Add benchmarking tests

[Procatv]

Summary

Adding to qiskit asv based on bench_press, specifically qiskit_gym tests

Making changes to the qiskit benchmarking suite by adding more tests with different types of circuits. Not yet finished implementing and would appreciate feedback regarding how I could better improve the benchmarking tests, and any other params I could keep track of.

Details and comments

Fixes #12595

[coveralls]

Pull Request Test Coverage Report for Build 9569038976

Details

• 0 of 0 changed or added relevant lines in 0 files are covered.
• 5 unchanged lines in 2 files lost coverage.
• Overall coverage decreased (-0.003%) to 89.75%

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Files with Coverage Reduction	New Missed Lines	%
qiskit/transpiler/passes/synthesis/unitary_synthesis.py	2	88.2%
crates/qasm2/src/lex.rs	3	92.11%

Totals
Change from base Build 9562946226:	-0.003%
Covered Lines:	63415
Relevant Lines:	70657

---

💛 - Coveralls

[qiskit-bot]

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• @Qiskit/terra-core

[coveralls]

Pull Request Test Coverage Report for Build 9636385838

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

• For more information on this, see Tracking coverage changes with pull request builds.
• To avoid this issue with future PRs, see these Recommended CI Configurations.
• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 0 of 0 changed or added relevant lines in 0 files are covered.
• 811 unchanged lines in 54 files lost coverage.
• Overall coverage increased (+0.03%) to 89.785%

---

Files with Coverage Reduction	New Missed Lines	%
qiskit/converters/circuit_to_gate.py	1	97.44%
qiskit/dagcircuit/dagdepnode.py	1	76.81%
qiskit/compiler/assembler.py	1	96.13%
qiskit/converters/circuit_to_instruction.py	1	98.21%
qiskit/assembler/assemble_schedules.py	1	98.35%
qiskit/qasm2/export.py	1	98.5%
qiskit/pulse/configuration.py	2	96.08%
qiskit/transpiler/passes/synthesis/unitary_synthesis.py	2	88.2%
qiskit/circuit/library/hamiltonian_gate.py	2	83.33%
qiskit/circuit/library/standard_gates/xx_plus_yy.py	2	95.74%

Totals
Change from base Build 9562946226:	0.03%
Covered Lines:	63662
Relevant Lines:	70905

---

💛 - Coveralls

[coveralls]

Pull Request Test Coverage Report for Build 9648917691

Details

• 0 of 0 changed or added relevant lines in 0 files are covered.
• 2 unchanged lines in 1 file lost coverage.
• Overall coverage increased (+0.03%) to 89.794%

---

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	2	92.88%

Totals
Change from base Build 9648699798:	0.03%
Covered Lines:	63754
Relevant Lines:	71000

---

💛 - Coveralls

[coveralls]

Pull Request Test Coverage Report for Build 9649517337

Details

• 0 of 0 changed or added relevant lines in 0 files are covered.
• 2 unchanged lines in 1 file lost coverage.
• Overall coverage increased (+0.02%) to 89.78%

---

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	2	91.86%

Totals
Change from base Build 9648699798:	0.02%
Covered Lines:	63744
Relevant Lines:	71000

---

💛 - Coveralls

[ShellyGarion]

it's also worth adding random cliffords synthesis benchmarks for various numbers of qubits:

from qiskit.quantum_info import *
cliff = random_clifford(num_qubits)
qc = cliff.to_circuit()

[coveralls]

Pull Request Test Coverage Report for Build 9994484740

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

• For more information on this, see Tracking coverage changes with pull request builds.
• To avoid this issue with future PRs, see these Recommended CI Configurations.
• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 0 of 0 changed or added relevant lines in 0 files are covered.
• 963 unchanged lines in 54 files lost coverage.
• Overall coverage increased (+0.2%) to 89.928%

---

Files with Coverage Reduction	New Missed Lines	%
qiskit/circuit/library/standard_gates/r.py	1	97.73%
crates/accelerate/src/synthesis/permutation/utils.rs	1	98.88%
qiskit/synthesis/evolution/lie_trotter.py	1	96.77%
qiskit/circuit/library/standard_gates/rxx.py	1	97.56%
qiskit/transpiler/passes/routing/commuting_2q_gate_routing/pauli_2q_evolution_commutation.py	1	97.92%
qiskit/circuit/library/standard_gates/rzx.py	1	97.56%
qiskit/circuit/library/standard_gates/u.py	1	95.92%
crates/accelerate/src/isometry.rs	1	99.65%
crates/accelerate/src/sampled_exp_val.rs	1	88.71%
qiskit/synthesis/evolution/product_formula.py	1	98.64%

Totals
Change from base Build 9648699798:	0.2%
Covered Lines:	65813
Relevant Lines:	73184

---

💛 - Coveralls

[sbrandhsn]

This looks great to me, thanks! :-) Can you also write a quick release note as described at https://github.com/Qiskit/qiskit/blob/main/CONTRIBUTING.md#release-notes ?

As this is not directly user-facing, I think it is fine to proceed without a release note. :-)