Change link from arXiv to citation of published paper (#344)

* Change link from arXiv to citation of published paper

* replace arXiv with paper citation

docs/kpz/kpz.ipynb

@@ -103,9 +103,9 @@
    "source": [
     "### Motivation and Background\n",
     "\n",
-    "Based on strong numerical evidence, it has been [conjectured](https://arxiv.org/abs/1903.01329) that the late-time dynamics of the 1D Heisenberg spin chain are described by the [Kardar-Parisi-Zhang universality class](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.56.889). Experiments, for example using [cold atoms](https://arxiv.org/abs/2107.00038), have provided further evidence for this conjecture. In [our work](https://arxiv.org/abs/2306.09333), we test this conjecture using 46 superconducting qubits, comparing the probability distribution of the transferred magnetization against predictions for the KPZ height function. We find that, while the mean and variance are consistent with KPZ, higher moments appear inconsistent.\n",
+    "Based on strong numerical evidence, it has been [conjectured](https://arxiv.org/abs/1903.01329) that the late-time dynamics of the 1D Heisenberg spin chain are described by the [Kardar-Parisi-Zhang universality class](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.56.889). Experiments, for example using [cold atoms](https://arxiv.org/abs/2107.00038), have provided further evidence for this conjecture. In [our work](https://research.google/pubs/dynamics-of-magnetization-at-infinite-temperature-in-a-heisenberg-spin-chain/), we test this conjecture using 46 superconducting qubits, comparing the probability distribution of the transferred magnetization against predictions for the KPZ height function. We find that, while the mean and variance are consistent with KPZ, higher moments appear inconsistent.\n",
     "\n",
-    "For further background, motivation, and explanation, please either read the paper, [arXiv:2306.09333](https://arxiv.org/abs/2306.09333), or watch the [talk](https://www.youtube.com/watch?v=U12xdMA3v1E).\n",
+    "For further background, motivation, and explanation, please either read the [paper](https://research.google/pubs/dynamics-of-magnetization-at-infinite-temperature-in-a-heisenberg-spin-chain/) or watch the [talk](https://www.youtube.com/watch?v=U12xdMA3v1E).\n",
     "\n",
     "### Simulating the 1D Floquet XXZ model using ReCirq\n",
     "\n",
@@ -115,7 +115,7 @@
     "\n",
     "where $N_Q$ is the number of qubits, $S^z$ is the $z$ component of the spin, and $\\mu$ is a parameter that acts like a chemical potential between the two sides of the chain, interpolating between a pure domain wall at $\\mu=\\infty$ and an infinite temperature state at $\\mu=0$. We implement this initial state by sampling pure states, namely bitstring product states, where each qubit on the left side of the chain is prepared in $|1\\rangle$ with probability $p = (e^\\mu)/(e^\\mu + e^{-\\mu})$, otherwise $|0\\rangle$, and each qubit on the right is prepared in $|0\\rangle$ with the same probability, $p$, otherwise $|1\\rangle$.\n",
     "\n",
-    "Next, we apply $t$ Floquet cycles of [fSim gates](https://quantumai.google/reference/python/cirq/FSimGate), where a cycle is depicted in Figure 1 of [arXiv:2306.09333](https://arxiv.org/abs/2306.09333) and consists of both an even layer and an odd layer. Finally, we measure all of the qubits and count how many excitations have crossed the center. Twice this quantity is the transferred magnetization, $\\mathcal{M}$.\n",
+    "Next, we apply $t$ Floquet cycles of [fSim gates](https://quantumai.google/reference/python/cirq/FSimGate), where a cycle is depicted in Figure 1 of [our paper](https://research.google/pubs/dynamics-of-magnetization-at-infinite-temperature-in-a-heisenberg-spin-chain/) and consists of both an even layer and an odd layer. Finally, we measure all of the qubits and count how many excitations have crossed the center. Twice this quantity is the transferred magnetization, $\\mathcal{M}$.\n",
     "\n",
     "To set up this experiment for a particular number of cycles, we create a `KPZExperiment`. This has five required input parameters, `num_cycles`, `mu`, `num_init_states`, `theta`, and `phi`. The conjecture that the late-time dynamics of this model are described by the Kardar-Parisi-Zhang (KPZ) universality class applies at the isotropic point (i.e. the XXX or Heisenberg model), which corresponds to $\\phi = 2\\theta$. Further, the conjecture applies at small $\\mu$, although the order of limits between $\\mu \\to 0$ and $t\\to\\infty$ is something that we explore in the paper. In Figure 3 of the paper, we pick $(\\theta, \\phi) = (0.4\\pi, 0.8\\pi)$. To initialize a `KPZExperiment` with these angles, $\\mu=0.5$ and 1000 initial states, for cycle 2, we run"
    ]