64, 66, 68, 69, 70, 71, 73, 74, 75, 78, 81, 82, 83], "kernel": [1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 38, 40, 42, 43, 44, 45, 46, 47, 48, 53, 54, 56, 57, 58, 60, 63, 64, 65, 66, 67, 68, 69, 70, 71, 79, 81, 82, 83], "librari": [1, 2, 8, 11, 13, 19, 22, 25, 31, 32, 33, 34, 38, 39, 41, 46, 47, 52, 56, 64, 71, 73, 74, 77, 79, 80, 83], "sinc": [1, 2, 4, 5, 7, 13, 14, 15, 16, 18, 19, 21, 24, 47, 51, 55, 56, 59, 64, 65, 68, 71, 77, 78, 81], "intrins": [1, 39, 46, 47, 49], "nativ": [1, 34, 40, 42, 43, 78], "support": [1, 2, 3, 4, 18, 24, 31, 32, 33, 34, 39, 40, 42, 44, 47, 52, 53, 59, 60, 65, 66, 69, 70, 73, 81, 82, 83], "specif": [1, 2, 3, 9, 12, 21, 26, 32, 35, 39, 41, 42, 43, 44, 47, 49, 52, 53, 54, 55, 56, 59, 60, 62, 66, 70, 71, 74, 75, 77, 79, 81], "target": [1, 2, 3, 7, 8, 9, 10, 11, 12, 14, 23, 24, 25, 27, 30, 31, 33, 35, 42, 45, 49, 52, 53, 54, 55, 56, 60, 62, 64, 65, 67, 70, 71, 73, 74, 75, 77, 82, 83], "depend": [1, 3, 7, 9, 12, 14, 16, 19, 20, 21, 26, 30, 32, 35, 40, 49, 54, 55, 56, 81, 82], "backend": [1, 2, 5, 6, 8, 9, 10, 13, 17, 23, 29, 30, 32, 33, 35, 52, 55, 60, 65, 68, 71, 74, 75, 77, 81, 82, 83], "architectur": [1, 2, 11, 32, 34, 40, 49, 53, 55, 65, 68, 70, 74, 75, 77, 82], "nvq": [1, 33, 35, 38, 53, 54, 55, 56, 60, 64, 65, 66, 67, 71, 74, 77, 78, 79, 81, 82, 83], "compil": [1, 2, 3, 9, 13, 32, 33, 34, 35, 38, 39, 40, 44, 46, 47, 53, 54, 55, 56, 60, 64, 65, 66, 67, 71, 74, 75, 77, 78, 79, 82, 83], "automat": [1, 3, 13, 23, 40, 53, 55, 56, 65, 75, 77, 81], "decompos": [1, 4, 17, 21], "appropri": [1, 2, 7, 8, 9, 15, 16, 34, 42, 55, 62, 75, 77], "The": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 60, 62, 64, 65, 66, 68, 69, 70, 71, 73, 74, 75, 77, 79, 81, 82, 83], "section": [1, 7, 8, 10, 13, 15, 19, 21, 23, 28, 30, 37, 55, 56, 62, 75, 77, 81, 82], "list": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 28, 29, 31, 33, 35, 39, 51, 52, 53, 54, 56, 62, 65, 68, 69, 70, 75, 77, 81, 82, 83], "implement": [1, 2, 3, 4, 7, 10, 12, 14, 15, 16, 17, 19, 20, 21, 27, 34, 35, 40, 41, 42, 44, 46, 47, 49, 53, 56, 65, 66, 69, 71, 73, 74, 75, 77, 81], "transform": [1, 4, 7, 11, 12, 21, 23, 32, 34, 38, 71, 73], "state": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 27, 31, 32, 33, 35, 39, 40, 42, 47, 49, 52, 53, 54, 58, 60, 62, 64, 65, 66, 68, 74, 75, 81, 82, 83], "ar": [1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 42, 44, 46, 47, 48, 49, 52, 53, 54, 55, 56, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 74, 75, 77, 79, 81, 82, 83], "templat": [1, 2, 22, 35, 37, 38, 39, 42, 46, 47, 66, 71, 73, 74, 79, 81], "argument": [1, 2, 3, 7, 9, 14, 16, 18, 24, 26, 31, 35, 37, 39, 46, 47, 52, 53, 58, 60, 64, 67, 68, 71, 74, 77, 81], "allow": [1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 21, 23, 24, 29, 33, 35, 37, 39, 40, 52, 56, 58, 59, 60, 67, 68, 69, 70, 71, 73, 77, 78, 83], "invok": [1, 2, 3, 35, 37, 39, 44, 52, 53, 56, 66, 71, 81], "version": [1, 3, 4, 5, 11, 13, 14, 15, 19, 21, 24, 25, 32, 33, 35, 44, 51, 52, 53, 54, 55, 56, 60, 71, 74, 75, 77, 78, 81, 82], "see": [1, 2, 3, 5, 6, 7, 8, 9, 15, 16, 17, 19, 21, 23, 30, 31, 33, 35, 37, 39, 47, 49, 51, 52, 53, 54, 55, 56, 58, 60, 66, 68, 69, 70, 71, 73, 75, 77, 78, 79, 81, 82, 83], "addition": [1, 19, 33, 53, 77, 83], "overload": [1, 2, 3, 35, 42, 43, 47, 49], "broadcast": [1, 2, 3, 12, 14, 42], "singl": [1, 2, 3, 4, 5, 9, 12, 13, 15, 16, 17, 20, 22, 23, 30, 31, 35, 38, 39, 40, 42, 47, 52, 53, 54, 55, 60, 62, 64, 65, 66, 68, 69, 70, 71, 81], "across": [1, 2, 3, 7, 10, 21, 23, 33, 42, 52, 54, 55, 56, 65, 75, 77, 83], "vector": [1, 2, 3, 4, 6, 9, 10, 11, 12, 16, 17, 21, 31, 35, 37, 38, 39, 42, 45, 47, 49, 53, 54, 55, 62, 65, 66, 67, 68, 74, 75], "For": [1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 15, 17, 18, 19, 21, 28, 31, 33, 35, 37, 42, 49, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 65, 67, 68, 69, 70, 74, 75, 77, 79, 81, 82, 83], "exampl": [1, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 42, 48, 49, 52, 53, 54, 55, 56, 58, 60, 62, 64, 65, 66, 68, 69, 70, 73, 74, 75, 77, 78, 79, 81, 82, 83], "cudaq": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 36, 37, 38, 39, 41, 44, 45, 46, 52, 53, 54, 55, 56, 58, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 77, 78, 81, 82], "qvector": [1, 2, 3, 5, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28, 29, 31, 35, 38, 39, 42, 46, 54, 55, 56, 58, 60, 62, 64, 65, 67, 68, 70, 71, 81, 82], "flip": [1, 2, 3, 6, 13, 17, 18, 27, 56, 70], "each": [1, 2, 3, 5, 7, 8, 9, 12, 14, 15, 16, 17, 18, 20, 21, 23, 24, 25, 29, 31, 33, 35, 37, 40, 45, 49, 52, 53, 54, 55, 56, 60, 65, 68, 70, 71, 75, 77, 81, 82, 83], "thi": [1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 47, 49, 52, 53, 54, 55, 56, 58, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 75, 77, 78, 79, 81, 82, 83], "pauli": [1, 2, 3, 8, 9, 10, 12, 14, 16, 20, 24, 35, 43, 52, 60, 70], "matrix": [1, 2, 3, 4, 13, 14, 16, 17, 20, 21, 24, 25, 27, 31, 32, 33, 51, 52, 54, 62, 70, 74, 83], "It": [1, 2, 4, 7, 9, 15, 16, 17, 18, 20, 23, 32, 33, 35, 42, 47, 49, 52, 55, 60, 62, 65, 69, 70, 71, 74, 77, 79, 82, 83], "i": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 47, 49, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83], "also": [1, 2, 3, 7, 9, 13, 15, 18, 19, 21, 22, 24, 27, 29, 31, 33, 35, 39, 43, 52, 53, 54, 55, 56, 58, 59, 60, 62, 65, 68, 70, 71, 73, 74, 75, 77, 79, 82, 83], "known": [1, 2, 19, 21, 23, 39, 52, 66, 71], "NOT": [1, 35, 42, 70], "gate": [1, 2, 3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 25, 27, 31, 32, 33, 42, 46, 47, 49, 53, 56, 58, 62, 66, 67, 74, 83], "appli": [1, 2, 3, 5, 7, 8, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 23, 25, 27, 28, 35, 38, 39, 42, 46, 49, 54, 55, 56, 58, 62, 65, 66, 67, 69, 70, 71, 74], "0": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35, 37, 38, 39, 42, 43, 44, 45, 47, 49, 51, 52, 53, 54, 55, 56, 58, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 74, 75, 77, 79, 81, 82, 83], "1": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 52, 53, 54, 55, 56, 58, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 74, 75, 77, 81, 82, 83], "rotat": [1, 3, 9, 10, 13, 14, 15, 18, 19, 27, 31, 42, 43, 58, 64, 74], "\u03c0": 1, "about": [1, 2, 3, 7, 9, 18, 19, 20, 21, 22, 31, 33, 35, 49, 52, 53, 54, 55, 56, 59, 60, 65, 68, 75, 77, 79, 80, 81, 82, 83], "axi": [1, 11, 21, 22, 31], "enabl": [1, 2, 3, 5, 9, 13, 15, 24, 25, 34, 35, 37, 39, 40, 42, 44, 45, 46, 47, 51, 52, 53, 55, 56, 59, 60, 64, 65, 68, 71, 74, 75, 77, 81, 82], "one": [1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 19, 20, 21, 23, 24, 25, 31, 33, 35, 37, 38, 40, 42, 45, 49, 52, 53, 54, 55, 56, 61, 62, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 77, 81, 82, 83], "superposit": [1, 5, 7, 14, 31, 35, 38, 47, 55, 58, 60, 69, 70], "comput": [1, 2, 3, 4, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 22, 23, 24, 25, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 45, 47, 49, 52, 54, 55, 56, 59, 60, 63, 68, 69, 74, 75, 79, 81, 82, 83], "basi": [1, 2, 3, 4, 10, 12, 13, 15, 18, 21, 23, 24, 26, 27, 47, 54, 55, 69, 70], "sqrt": [1, 3, 5, 7, 10, 12, 13, 15, 16, 18, 27, 31, 38, 52, 56, 65, 70, 82], "2": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 52, 53, 54, 55, 56, 60, 62, 64, 65, 67, 68, 69, 70, 71, 75, 77, 79, 81, 82, 83], "an": [1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 26, 27, 28, 29, 30, 31, 32, 33, 35, 37, 39, 40, 42, 43, 45, 46, 47, 49, 50, 52, 53, 54, 55, 56, 58, 60, 62, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 79, 82, 83], "arbitrari": [1, 2, 3, 21, 33, 52, 53, 67, 81, 83], "\u03bb": 1, "exp": [1, 2, 12, 19, 38, 43, 52, 69], "i\u03bb": 1, "math": [1, 4, 7, 19, 54, 69], "pi": [1, 8, 9, 11, 14, 15, 17, 19, 20, 22, 23, 25, 29, 31, 38, 39, 44, 46, 52, 53, 54, 65, 69], "std": [1, 2, 3, 35, 37, 38, 39, 42, 43, 45, 46, 47, 54, 55, 56, 60, 65, 66, 68, 73, 74, 79, 81], "number": [1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 28, 29, 31, 35, 38, 43, 45, 47, 49, 52, 53, 54, 55, 56, 58, 60, 64, 65, 66, 67, 68, 69, 70, 71, 74, 77, 82], "\u03b8": 1, "co": [1, 15, 20, 31, 52, 69], "isin": 1, "sin": [1, 15, 31], "its": [1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 15, 16, 17, 18, 27, 33, 34, 35, 45, 47, 49, 50, 54, 55, 56, 60, 62, 65, 66, 70, 71, 74, 75, 77, 81, 82, 83], "4": [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 35, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 53, 54, 55, 56, 62, 65, 68, 69, 71, 75, 77, 81, 83], "i\u03c0": 1, "two": [1, 2, 3, 4, 7, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 27, 29, 31, 40, 49, 52, 53, 55, 56, 60, 62, 64, 65, 67, 69, 70, 77, 81], "qubit_1": [1, 7, 14, 62], "qubit_2": [1, 16], "univers": [1, 2, 9, 16, 21, 54, 70], "three": [1, 10, 18, 19, 21, 23, 40, 53, 54, 64, 69], "paramet": [1, 2, 3, 6, 8, 9, 11, 12, 13, 14, 17, 19, 21, 22, 24, 35, 39, 42, 47, 52, 53, 54, 56, 58, 62, 64, 65, 66, 68, 74, 75], "euler": [1, 52], "angl": [1, 2, 3, 6, 10, 13, 15, 18, 19, 29, 31, 38, 39, 42, 55, 58, 64, 65, 69], "theta": [1, 8, 9, 10, 11, 14, 15, 22, 23, 27, 29, 31, 35, 37, 38, 54, 55, 62, 64, 69], "phi": [1, 3, 4, 10, 35, 37, 53, 65, 69, 71], "\u03c6": 1, "lambda": [1, 2, 8, 9, 12, 13, 14, 18, 19, 20, 23, 29, 35, 38, 39, 44, 52, 65, 67, 68, 71], "i\u03c6": 1, "np": [1, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 31, 38, 39, 44, 46, 52, 53, 55, 56, 62, 65, 68, 75], "m_pi": [1, 38, 46, 65], "m_pi_2": [1, 38, 39, 54], "adj": [1, 42, 62], "method": [1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 18, 19, 20, 21, 22, 23, 28, 29, 35, 37, 42, 47, 52, 53, 55, 56, 60, 62, 65, 66], "ani": [1, 2, 3, 9, 12, 14, 19, 20, 21, 23, 24, 27, 29, 31, 35, 39, 41, 42, 44, 46, 47, 52, 53, 54, 56, 58, 60, 61, 62, 65, 66, 67, 74, 75, 77, 81, 82], "alloc": [1, 2, 3, 6, 14, 21, 35, 37, 38, 39, 40, 47, 55, 56, 58, 60, 66, 67, 74], "now": [1, 4, 5, 7, 9, 13, 14, 15, 16, 19, 21, 22, 23, 33, 49, 53, 60, 65, 66, 67, 68, 77, 82, 83], "again": [1, 5, 23, 24, 35, 49, 77, 79], "initi": [1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 14, 15, 16, 19, 20, 22, 23, 29, 35, 52, 53, 55, 62, 65, 68, 69, 70, 75, 77], "ctrl": [1, 2, 5, 7, 14, 17, 19, 24, 29, 31, 35, 37, 38, 42, 54, 55, 58, 62, 64, 65, 66, 67, 70, 71, 77, 82], "condit": [1, 2, 15, 16, 21, 27, 35, 36, 37, 39, 40, 56, 59, 70, 71], "more": [1, 2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 15, 18, 19, 21, 23, 28, 31, 33, 37, 40, 42, 43, 49, 53, 54, 55, 56, 59, 60, 62, 65, 68, 70, 75, 77, 79, 81, 82, 83], "wikipedia": [1, 52], "entri": [1, 3, 12, 35, 39, 55, 62, 65, 71, 77, 81], "ctrl_1": 1, "ctrl_2": 1, "00": [1, 4, 9, 13, 16, 24, 25, 27, 29, 56, 60, 68, 69, 70, 81, 82], "11": [1, 3, 4, 9, 11, 13, 16, 17, 18, 20, 21, 23, 24, 25, 27, 29, 31, 35, 52, 56, 60, 68, 69, 70, 71, 75, 77, 81, 82], "onli": [1, 2, 3, 5, 7, 9, 16, 18, 19, 21, 23, 24, 26, 31, 33, 35, 39, 40, 44, 47, 49, 52, 53, 54, 55, 59, 65, 70, 71, 73, 75, 77, 81, 82, 83], "both": [1, 3, 4, 5, 7, 11, 13, 19, 40, 49, 53, 55, 56, 70, 75, 77, 79], "000": [1, 15, 16, 18, 19, 54, 60], "111": [1, 9, 15, 16, 18, 19], "follow": [1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 28, 29, 31, 33, 35, 37, 39, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 58, 60, 61, 62, 64, 65, 66, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83], "common": [1, 3, 9, 10, 18, 19, 21, 22, 23, 35, 39, 42, 43, 71, 75], "convent": [1, 8, 11, 14, 24, 25], "all": [1, 2, 3, 9, 13, 16, 17, 18, 19, 20, 21, 23, 24, 25, 29, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 44, 45, 47, 49, 52, 53, 54, 55, 56, 60, 62, 64, 65, 68, 69, 70, 71, 75, 77, 78, 79, 81, 82, 83], "howev": [1, 4, 9, 13, 15, 16, 18, 21, 23, 24, 33, 49, 52, 53, 55, 81, 83], "behavior": [1, 2, 3, 9, 23, 33, 56, 83], "chang": [1, 2, 5, 9, 13, 15, 19, 30, 33, 35, 39, 52, 60, 77, 82, 83], "instead": [1, 2, 4, 9, 27, 41, 44, 53, 55, 56, 60, 75, 77, 81], "when": [1, 2, 3, 9, 12, 13, 14, 18, 19, 21, 33, 35, 40, 47, 49, 54, 55, 56, 60, 64, 65, 66, 71, 74, 75, 77, 81, 82, 83], "negat": [1, 2, 3, 42, 46, 47], "polar": [1, 42, 46, 56], "syntax": [1, 9, 33, 34, 39, 40, 42, 44, 53, 62, 65, 79, 83], "preced": [1, 42, 53], "01": [1, 4, 7, 13, 16, 21, 27, 29, 56, 69, 70], "10": [1, 4, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 23, 25, 27, 29, 31, 35, 38, 39, 56, 60, 62, 65, 66, 68, 69, 70, 71, 75, 77, 79], "notat": [1, 16, 69, 70], "context": [1, 2, 11, 40, 55, 56, 74], "valid": [1, 2, 3, 32, 39, 53, 56, 62, 65, 75, 77, 81], "either": [1, 7, 11, 14, 19, 40, 53, 55, 56, 65, 69, 70, 75, 77, 82], "similarli": [1, 7, 23, 55, 61, 70], "condition": 1, "respect": [1, 2, 3, 4, 8, 13, 14, 19, 23, 29, 35, 52, 53, 55, 60, 64, 68, 69, 70, 75, 77, 82], "e": [1, 2, 3, 4, 7, 8, 9, 10, 12, 14, 15, 16, 18, 19, 20, 21, 22, 28, 31, 34, 35, 36, 38, 39, 40, 41, 42, 43, 49, 52, 53, 54, 55, 56, 65, 71, 74, 75, 77, 81, 82], "project": [1, 56, 74, 75, 77, 78, 81], "onto": [1, 70], "eigenvector": [1, 2, 10, 12], "non": [1, 2, 3, 8, 10, 12, 18, 19, 33, 35, 39, 40, 47, 55, 56, 60, 64, 66, 83], "linear": [1, 5, 9, 11, 12, 15, 22, 27, 54, 60, 65, 69, 70], "avail": [1, 2, 3, 8, 9, 10, 21, 23, 29, 32, 33, 34, 35, 39, 40, 42, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 59, 60, 62, 63, 64, 65, 71, 75, 77, 82, 83], "first": [1, 2, 3, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 27, 29, 31, 32, 35, 47, 53, 54, 55, 56, 57, 62, 64, 65, 66, 67, 71, 77, 82], "api": [1, 13, 24, 28, 31, 32, 33, 35, 37, 41, 42, 45, 47, 52, 53, 54, 55, 56, 60, 62, 65, 66, 74, 75, 77, 79, 81, 83], "regist": [1, 2, 3, 5, 10, 13, 15, 19, 22, 26, 35, 38, 40, 47, 53, 55, 62, 65, 66, 67, 71, 74], "outsid": [1, 9, 33, 77, 81, 83], "Then": [1, 7, 18, 21, 26, 53, 65, 73, 74], "within": [1, 2, 3, 13, 22, 33, 35, 39, 41, 43, 47, 53, 55, 56, 59, 60, 62, 65, 66, 70, 73, 75, 77, 78, 79, 81, 82, 83], "like": [1, 2, 3, 4, 7, 8, 9, 10, 12, 13, 14, 15, 16, 19, 21, 22, 23, 24, 29, 30, 33, 35, 39, 47, 53, 55, 60, 62, 65, 66, 68, 69, 70, 71, 75, 77, 78, 81, 82, 83], "built": [1, 2, 4, 6, 8, 9, 12, 15, 23, 24, 27, 33, 53, 56, 59, 60, 75, 81, 82, 83], "abov": [1, 2, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 21, 23, 24, 35, 37, 42, 52, 53, 54, 55, 56, 60, 62, 64, 65, 67, 69, 70, 71, 74, 75, 77, 79, 81, 82], "level": [1, 2, 3, 13, 23, 25, 30, 33, 34, 35, 40, 42, 52, 53, 54, 55, 56, 69, 71, 74, 78, 83], "register_oper": [1, 13, 62], "accept": [1, 2, 3, 23, 24, 58, 75, 77, 82], "identifi": [1, 2, 3, 4, 13, 14, 19, 21, 75, 77], "string": [1, 2, 3, 5, 19, 25, 28, 31, 35, 37, 38, 45, 52, 56, 60, 66, 71, 77, 81], "numpi": [1, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 31, 38, 52, 62, 65, 68, 75], "arrai": [1, 2, 3, 4, 7, 10, 12, 13, 15, 16, 17, 18, 21, 24, 25, 27, 29, 47, 49, 52, 53, 55, 56, 62, 65, 66, 68, 71], "complex": [1, 2, 3, 4, 7, 8, 12, 16, 20, 27, 43, 49, 52, 55, 60, 62, 68, 69, 70, 81], "A": [1, 2, 3, 4, 7, 8, 9, 10, 12, 14, 16, 17, 18, 19, 20, 22, 29, 30, 31, 35, 38, 39, 42, 49, 52, 53, 60, 62, 65, 67, 68, 69, 70, 73, 74, 75, 77], "1d": [1, 2], "interpret": [1, 8, 59, 65, 75], "row": [1, 2, 3, 31, 62], "major": [1, 75], "import": [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 38, 43, 52, 53, 54, 55, 56, 58, 60, 62, 64, 65, 66, 68, 69, 70, 71, 75, 81, 82], "custom_h": 1, "custom_x": [1, 62], "def": [1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 35, 38, 39, 44, 46, 52, 54, 55, 56, 58, 60, 62, 64, 65, 66, 67, 68, 69, 70, 77, 82], "bell": [1, 13, 16, 35, 81], "sampl": [1, 2, 3, 5, 7, 8, 9, 13, 14, 17, 18, 19, 21, 27, 37, 53, 54, 55, 56, 57, 59, 62, 65, 66, 67, 68, 69, 70, 74, 77, 81, 82], "dump": [1, 2, 3, 27, 35, 38, 54, 55, 56, 60, 65, 66, 68, 81, 82], "macro": [1, 74], "cudaq_register_oper": 1, "uniqu": [1, 2, 3, 9, 14, 18, 21, 35, 40, 42, 47, 55, 79], "name": [1, 2, 3, 9, 13, 14, 16, 19, 35, 37, 42, 45, 51, 52, 53, 54, 55, 56, 64, 68, 70, 71, 74, 75, 77, 78, 81, 82], "represent": [1, 2, 3, 15, 16, 21, 24, 25, 31, 35, 39, 49, 52, 56, 71, 73, 74], "includ": [1, 2, 3, 4, 12, 13, 14, 17, 23, 33, 35, 38, 47, 52, 54, 56, 58, 59, 60, 62, 64, 65, 66, 67, 71, 73, 74, 75, 77, 79, 81, 82, 83], "m_sqrt1_2": 1, "__qpu__": [1, 2, 35, 38, 39, 46, 54, 55, 56, 58, 60, 64, 65, 66, 67, 71, 81, 82], "void": [1, 2, 3, 35, 37, 38, 39, 42, 43, 45, 46, 47, 56, 58, 60, 65, 67, 71, 73, 74, 79, 81, 82], "bell_pair": [1, 2, 3], "r": [1, 4, 13, 18, 19, 42, 47, 53, 54, 55, 56, 64, 65, 71, 77], "int": [1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 27, 35, 38, 39, 46, 47, 52, 54, 55, 56, 58, 60, 62, 64, 65, 66, 67, 68, 71, 74, 75, 79, 81, 82], "main": [1, 4, 5, 9, 19, 21, 33, 35, 38, 49, 54, 56, 60, 64, 65, 66, 67, 71, 75, 77, 79, 81, 82, 83], "auto": [1, 2, 35, 37, 38, 39, 43, 46, 47, 54, 55, 56, 58, 60, 64, 65, 66, 67, 71, 73, 81, 82], "count": [1, 2, 3, 5, 8, 9, 10, 12, 13, 14, 18, 19, 24, 25, 35, 37, 38, 47, 53, 54, 55, 56, 60, 65, 66, 67, 68, 71, 74], "bit": [1, 2, 3, 4, 5, 7, 13, 16, 17, 18, 19, 24, 25, 27, 35, 38, 40, 47, 49, 55, 56, 65, 66, 67, 69, 70, 74], "printf": [1, 35, 38, 47, 55, 64, 66, 67, 75], "n": [1, 2, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 23, 35, 37, 38, 39, 42, 43, 46, 52, 54, 55, 56, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 75, 79, 82], "data": [1, 2, 8, 11, 12, 13, 14, 15, 22, 32, 35, 39, 41, 43, 49, 55, 56, 64, 66, 67, 71, 74, 76, 77, 79, 81], "multi": [1, 4, 15, 16, 24, 25, 31, 32, 33, 34, 37, 40, 42, 46, 51, 53, 54, 60, 62, 63, 64, 69, 70, 74, 75, 81, 82, 83], "msb": 1, "order": [1, 2, 3, 4, 9, 12, 13, 14, 16, 31, 35, 43, 52, 53, 56, 60, 64], "big": [1, 8, 17, 24], "endian": [1, 17, 24, 25], "show": [1, 8, 9, 11, 13, 14, 15, 16, 18, 21, 22, 23, 31, 52, 55, 62, 64, 65, 75, 77], "differ": [1, 2, 3, 7, 9, 10, 11, 12, 13, 15, 16, 18, 19, 23, 24, 29, 31, 49, 53, 54, 55, 59, 60, 65, 68, 75, 77, 79, 82], "test": [1, 9, 11, 12, 17, 18, 19, 23, 32, 37, 68, 75, 77], "cnot": [1, 5, 9, 42, 58, 62, 70, 81], "my_cnot": 1, "print": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 31, 35, 38, 47, 52, 54, 55, 56, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 75, 81, 82], "500": [1, 23, 70, 82], "exact": [1, 9, 10, 13, 17, 21, 56], "random": [1, 2, 3, 4, 5, 8, 9, 13, 14, 16, 17, 18, 19, 21, 22, 23, 29, 31, 55, 56, 68], "construct": [1, 2, 8, 9, 10, 12, 17, 18, 20, 23, 29, 31, 32, 33, 35, 36, 37, 39, 47, 49, 52, 55, 58, 59, 60, 62, 63, 66, 71, 83], "second": [1, 2, 3, 4, 7, 8, 9, 12, 14, 18, 20, 47, 52, 54, 56, 60, 62, 65], "1j": [1, 12, 13], "xy": [1, 31], "kron": [1, 18], "my_xi": 1, "custom_xy_test": 1, "undo": 1, "prior": [1, 56, 65, 69, 70, 75, 77, 82], "1000": [1, 3, 9, 11, 13, 17, 18, 21, 24, 25, 27, 35, 53, 56, 60, 66, 68, 69, 70, 82], "mycnot": 1, "myxi": 1, "hardwar": [1, 9, 15, 19, 21, 24, 32, 33, 51, 56, 60, 63, 81, 83], "synthes": [1, 3, 21, 42, 46, 71], "current": [1, 2, 3, 9, 31, 33, 35, 45, 53, 55, 56, 74, 77, 81, 83], "orca": [1, 2, 25, 33, 51, 56, 69, 83], "which": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 27, 29, 31, 33, 35, 37, 40, 43, 47, 49, 52, 53, 55, 56, 62, 64, 65, 66, 68, 69, 70, 71, 74, 75, 77, 78, 81, 83], "doe": [1, 2, 3, 7, 9, 15, 16, 21, 31, 33, 35, 39, 47, 52, 54, 55, 75, 77, 79, 81, 82, 83], "increment": [1, 2, 68], "qumod": [1, 25, 69], "up": [1, 2, 3, 7, 9, 14, 15, 17, 21, 31, 37, 43, 52, 53, 56, 59, 64, 65, 68, 69, 71, 74, 77], "maximum": [1, 3, 8, 9, 21, 56, 69], "valu": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 29, 31, 32, 35, 37, 39, 43, 47, 49, 52, 54, 55, 56, 60, 63, 65, 68, 69, 70, 71, 75, 81, 82], "repres": [1, 2, 3, 4, 7, 8, 9, 14, 15, 16, 21, 27, 31, 35, 49, 52, 53, 56, 65, 69, 70, 71], "If": [1, 2, 3, 5, 7, 9, 11, 15, 16, 17, 18, 19, 20, 24, 26, 31, 35, 49, 52, 53, 54, 56, 60, 65, 68, 70, 75, 77, 81, 82], "where": [1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 23, 24, 30, 31, 34, 40, 42, 43, 47, 49, 52, 53, 56, 60, 62, 65, 68, 69, 70, 74, 75, 77, 79, 82], "alreadi": [1, 2, 3, 13, 19, 31, 69, 75, 77, 82], "ha": [1, 2, 3, 4, 5, 7, 9, 13, 14, 16, 17, 18, 19, 21, 24, 27, 29, 35, 42, 49, 53, 54, 56, 59, 60, 65, 68, 69, 70, 75, 77, 81], "effect": [1, 13, 21, 49, 56, 60, 68, 69, 70, 82], "rangl": [1, 4, 15, 18, 19, 21, 35, 82], "3": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 31, 33, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 52, 53, 54, 55, 56, 60, 62, 65, 67, 68, 69, 71, 74, 75, 77, 78, 82, 83], "cdot": [1, 5, 9, 12, 19], "d": [1, 2, 3, 9, 12, 16, 38, 39, 40, 47, 53, 65, 69, 75, 77], "reduc": [1, 2, 10, 13, 18, 19, 56], "minimum": [1, 14, 22, 54, 56, 69], "vacuum": [1, 65], "phase": [1, 2, 3, 5, 12, 15, 21, 42, 53, 65, 69], "shifter": [1, 65, 69], "add": [1, 2, 3, 9, 12, 14, 22, 27, 31, 33, 44, 52, 56, 65, 66, 69, 71, 73, 74, 75, 77, 83], "a_1": [1, 18, 19, 69], "creation": [1, 2, 4, 9, 34, 48, 52, 69, 74], "dagger": [1, 4, 10, 12, 21, 27, 44, 52, 69, 70], "shift": [1, 11, 54, 69, 77], "p": [1, 4, 8, 9, 10, 18, 27, 69, 75, 77], "left": [1, 2, 4, 5, 7, 10, 12, 13, 14, 15, 16, 24, 65, 69, 74, 77], "right": [1, 4, 10, 13, 14, 15, 25, 69], "17": [1, 9, 13, 16, 17, 18, 21, 31, 62, 71, 79], "beam": [1, 53, 65, 69], "splitter": [1, 53, 65, 69], "act": [1, 2, 3, 6, 7, 9, 14, 28, 49, 52, 56, 69, 70], "togeth": [1, 18, 32, 56, 69, 71, 82], "parameter": [1, 2, 3, 8, 9, 10, 13, 14, 20, 22, 23, 35, 37, 39, 42, 52, 54, 59, 62, 64, 66, 68, 69], "relat": [1, 2, 9, 14, 19, 21, 69, 71], "reflect": [1, 38, 56], "a_2": [1, 19, 69], "b": [1, 9, 23, 29, 35, 62, 65, 69], "_": [1, 4, 7, 11, 13, 18, 19, 21, 25, 31, 52, 69], "rang": [1, 2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 29, 31, 33, 38, 39, 46, 47, 52, 54, 55, 58, 62, 68, 69, 77, 82, 83], "34": [1, 9, 18], "return": [1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 29, 31, 35, 37, 38, 39, 42, 47, 49, 52, 54, 55, 56, 60, 64, 65, 66, 68, 69, 71, 73, 74, 75, 79, 81], "result": [1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 35, 36, 37, 38, 40, 49, 52, 53, 54, 55, 56, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 74, 77, 81, 82], "input": [1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 16, 21, 23, 28, 29, 35, 37, 38, 39, 46, 47, 55, 60, 62, 64, 65, 68], "class": [2, 3, 4, 9, 11, 21, 35, 37, 39, 43, 45, 47, 55, 56, 73, 74], "spin_op": [2, 8, 28, 35, 38, 42, 54, 55, 60, 64], "gener": [2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 18, 19, 22, 24, 25, 28, 31, 35, 37, 38, 39, 40, 42, 43, 46, 48, 53, 54, 56, 59, 64, 65, 66, 67, 70, 71, 73, 77, 81], "sum": [2, 3, 4, 11, 12, 13, 14, 17, 18, 21, 28, 43, 47, 65, 69, 70], "tensor": [2, 3, 11, 18, 28, 33, 43, 54, 55, 74, 83], "product": [2, 3, 5, 18, 28, 32, 33, 43, 54, 82, 83], "expos": [2, 3, 9, 13, 35, 37, 43, 45, 49, 55, 74], "typic": [2, 21, 35, 47, 54, 58, 59, 64, 71, 78, 79], "algebra": [2, 43, 64, 70], "programm": [2, 3, 35, 36, 37, 39, 40, 42, 44, 45, 47, 53, 55, 66], "defin": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 31, 33, 34, 35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 52, 54, 55, 56, 58, 59, 60, 62, 64, 65, 66, 67, 69, 70, 71, 74, 75, 77, 79, 81, 83], "primit": [2, 14, 34, 37, 40, 43, 47, 48, 55, 59, 81], "them": [2, 3, 8, 9, 10, 13, 16, 18, 21, 31, 33, 49, 52, 58, 70, 71, 75, 77, 79, 81, 82, 83], "compos": [2, 3, 11, 14, 21, 39, 40, 53, 65, 71], "larger": [2, 3, 7, 9, 10, 14, 21, 54, 56], "thereof": [2, 40, 43], "public": [2, 9, 35, 37, 43, 45, 47, 55, 73, 74, 77], "type": [2, 4, 5, 6, 7, 9, 13, 14, 15, 18, 20, 28, 34, 35, 37, 39, 40, 42, 43, 48, 52, 53, 55, 56, 58, 62, 64, 66, 70, 71, 74, 77, 81], "spin_op_term": 2, "bool": [2, 3, 13, 35, 39, 42, 43, 45, 55, 74, 81], "we": [2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 21, 22, 24, 25, 27, 31, 33, 35, 38, 42, 44, 49, 52, 53, 55, 56, 58, 59, 60, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83], "term": [2, 3, 4, 5, 8, 12, 13, 14, 16, 19, 20, 23, 24, 35, 42, 52, 53, 55, 56, 60, 64, 77], "binari": [2, 3, 5, 9, 11, 14, 15, 19, 24, 33, 53, 75, 79, 82, 83], "symplect": 2, "form": [2, 3, 9, 21, 23, 24, 31, 33, 35, 42, 47, 49, 52, 56, 71, 83], "size": [2, 3, 5, 8, 9, 10, 11, 12, 16, 17, 18, 19, 20, 35, 37, 38, 39, 40, 47, 54, 55, 56, 65, 66, 68, 77, 81], "nqubit": [2, 37, 38, 74], "element": [2, 3, 4, 15, 18, 19, 21, 29, 32, 35, 47, 55, 70], "x": [2, 3, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 31, 35, 37, 38, 39, 42, 43, 44, 46, 52, 53, 54, 55, 56, 58, 60, 62, 64, 65, 66, 67, 70, 71, 75, 77, 79, 82], "next": [2, 4, 5, 8, 9, 10, 12, 13, 17, 19, 20, 21, 23, 29, 31, 49, 65, 66, 71, 75], "z": [2, 3, 6, 8, 9, 11, 12, 13, 14, 16, 20, 21, 22, 24, 26, 27, 28, 29, 31, 35, 38, 42, 43, 52, 54, 55, 56, 60, 64, 66, 68, 75], "y": [2, 3, 5, 7, 8, 9, 11, 12, 13, 15, 18, 19, 20, 24, 26, 28, 29, 31, 35, 38, 42, 43, 52, 54, 55, 60, 64, 66, 75, 77, 79, 82], "site": [2, 3, 8, 13, 65, 82], "csr_spmatrix": 2, "tupl": [2, 3, 9, 13, 29, 35, 39, 65], "doubl": [2, 3, 22, 23, 35, 37, 38, 39, 42, 43, 46, 54, 55, 56, 60, 64, 65, 74, 75, 77], "size_t": [2, 35, 37, 39, 43, 45, 47, 55, 65, 66, 74, 79, 81], "typedef": 2, "zero": [2, 3, 5, 6, 10, 11, 12, 18, 19, 21, 40, 52, 55, 60, 69, 70], "spars": [2, 56], "function": [2, 3, 5, 6, 7, 8, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 31, 33, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 52, 53, 54, 55, 56, 58, 59, 60, 64, 66, 68, 69, 71, 74, 79, 81, 83], "pair": [2, 3, 8, 12, 14, 16, 17, 39, 45, 49, 77], "const": [2, 35, 37, 38, 39, 42, 43, 45, 47, 54, 56, 65, 73, 74, 79, 81], "termdata": 2, "constructor": [2, 3], "take": [2, 3, 4, 5, 7, 9, 12, 13, 14, 15, 17, 18, 20, 23, 29, 30, 33, 35, 37, 38, 39, 42, 43, 44, 45, 46, 47, 49, 53, 56, 59, 60, 62, 64, 65, 66, 67, 68, 71, 75, 77, 82, 83], "coeffici": [2, 3, 8, 12, 20, 28, 52, 69, 70], "constant": [2, 7, 20, 47, 49, 71], "id": [2, 3, 35, 45, 47, 53, 55, 56, 75, 77], "coeff": 2, "qubit": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 35, 37, 38, 39, 40, 43, 45, 46, 49, 52, 53, 54, 55, 56, 58, 59, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 74, 77, 82], "unordered_map": [2, 35], "_term": 2, "full": [2, 3, 4, 13, 19, 30, 33, 54, 55, 56, 68, 69, 70, 71, 73, 75, 77, 78, 83], "composit": [2, 52], "spin": [2, 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 20, 23, 24, 27, 29, 35, 38, 43, 49, 52, 54, 55, 56, 60, 64, 65, 68, 71], "op": [2, 3, 12, 13, 20, 49, 64, 71], "map": [2, 3, 5, 7, 8, 9, 13, 18, 21, 23, 27, 35, 47, 52, 71, 77], "individu": [2, 3, 40, 47, 55, 56, 62], "bsf": 2, "from": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 27, 28, 29, 31, 33, 35, 36, 38, 39, 40, 43, 47, 49, 52, 54, 55, 56, 59, 60, 62, 64, 65, 68, 71, 74, 77, 78, 79, 82, 83], "creat": [2, 3, 5, 8, 9, 13, 14, 15, 16, 18, 19, 21, 22, 25, 27, 31, 32, 35, 37, 43, 46, 52, 53, 54, 55, 59, 60, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 79, 81, 82], "ident": [2, 12, 13, 14, 18, 19, 21, 49, 52, 64, 69], "numqubit": [2, 38], "given": [2, 3, 4, 7, 8, 9, 10, 14, 18, 19, 20, 21, 23, 24, 25, 35, 47, 52, 53, 55, 56, 60, 64, 69, 74], "o": [2, 9, 10, 13, 15, 23, 38, 53, 54, 55, 56, 64, 65, 66, 67, 71, 75, 77, 79, 81, 82], "copi": [2, 16, 21, 31, 47, 49, 75, 77], "data_rep": 2, "serial": [2, 3, 12], "encod": [2, 3, 5, 9, 14, 19, 21, 35, 43, 55, 66, 70, 74], "via": [2, 3, 4, 5, 11, 13, 16, 21, 24, 27, 32, 34, 35, 37, 40, 42, 44, 46, 47, 49, 52, 53, 55, 56, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75], "real": [2, 8, 10, 12, 13, 15, 17, 20, 21, 31, 59], "imaginari": [2, 4, 12], "part": [2, 3, 4, 12, 17, 19, 23, 35, 47, 71, 73, 75, 77], "append": [2, 3, 6, 8, 10, 11, 12, 13, 17, 18, 19, 20, 21, 22, 23, 29, 31, 39, 53, 55, 56, 62, 65, 68], "larg": [2, 4, 5, 12, 18, 23, 30, 33, 42, 55, 56, 59, 69, 70, 83], "end": [2, 3, 4, 7, 10, 13, 15, 16, 17, 18, 20, 21, 24, 25, 27, 31, 35, 47, 53, 55, 56, 60, 62, 65, 69, 70, 75, 77], "total": [2, 3, 4, 8, 9, 11, 12, 13, 15, 21, 23, 54, 55, 56, 60, 65, 68, 77], "destructor": 2, "iter": [2, 3, 4, 9, 12, 19, 21, 23, 24, 28, 29, 35, 47], "begin": [2, 3, 4, 7, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27, 31, 35, 47, 58, 65, 66, 69, 70], "start": [2, 3, 4, 6, 13, 15, 16, 19, 21, 24, 32, 33, 42, 47, 53, 55, 60, 62, 65, 71, 73, 79, 83], "equal": [2, 10, 21, 24, 31, 49, 55, 56, 60, 70], "v": [2, 3, 4, 8, 10, 12, 13, 14, 19, 35, 38, 39, 44, 49, 54, 68, 71, 75], "noexcept": [2, 42], "subtract": 2, "multipli": [2, 12, 13, 19], "true": [2, 3, 4, 5, 9, 11, 12, 13, 16, 17, 18, 19, 21, 23, 29, 35, 39, 52, 53, 56, 68, 75, 77, 82], "here": [2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 15, 18, 19, 21, 22, 23, 27, 28, 32, 33, 35, 37, 38, 39, 42, 44, 52, 53, 54, 55, 62, 64, 65, 66, 67, 71, 73, 75, 77, 81, 82, 83], "consid": [2, 4, 5, 7, 9, 13, 17, 18, 19, 20, 21, 38, 40, 49, 54, 55, 71, 77], "num_qubit": [2, 3, 13, 20, 43, 54], "num_term": [2, 43], "get_coeffici": [2, 8, 12, 20, 43], "get": [2, 3, 10, 12, 13, 15, 17, 18, 19, 21, 23, 27, 29, 31, 33, 35, 37, 38, 47, 53, 54, 55, 56, 60, 64, 65, 68, 74, 75, 79, 82, 83], "throw": [2, 31], "except": [2, 3, 9, 12, 13, 21, 31, 81], "get_raw_data": 2, "is_ident": [2, 43], "standard": [2, 3, 10, 21, 23, 29, 34, 35, 36, 37, 39, 42, 48, 55, 58, 59, 71, 73, 75, 77, 79, 81], "out": [2, 3, 7, 8, 9, 11, 12, 14, 15, 16, 19, 21, 23, 27, 29, 33, 35, 40, 47, 49, 55, 56, 60, 61, 62, 64, 65, 74, 77, 78, 81, 83], "to_str": [2, 8, 12, 20, 60], "printcoeffici": 2, "getdatarepresent": 2, "getdatatupl": 2, "fulli": [2, 3, 9, 11, 13, 21, 33, 34, 53, 55, 66, 71, 75, 77, 81, 83], "distribute_term": 2, "numchunk": 2, "distribut": [2, 10, 17, 18, 21, 23, 24, 27, 33, 40, 52, 54, 56, 60, 64, 66, 75, 81, 82, 83], "chunk": [2, 40], "for_each_term": [2, 8, 12, 20, 43], "give": [2, 14, 15, 18, 24, 25, 33, 35, 50, 55, 56, 75, 77, 83], "functor": 2, "reduct": 2, "captur": [2, 14, 19, 23, 31, 33, 39, 52, 62, 83], "variabl": [2, 9, 12, 14, 16, 19, 23, 30, 33, 39, 40, 52, 53, 54, 55, 61, 65, 68, 75, 77, 82, 83], "for_each_pauli": [2, 43], "thrown": [2, 81], "than": [2, 3, 12, 13, 14, 15, 16, 17, 19, 20, 23, 24, 26, 31, 42, 49, 54, 56, 60, 62, 70, 75, 77, 81], "user": [2, 3, 4, 5, 8, 9, 13, 18, 21, 30, 33, 35, 37, 38, 40, 41, 44, 47, 52, 53, 54, 55, 56, 65, 68, 71, 74, 75, 77, 83], "should": [2, 3, 13, 15, 19, 20, 23, 34, 35, 40, 42, 43, 45, 47, 53, 55, 56, 60, 74, 75, 77, 81, 82], "pass": [2, 3, 8, 9, 11, 12, 13, 17, 20, 23, 31, 32, 33, 35, 39, 40, 43, 47, 53, 55, 56, 62, 65, 67, 71, 72, 77, 81, 83], "index": [2, 3, 5, 9, 11, 12, 17, 43, 45, 47, 49, 52, 55, 56, 74], "complex_matrix": 2, "to_matrix": [2, 10, 12, 52], "dens": 2, "to_sparse_matrix": 2, "col": 2, "static": [2, 3, 35, 42, 47, 52, 71, 75, 81], "nterm": 2, "unsign": 2, "seed": [2, 3, 4, 8, 9, 13, 14, 18, 21, 22, 23, 31, 68], "random_devic": 2, "specifi": [2, 3, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 23, 24, 26, 28, 29, 31, 35, 38, 39, 40, 42, 43, 44, 45, 47, 52, 53, 54, 55, 56, 60, 62, 65, 66, 68, 71, 74, 75, 77], "overrid": [2, 3, 35, 56, 73, 75], "repeat": [2, 17, 18, 19, 23, 35], "from_word": 2, "pauliword": 2, "word": [2, 3, 8, 12, 19, 20], "g": [2, 3, 9, 14, 19, 20, 21, 28, 34, 35, 36, 39, 40, 41, 42, 43, 49, 52, 53, 54, 55, 56, 65, 71, 74, 75, 77, 78, 81, 82], "xyx": 2, "3rd": 2, "typenam": [2, 35, 37, 38, 39, 42, 46, 47, 79, 81], "qualifiedspinop": 2, "struct": [2, 35, 37, 38, 39, 42, 46, 54, 55, 56, 64, 65, 66, 67, 71, 73, 81], "constexpr": [2, 37, 47, 54], "dyn": [2, 47], "qudit": [2, 25, 36, 40, 42, 69], "system": [2, 3, 4, 9, 12, 13, 16, 20, 22, 23, 24, 25, 30, 33, 35, 40, 45, 47, 49, 52, 53, 55, 56, 59, 60, 64, 65, 68, 69, 70, 73, 75, 78, 79, 81, 82, 83], "inlin": [2, 35, 71], "new": [2, 3, 4, 8, 9, 12, 15, 21, 32, 33, 35, 37, 49, 59, 71, 72, 75, 77, 81, 82, 83], "enable_if_t": 2, "qreg": [2, 3, 12, 14, 54], "contain": [2, 3, 4, 9, 10, 13, 14, 18, 21, 32, 33, 35, 40, 42, 45, 49, 54, 56, 59, 60, 64, 65, 71, 74, 75, 81, 82, 83], "dynam": [2, 13, 32, 33, 37, 39, 40, 47, 53, 56, 58, 59, 71, 81, 83], "time": [2, 3, 4, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 23, 24, 25, 26, 27, 31, 32, 33, 34, 35, 38, 40, 47, 48, 53, 54, 55, 56, 60, 65, 66, 68, 69, 70, 71, 75, 77, 82, 83], "By": [2, 9, 10, 23, 30, 35, 42, 52, 53, 54, 55, 56, 60, 65, 79], "value_typ": 2, "indic": [2, 3, 4, 8, 21, 39, 42, 43, 47, 52, 74], "underli": [2, 3, 9, 23, 35, 45, 47, 53, 55, 74], "interfac": [2, 3, 47, 56, 74, 75, 77, 79], "idx": [2, 3, 11, 13, 19, 21, 47, 52, 55], "qspan": 2, "front": [2, 38, 46, 47, 67], "back": [2, 21, 38, 47, 49, 55, 65, 66, 77], "last": [2, 18, 19, 21, 38, 47, 55, 62, 64], "slice": [2, 3, 47], "clear": [2, 3, 16, 35, 47, 74], "destroi": [2, 47], "postcondit": [2, 47], "own": [2, 3, 9, 18, 27, 40, 45, 47, 56, 71, 74, 75, 77, 81], "semant": [2, 3, 34, 39, 40, 41, 44, 46, 47, 49, 71], "held": 2, "explicit": [2, 10, 35, 46, 52, 56, 65, 81], "determin": [2, 4, 5, 7, 8, 9, 17, 20, 23, 32, 56, 60], "check": [2, 9, 19, 21, 33, 53, 54, 65, 70, 75, 77, 82, 83], "norm": [2, 18], "pre": [2, 3, 13, 21, 33, 35, 53, 56, 65, 67, 75, 81, 83], "exist": [2, 3, 8, 16, 21, 31, 33, 34, 35, 40, 41, 60, 73, 75, 77, 81, 82, 83], "could": [2, 9, 10, 12, 19, 23, 31, 33, 54, 58, 70, 75, 83], "from_data": [2, 3, 52], "retriev": [2, 3, 13, 24, 35, 52, 55, 65], "get_stat": [2, 3, 10, 15, 16, 17, 20, 21, 24, 25, 31, 55, 62], "delet": [2, 47, 53, 77, 81], "cannot": [2, 3, 15, 25, 31, 38, 39, 47, 49, 70, 77], "move": [2, 11, 47, 73, 75, 77, 82], "assign": [2, 9, 14, 45, 55, 56, 75], "qview": [2, 5, 10, 12, 15, 19, 38, 39, 46], "observe_result": [2, 3, 12, 35, 64], "encapsul": [2, 11, 35, 47, 55, 81], "observ": [2, 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 18, 20, 22, 23, 27, 29, 38, 52, 53, 55, 56, 57, 59, 64, 66, 67, 68, 69, 70, 74, 82], "call": [2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 19, 21, 22, 23, 24, 25, 27, 29, 31, 37, 38, 39, 42, 46, 52, 55, 56, 59, 60, 62, 65, 66, 67, 68, 70, 71, 74, 75, 77, 79], "measur": [2, 3, 5, 7, 9, 10, 11, 12, 13, 15, 16, 18, 23, 24, 25, 27, 32, 35, 36, 38, 39, 40, 42, 49, 52, 53, 55, 56, 58, 59, 60, 63, 65, 66, 71, 74, 82], "execut": [2, 4, 9, 13, 15, 21, 31, 32, 33, 34, 35, 37, 39, 40, 45, 46, 53, 55, 56, 59, 60, 61, 63, 64, 65, 66, 68, 71, 74, 77, 78, 79, 81, 82, 83], "ansatz": [2, 4, 6, 9, 13, 14, 22, 23, 35, 38, 54, 55, 64], "circuit": [2, 3, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 29, 34, 35, 39, 40, 43, 44, 48, 49, 53, 54, 55, 56, 59, 60, 62, 64, 65, 71, 73], "global": [2, 3, 9, 14, 21, 35, 39, 54, 60, 65, 75], "expect": [2, 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 18, 20, 21, 22, 23, 24, 27, 29, 32, 35, 52, 54, 55, 56, 60, 63, 68, 75, 77, 81, 82], "h": [2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 26, 29, 31, 35, 37, 38, 42, 43, 44, 46, 47, 49, 52, 53, 54, 55, 56, 58, 60, 62, 64, 65, 66, 67, 68, 70, 71, 73, 74, 75, 77, 79, 81, 82], "precomput": 2, "psi": [2, 6, 7, 10, 12, 16, 24, 31, 35, 38, 60, 69, 70], "sample_result": [2, 3, 19, 24, 35, 65, 81], "wa": [2, 3, 4, 7, 9, 12, 21, 35, 55, 56, 66, 71, 75, 78, 82], "shot": [2, 3, 8, 9, 10, 17, 18, 19, 24, 35, 38, 53, 56, 60, 65, 66, 69, 70, 74], "base": [2, 3, 8, 9, 11, 13, 15, 18, 19, 21, 23, 28, 33, 34, 35, 37, 41, 42, 47, 52, 53, 54, 55, 56, 60, 68, 71, 74, 75, 77, 79, 83], "raw_data": [2, 9, 35], "raw": [2, 3, 9], "convers": [2, 35], "simpli": [2, 31, 70, 77, 82], "ignor": [2, 9, 19, 56], "fine": [2, 35, 66, 67, 70], "grain": [2, 35, 66, 67], "explicitli": [2, 9, 10, 49, 53, 56, 71, 79, 81], "request": [2, 3, 35, 53, 54, 55, 56, 65, 77], "oppos": [2, 81], "observe_data": 2, "spinoptyp": [2, 35], "sub": [2, 3, 34, 35, 38, 39, 47, 48, 52, 77], "id_coeffici": [2, 35], "observe_opt": [2, 35], "option": [2, 3, 4, 7, 9, 10, 12, 13, 17, 18, 22, 23, 24, 29, 30, 35, 37, 42, 45, 52, 53, 54, 55, 60, 64, 65, 67, 68, 74, 75, 77], "async_observ": 2, "param": [2, 4, 13, 14, 17, 38, 39, 42, 54, 68], "run": [2, 3, 5, 7, 8, 9, 11, 12, 17, 18, 23, 24, 32, 33, 34, 35, 38, 52, 53, 54, 55, 56, 57, 59, 64, 65, 66, 67, 68, 71, 74, 75, 77, 78, 81, 82, 83], "applic": [2, 4, 5, 7, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 28, 32, 35, 42, 46, 52, 53, 56, 59, 60, 62, 63, 77, 78, 81, 82], "num_trajectori": [2, 3, 56], "trajectori": [2, 3], "presenc": 2, "simul": [2, 4, 6, 8, 10, 12, 17, 18, 19, 23, 24, 25, 29, 30, 31, 32, 33, 34, 35, 51, 52, 53, 57, 59, 60, 63, 65, 66, 68, 69, 71, 72, 75, 82, 83], "noisi": [2, 17, 18, 21, 32, 63, 65], "quantumkernel": [2, 35, 46], "arg": [2, 3, 9, 11, 15, 18, 35, 37, 42, 46, 52, 55, 60, 71, 77], "is_invocable_r_v": 2, "member": [2, 3, 14, 39], "conveni": [2, 15, 28, 43, 49, 75, 77], "what": [2, 3, 4, 8, 9, 10, 14, 16, 18, 19, 23, 31, 32, 33, 57, 68, 74, 81, 83], "": [2, 3, 4, 5, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 23, 24, 27, 29, 31, 32, 33, 35, 42, 45, 49, 52, 53, 54, 55, 56, 58, 59, 60, 64, 65, 66, 67, 68, 71, 73, 75, 77, 78, 79, 82, 83], "spinopcontain": 2, "termlist": 2, "everi": [2, 3, 14, 17, 18, 20, 33, 54, 55, 59, 60, 65, 66, 75, 82, 83], "concept": [2, 34, 35, 39, 41], "executioncontext": 2, "abstract": [2, 3, 28, 34, 35, 37, 42, 43, 45, 47, 55, 59], "how": [2, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 28, 29, 31, 33, 35, 37, 42, 52, 54, 55, 56, 59, 60, 62, 63, 65, 66, 67, 68, 71, 74, 75, 77, 78, 81, 82, 83], "shots_": 2, "basic": [2, 6, 32, 54, 62, 77, 82], "invoc": [2, 3, 37, 39, 45, 47, 55, 56, 74], "expectationvalu": 2, "nullopt": 2, "optimization_result": [2, 35], "optresult": 2, "optim": [2, 4, 6, 8, 9, 11, 12, 13, 14, 18, 19, 23, 32, 33, 34, 44, 47, 49, 52, 53, 54, 56, 63, 71, 73, 75, 77, 83], "hasconditionalsonmeasureresult": 2, "fals": [2, 3, 4, 8, 9, 12, 13, 16, 17, 19, 20, 21, 56, 75, 77], "being": [2, 3, 5, 6, 16, 27, 34, 35, 49, 56, 65, 81], "statement": [2, 7, 26, 35, 36, 59], "noise_model": [2, 3, 13, 17, 18, 27, 56], "noisemodel": [2, 3, 13, 17, 18, 27, 56], "nullptr": 2, "canhandleobserv": 2, "flag": [2, 13, 33, 39, 52, 53, 55, 56, 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Patterns": [[44, "common-quantum-programming-patterns"]], "Compute-Action-Uncompute": [[44, "compute-action-uncompute"]], "Machine Model": [[40, "machine-model"]], "Quantum Operators": [[43, "quantum-operators"]], "cudaq::spin_op": [[43, "cudaq-spin-op"]], "Namespace and Standard": [[41, "namespace-and-standard"]], "Quake Dialect": [[49, "quake-dialect"]], "General Introduction": [[49, "general-introduction"]], "Motivation": [[49, "motivation"]], "Specifications": [[48, "specifications"]], "Sub-circuit Synthesis": [[46, "sub-circuit-synthesis"]], "Quantum Types": [[47, "quantum-types"]], "cudaq::qudit": [[47, "cudaq-qudit-levels"]], "cudaq::qubit": [[47, "cudaq-qubit"]], "Quantum Containers": [[47, "quantum-containers"]], "cudaq::qview": [[47, "cudaq-qview-levels-2"]], "cudaq::qvector": [[47, "cudaq-qvector-levels-2"]], "cudaq::qarray": [[47, "cudaq-qarray-n-levels-2"]], "cudaq::qspan (Deprecated. Use cudaq::qview instead.)": [[47, "cudaq-qspan-n-levels-deprecated-use-cudaq-qview-levels-instead"]], "cudaq::qreg (Deprecated. Use cudaq::qvector instead.)": [[47, "cudaq-qreg-n-levels-deprecated-use-cudaq-qvector-levels-instead"]], "Quantum Platform": [[45, "quantum-platform"]], "Just-in-Time Kernel Creation": [[37, "just-in-time-kernel-creation"]], "Control Flow": [[36, "control-flow"]], "Example Programs": [[38, "example-programs"]], "Hello World - Simple Bell State": [[38, "hello-world-simple-bell-state"]], "GHZ State Preparation and Sampling": [[38, "ghz-state-preparation-and-sampling"]], "Quantum Phase Estimation": [[38, "quantum-phase-estimation"]], "Deuteron Binding Energy Parameter Sweep": [[38, "deuteron-binding-energy-parameter-sweep"]], "Grover\u2019s Algorithm": [[38, "grover-s-algorithm"]], "Iterative Phase Estimation": [[38, "iterative-phase-estimation"]], "Quantum Algorithmic Primitives": [[35, "quantum-algorithmic-primitives"]], "cudaq::sample": [[35, "cudaq-sample"]], "cudaq::observe": [[35, "cudaq-observe"]], "cudaq::optimizer (deprecated, functionality moved to CUDA-Q libraries)": [[35, 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"using-a-singularity-container"]], "Connecting to a Remote Host": [[77, "connecting-to-a-remote-host"]], "Developing with Remote Tunnels": [[77, "developing-with-remote-tunnels"]], "Remote Access via SSH": [[77, "remote-access-via-ssh"]], "DGX Cloud": [[77, "dgx-cloud"]], "Get Started": [[77, "get-started"]], "Use JupyterLab": [[77, "use-jupyterlab"]], "Use VS Code": [[77, "use-vs-code"]], "Additional CUDA Tools": [[77, "additional-cuda-tools"]], "Installation via PyPI": [[77, "installation-via-pypi"]], "Installation In Container Images": [[77, "installation-in-container-images"]], "Installing Pre-built Binaries": [[77, "installing-pre-built-binaries"]], "Distributed Computing with MPI": [[77, "distributed-computing-with-mpi"]], "Updating CUDA-Q": [[77, "updating-cuda-q"]], "Dependencies and Compatibility": [[77, "dependencies-and-compatibility"]], "Supported Systems": [[77, "id10"]], "Requirements for GPU Simulation": [[77, "id11"]], "Next Steps": [[77, "next-steps"]], "Installation Guide": [[76, "installation-guide"]], "Contents": [[76, null], [57, null], [32, null]], "Installation from Source": [[75, "installation-from-source"]], "Prerequisites": [[75, "prerequisites"]], "Build Dependencies": [[75, "build-dependencies"]], "CUDA": [[75, "cuda"]], "Toolchain": [[75, "toolchain"]], "Building CUDA-Q": [[75, "building-cuda-q"]], "Python Support": [[75, "python-support"]], "C++ Support": [[75, "c-support"]], "Installation on the Host": [[75, "installation-on-the-host"]], "CUDA Runtime Libraries": [[75, "cuda-runtime-libraries"]], "MPI": [[75, "mpi"]], "Multi-Processor Platforms": [[55, "multi-processor-platforms"]], "NVIDIA MQPU Platform": [[55, "nvidia-mqpu-platform"]], "Parallel distribution mode": [[55, "parallel-distribution-mode"]], "Remote MQPU Platform": [[55, "remote-mqpu-platform"]], "Supported Kernel Arguments": [[55, "supported-kernel-arguments"]], "Kernel argument serialization": [[55, "id4"]], "Accessing Simulated Quantum State": [[55, "accessing-simulated-quantum-state"]], "CUDA-Q Basics": [[57, "cuda-q-basics"]], "Building your first CUDA-Q Program": [[58, "building-your-first-cuda-q-program"]], "CUDA-Q Simulation Backends": [[56, "cuda-q-simulation-backends"]], "State Vector Simulators": [[56, "state-vector-simulators"]], "Features": [[56, "features"]], "Single-GPU": [[56, "single-gpu"]], "Environment variable options supported in single-GPU mode": [[56, "id6"]], "Multi-node multi-GPU": [[56, "multi-node-multi-gpu"], [56, "id2"]], "Additional environment variable options for multi-node multi-GPU mode": [[56, "id7"]], "Trajectory Noisy Simulation": [[56, "trajectory-noisy-simulation"]], "Additional environment variable options for trajectory simulation": [[56, "id8"]], "OpenMP CPU-only": [[56, "openmp-cpu-only"], [56, "id3"]], "Tensor Network Simulators": [[56, "tensor-network-simulators"]], "Matrix product state": [[56, "matrix-product-state"]], "Clifford-Only Simulator": [[56, "clifford-only-simulator"]], "Stim (CPU)": [[56, "stim-cpu"]], "Photonics Simulators": [[56, "photonics-simulators"]], "Fermioniq": [[56, "fermioniq"]], "Default Simulator": [[56, "default-simulator"]], "What is a CUDA-Q kernel?": [[59, "what-is-a-cuda-q-kernel"]], "NVIDIA Quantum Cloud": [[54, "nvidia-quantum-cloud"]], "Simulator Backend Selection": [[54, "simulator-backend-selection"]], "Multiple GPUs": [[54, "multiple-gpus"]], "Simulator Backends": [[54, "id1"]], "Multiple QPUs Asynchronous Execution": [[54, "multiple-qpus-asynchronous-execution"]], "FAQ": [[54, "faq"]], "CUDA-Q Dynamics": [[52, "cuda-q-dynamics"]], "Operator": [[52, "operator"]], "Builtin Operators": [[52, "id1"]], "Time-Dependent Dynamics": [[52, "time-dependent-dynamics"]], "Numerical Integrators": [[52, "numerical-integrators"], [52, "id2"]], "Multi-GPU Multi-Node Execution": [[52, "multi-gpu-multi-node-execution"]], "CUDA-Q Hardware Backends": [[53, "cuda-q-hardware-backends"]], "Setting Credentials": [[53, "setting-credentials"], [53, "id1"], [53, "ionq-backend"], [53, "anyon-backend"], [53, "id10"], [53, "id13"], [53, "id16"], [53, "quantinuum-backend"], [53, "quera-backend"]], "Submission from C++": [[53, "submission-from-c"], [53, "id2"], [53, "id5"], [53, "id8"], [53, "id11"], [53, "id14"], [53, "id17"], [53, "id20"], [53, "id23"]], "Submission from Python": [[53, "submission-from-python"], [53, "id3"], [53, "id6"], [53, "id9"], [53, "id12"], [53, "id15"], [53, "id18"], [53, "id21"], [53, "id24"]], "Anyon Technologies/Anyon Computing": [[53, "anyon-technologies-anyon-computing"]], "CUDA-Q Backends": [[51, "cuda-q-backends"]], "Backend Targets": [[51, null]], "CUDA-Q Applications": [[50, "cuda-q-applications"]], "Visualization": [[31, "Visualization"]], "Qubit Visualization": [[31, "Qubit-Visualization"]], "Kernel Visualization": [[31, "Kernel-Visualization"]], "Language Specification": [[34, "language-specification"]], "CUDA-Q": [[34, null], [32, "cuda-q"]], "CUDA-Q Releases": [[33, "cuda-q-releases"]], "Optimizing Performance": [[30, "Optimizing-Performance"]], "Gate Fusion": [[30, "Gate-Fusion"]], "Anderson Impurity Model ground state solver on Infleqtion\u2019s Sqale": [[13, "Anderson-Impurity-Model-ground-state-solver-on-Infleqtion's-Sqale"]], "Performing logical Variational Quantum Eigensolver (VQE) with CUDA-QX": [[13, "Performing-logical-Variational-Quantum-Eigensolver-(VQE)-with-CUDA-QX"]], "Constructing circuits in the [[4,2,2]] encoding": [[13, "Constructing-circuits-in-the-[[4,2,2]]-encoding"]], "Setting up submission and decoding workflow": [[13, "Setting-up-submission-and-decoding-workflow"]], "Running a CUDA-Q noisy simulation": [[13, "Running-a-CUDA-Q-noisy-simulation"]], "Running logical AIM on Infleqtion\u2019s hardware": [[13, "Running-logical-AIM-on-Infleqtion's-hardware"]], "Multi-reference Quantum Krylov Algorithm - H_2 Molecule": [[12, "Multi-reference-Quantum-Krylov-Algorithm---H_2-Molecule"]], "Setup": [[12, "Setup"]], "Computing the matrix elements": [[12, "Computing-the-matrix-elements"]], "Determining the ground state energy of the subspace": [[12, "Determining-the-ground-state-energy-of-the-subspace"]], "Max-Cut with QAOA": [[14, "Max-Cut-with-QAOA"]], "Hybrid Quantum Neural Networks": [[11, "Hybrid-Quantum-Neural-Networks"]], "Using the Hadamard Test to Determine Quantum Krylov Subspace Decomposition Matrix Elements": [[10, "Using-the-Hadamard-Test-to-Determine-Quantum-Krylov-Subspace-Decomposition-Matrix-Elements"]], "Numerical result as a reference:": [[10, "Numerical-result-as-a-reference:"]], "Using Sample to perform the Hadamard test": [[10, "Using-Sample-to-perform-the-Hadamard-test"]], "Multi-GPU evaluation of QKSD matrix elements using the Hadamard Test": [[10, "Multi-GPU-evaluation-of-QKSD-matrix-elements-using-the-Hadamard-Test"]], "Classically Diagonalize the Subspace Matrix": [[10, "Classically-Diagonalize-the-Subspace-Matrix"]], "Divisive Clustering With Coresets Using CUDA-Q": [[9, "Divisive-Clustering-With-Coresets-Using-CUDA-Q"]], "Data preprocessing": [[9, "Data-preprocessing"]], "Quantum functions": [[9, "Quantum-functions"]], "Divisive Clustering Function": [[9, "Divisive-Clustering-Function"]], "QAOA Implementation": [[9, "QAOA-Implementation"]], "Scaling simulations with CUDA-Q": [[9, "Scaling-simulations-with-CUDA-Q"]], "Molecular docking via DC-QAOA": [[8, "Molecular-docking-via-DC-QAOA"]], "Setting up the Molecular Docking Problem": [[8, "Setting-up-the-Molecular-Docking-Problem"]], "CUDA-Q Implementation": [[8, "CUDA-Q-Implementation"]], "Deutsch\u2019s Algorithm": [[7, "Deutsch's-Algorithm"]], "XOR \\oplus": [[7, "XOR-\\oplus"]], "Quantum oracles": [[7, "Quantum-oracles"]], "Phase oracle": [[7, "Phase-oracle"]], "Quantum parallelism": [[7, "Quantum-parallelism"]], "Deutsch\u2019s Algorithm:": [[7, "Deutsch's-Algorithm:"]], "Cost Minimization": [[6, "Cost-Minimization"]], "Bernstein-Vazirani Algorithm": [[5, "Bernstein-Vazirani-Algorithm"]], "Classical case": [[5, "Classical-case"]], "Quantum case": [[5, "Quantum-case"]], "Implementing in CUDA-Q": [[5, "Implementing-in-CUDA-Q"]], "Factoring Integers With Shor\u2019s Algorithm": [[19, "Factoring-Integers-With-Shor's-Algorithm"]], "Shor\u2019s algorithm": [[19, "Shor's-algorithm"]], "Solving the order-finding problem classically": [[19, "Solving-the-order-finding-problem-classically"]], "Solving the order-finding problem with a quantum algorithm": [[19, "Solving-the-order-finding-problem-with-a-quantum-algorithm"]], "Inverse quantum Fourier transform": [[19, "Inverse-quantum-Fourier-transform"]], "Quantum kernels for modular exponentiation": [[19, "Quantum-kernels-for-modular-exponentiation"]], "The case N = 21 and a = 5:": [[19, "The-case-N-=-21-and-a-=-5:"]], "The case N = 21 and a = 4:": [[19, "The-case-N-=-21-and-a-=-4:"]], "Determining the order from the measurement results of the phase kernel": [[19, "Determining-the-order-from-the-measurement-results-of-the-phase-kernel"]], "Postscript": [[19, "Postscript"]], "Readout Error Mitigation": [[18, "Readout-Error-Mitigation"]], "Inverse confusion matrix from single-qubit noise model": [[18, "Inverse-confusion-matrix-from-single-qubit-noise-model"]], "Inverse confusion matrix from k local confusion matrices": [[18, "Inverse-confusion-matrix-from-k-local-confusion-matrices"]], "Inverse of full confusion matrix": [[18, "Inverse-of-full-confusion-matrix"]], "Quantum Fourier Transform": [[15, "Quantum-Fourier-Transform"]], "Quantum Fourier Transform revisited": [[15, "Quantum-Fourier-Transform-revisited"]], "Quantum Volume": [[17, "Quantum-Volume"]], "Quantum Teleporation": [[16, "Quantum-Teleporation"]], "Teleportation explained": [[16, "Teleportation-explained"]], "Compiling Unitaries Using Diffusion Models": [[21, "Compiling-Unitaries-Using-Diffusion-Models"]], "Diffusion model pipeline": [[21, "Diffusion-model-pipeline"]], "Setup and compilation": [[21, "Setup-and-compilation"]], "Load model": [[21, 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                                                                                                                                              • Measurements
                                                                                                                                              • +
                                                                                                                                            • Photonic Operations +
                                                                                                                                            • Measuring Kernels @@ -149,6 +155,12 @@
                                                                                                                                            • +
                                                                                                                                          • Executing Photonic Kernels +
                                                                                                                                          • Computing Expectation Values @@ -181,6 +193,7 @@
                                                                                                                                          • Using Quantum Hardware Providers
                                                                                                                                          • Divisive Clustering With Coresets Using CUDA-Q
                                                                                                                                            • @@ -322,6 +344,10 @@
                                                                                                                                          • Stim (CPU)
                                                                                                                                          • +
                                                                                                                                        • Photonics Simulators +
                                                                                                                                        • Fermioniq
                                                                                                                                        • Default Simulator
                                                                                                                                        @@ -333,48 +359,54 @@
                                                                                                                                      • Submission from Python
                                                                                                                                      • -
                                                                                                                                    • IonQ