Fix performance regression in 3 or more qubits RB

[itoko]

Summary

Fix the performance regression of RB for 3 or more qubits Cliffords, which was introduced in the recent refactoring of RB module #898

Details and comments

Change back to avoid using slow Clifford.compose as much as possible and use faster QuantumCircuit.compose and Clifford.from_circuit instead for 3 or more qubits Cliffords, that was the technique used in the original code before #898 but missed to be included in #898.

As shown in the table below, this PR recovers the original performance. (Code to measure the performance of 3Q RB)

[after-this-PR]
    full_sampling          backend  max_length  num_samples                    method    seconds  num_runs
0           False      fake_manila          20            3             time_circuits   1.661291         1
1           False      fake_manila          20            3  time_transpiled_circuits   4.292393         1
2           False      fake_manila          20            6             time_circuits   3.375736         1
3           False      fake_manila          20            6  time_transpiled_circuits   7.549929         1
4           False      fake_manila          40            3             time_circuits   2.772556         1
5           False      fake_manila          40            3  time_transpiled_circuits   6.404932         1
6           False      fake_manila          40            6             time_circuits   5.390166         1
7           False      fake_manila          40            6  time_transpiled_circuits  12.694415         1
8           False      fake_mumbai          20            3             time_circuits   1.630835         1
9           False      fake_mumbai          20            3  time_transpiled_circuits   5.511165         1
10          False      fake_mumbai          20            6             time_circuits   3.343967         1
11          False      fake_mumbai          20            6  time_transpiled_circuits  10.307006         1
12          False      fake_mumbai          40            3             time_circuits   2.551411         1
13          False      fake_mumbai          40            3  time_transpiled_circuits   8.743302         1
14          False      fake_mumbai          40            6             time_circuits   5.347619         1
15          False      fake_mumbai          40            6  time_transpiled_circuits  17.490494         1
16          False  fake_washington          20            3             time_circuits   1.590835         1
17          False  fake_washington          20            3  time_transpiled_circuits  15.676607         1
18          False  fake_washington          20            6             time_circuits   3.243143         1
19          False  fake_washington          20            6  time_transpiled_circuits  23.216102         1
20          False  fake_washington          40            3             time_circuits   2.629359         1
21          False  fake_washington          40            3  time_transpiled_circuits  20.105627         1
22          False  fake_washington          40            6             time_circuits   5.276347         1
23          False  fake_washington          40            6  time_transpiled_circuits  41.768356         1

[main]
    full_sampling          backend  max_length  num_samples                    method    seconds  num_runs
0           False      fake_manila          20            3             time_circuits   6.361049         1
1           False      fake_manila          20            3  time_transpiled_circuits   9.400935         1
2           False      fake_manila          20            6             time_circuits  13.168127         1
3           False      fake_manila          20            6  time_transpiled_circuits  17.275917         1
4           False      fake_manila          40            3             time_circuits  10.803795         1
5           False      fake_manila          40            3  time_transpiled_circuits  14.360775         1
6           False      fake_manila          40            6             time_circuits  21.231920         1
7           False      fake_manila          40            6  time_transpiled_circuits  32.218625         1
8           False      fake_mumbai          20            3             time_circuits   6.478630         1
9           False      fake_mumbai          20            3  time_transpiled_circuits  10.717985         1
10          False      fake_mumbai          20            6             time_circuits  12.797258         1
11          False      fake_mumbai          20            6  time_transpiled_circuits  20.825657         1
12          False      fake_mumbai          40            3             time_circuits  11.569653         1
13          False      fake_mumbai          40            3  time_transpiled_circuits  18.167764         1
14          False      fake_mumbai          40            6             time_circuits  23.377687         1
15          False      fake_mumbai          40            6  time_transpiled_circuits  35.131031         1
16          False  fake_washington          20            3             time_circuits   5.729617         1
17          False  fake_washington          20            3  time_transpiled_circuits  21.061335         1
18          False  fake_washington          20            6             time_circuits  11.404692         1
19          False  fake_washington          20            6  time_transpiled_circuits  33.093630         1
20          False  fake_washington          40            3             time_circuits  10.356137         1
21          False  fake_washington          40            3  time_transpiled_circuits  32.811150         1
22          False  fake_washington          40            6             time_circuits  24.519854         1
23          False  fake_washington          40            6  time_transpiled_circuits  65.782916         1

[before-898]
    full_sampling          backend  max_length  num_samples                    method    seconds  num_runs
0           False      fake_manila          20            3             time_circuits   1.239760         1
1           False      fake_manila          20            3  time_transpiled_circuits   4.570645         1
2           False      fake_manila          20            6             time_circuits   2.490214         1
3           False      fake_manila          20            6  time_transpiled_circuits   8.229670         1
4           False      fake_manila          40            3             time_circuits   2.401180         1
5           False      fake_manila          40            3  time_transpiled_circuits   7.136153         1
6           False      fake_manila          40            6             time_circuits   4.711962         1
7           False      fake_manila          40            6  time_transpiled_circuits  13.858979         1
8           False      fake_mumbai          20            3             time_circuits   1.182070         1
9           False      fake_mumbai          20            3  time_transpiled_circuits   5.678319         1
10          False      fake_mumbai          20            6             time_circuits   2.271423         1
11          False      fake_mumbai          20            6  time_transpiled_circuits  10.940199         1
12          False      fake_mumbai          40            3             time_circuits   2.332980         1
13          False      fake_mumbai          40            3  time_transpiled_circuits   9.905238         1
14          False      fake_mumbai          40            6             time_circuits   4.764303         1
15          False      fake_mumbai          40            6  time_transpiled_circuits  19.541976         1
16          False  fake_washington          20            3             time_circuits   1.219157         1
17          False  fake_washington          20            3  time_transpiled_circuits  16.669695         1
18          False  fake_washington          20            6             time_circuits   2.551022         1
19          False  fake_washington          20            6  time_transpiled_circuits  25.928957         1
20          False  fake_washington          40            3             time_circuits   2.294674         1
21          False  fake_washington          40            3  time_transpiled_circuits  21.894724         1
22          False  fake_washington          40            6             time_circuits   4.168826         1
23          False  fake_washington          40            6  time_transpiled_circuits  44.483864         1

[itoko]

Close as this fix is included in #982 (via #922)