Check which terms of an observable could be diagonalised simoultaneously

[BrunoLiegiBastonLiegi]

#1489 introduced the possibility of calculating the expectation value of observables not diagonal in the computational basis. However, it is assumed there that each term of the hamiltonian cannot be diagonalised simultaneously with the others, which in general will not hold. Therefore, it would be more efficient to check first which terms could be treated together to reduce the number of circuits executed. https://arxiv.org/abs/1907.03358 this could be of some help.

[renatomello]

Related references:

arXiv 2103.07510

arXiv 2105.13091