Add a near-Clifford simulator for CDR

[rmlarose]

The CDR method needs a near-Clifford simulator to be efficient at scale. Currently, this is sort-of placed on the user as an argument to execute_with_cdr. It would be good to have such a simulator available in Mitiq for this purpose.

Description

The function should be able to efficiently simulate near-Clifford circuits, i.e., circuits where most operations are Clifford except for a small number (possible zero) of operations. Such near-Clifford circuits are generated by generate_training_circuits in CDR. The simulator should input a near-Clifford circuit as a QPROGRAM with computational basis measurements and return measurement samples, for example as a dictionary {bitstring_1: counts_1, ..., bitstring_n: counts_n}.

Notes

• Several packages have implemented Clifford simulators, so one does not necessarily need to start from scratch on this.
• Any classical (noiseless) simulator works with CDR but is not necessarily efficient. For example, in tests we currently use a simple wavefunction simulator and sample from the resulting state.

[github-actions[bot]]

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

[github-actions[bot]]

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

[github-actions[bot]]

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

[github-actions[bot]]

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

[natestemen]

With https://github.com/unitaryfund/mitiq/issues/2241 open we will now close this in favor of adding some documentation.