New algorithm for generating Clifford circuits for single qubit.

[merav-aharoni]

Summary

We generate all 24 transpiled Cliffords once (in the basis {rz, sx}. Then, for every rb_circuit, select Cliffords at random and compose them to a circuit

Details and comments

Current version is faster than the original version. The main change I made since the previous version, is adding the parameter inplace to the QuantumCircuit.compose() operation. This uses the existing circuit, rather than copying to a new circuit.

For benchmarking, I ran the test test.randomized_benchmarking.test_randomized_benchmarking.TestStandardRB.test_single_qubit from the test suite. Here are a few measurements (average of 5 runs):
With num_samples = 1, existing rb_experiment: time = 1.2374 sec
this branch: time = 0.7710 sec
With num_samples = 10 existing rb_experiment: time = 8.3614 sec
this branch: time = 1.2056 sec

[merav-aharoni]

There is a difference between the EPC computed by this branch as compared to the existing rb_experiment. This must be investigated.

[merav-aharoni]

After fixing the random number generator, the new algorithm generates the exact same circuits as the original algorithm, as well as the same result for EPC.
I ran performance comparison on three circuits, 3 iterations each, StandardRB.num_samples=1, same seed for both algorithms, full_sampling=False.
Here are the results:

[merav-aharoni]

@dekel.meirom ran a comparison between the RB version in this PR and QC code on Bangkok. The experiment consists of circuits with lengths = [1, 2, 3, 5, 9, 17, 31, 56, 99, 177, 316, 562, 999, 1778, 3162]. QC code takes 83 sec while this version takes 100 sec

[merav-aharoni]

A few comments on future work:

1. For 1-qubit RB, need to implement with full_sampling=True, and check performance in this case.
2. The current version is a draft - need to re-write the code.
3. For 2-qubit RB, creating the transpiled circuits during __init__ will not be efficient. We should consider creating them once and storing in a file. Or perhaps randomly generating transpiled cliffords according to the length of the circuit, e.g., if we have 1 circuit of length 100, generate only 100 random cliffords.