Add a new example in docs where pyGSTi is used to apply PEC.

[andreamari]

Issue Description

Mitiq users can currently apply probabilistic error cancellation (PEC) only in the following cases:

• If they know the quasi-probability representations of ideal gates as linear combinations of noisy gates.
• If they know the noise channels (super-oprerators) associated to a set of implementable gates. In this case, they can numerically compute optimal the necessary quasi-probability representations.

In many practical situations the user doesn't know what are the noise channels associated to the hardware gateset.

Noise characterization tools are beyond the scope of Mitiq. However, it would be helpful to show an example in which an external noise characterization library (e.g. pyGSTi) is used to characterize gate noise channels in order to apply PEC.

Proposed Solution

Write a new documentation example (i.e. a myst notebook) in which:

• pyGSTi is used to get the noise superoperators of a noisy gateset (of a simulated device).
• The find_optimal_representation()` function is used to get a list of OperationRepresentaiton objects for some circuit of interest. Maybe, it is enough to consider only two-qubit gates (e.g. CNOT gates associated to all pairs of qubits).
• The list of OperationRepresentaiton objects is used to apply PEC.

[github-actions]

This issue had no activity for 4 months, and will be closed in 2 weeks unless there is new activity. Cheers!

[andreamari]

(we have ongoing plans about this)