Add check for the size during transpiler optimization

[TheGupta2012]

Summary

Add check for the size during transpiler optimization fixing #7386

Details and comments

• This PR introduces the size check on a dag during transpiler optimization
• In qiskit/transpiler/preset_passmanagers/level2.py, a size check loop is introduced.
• A new list of transpiler passes is introduced to the PassManager which are iterated till the size is not constant across consecutive iterations.

Code for Results

from qiskit import QuantumCircuit, transpile

qc = QuantumCircuit.from_qasm_str(
    """
                    OPENQASM 2.0;
                    include "qelib1.inc";
                    qreg q[8];
                    cx q[1],q[2];
                    cx q[2],q[3];
                    cx q[5],q[4];
                    cx q[6],q[5];
                    cx q[4],q[5];
                    cx q[3],q[4];
                    cx q[5],q[6];
                    cx q[5],q[4];
                    cx q[3],q[4];
                    cx q[2],q[3];
                    cx q[1],q[2];
                    cx q[6],q[7];
                    cx q[6],q[5];
                    cx q[5],q[4];
                    cx q[7],q[6];
                    cx q[6],q[7];
                """
)

print("Original :", qc.draw())

print(
    f"Circuit transpiled with opt level 2 :", transpile(qc, optimization_level=2).draw()
)

Resultant Output

Original :                                              
q_0: ────────────────────────────────────────
                                             
q_1: ──■──────────────────────────────────■──
     ┌─┴─┐                              ┌─┴─┐
q_2: ┤ X ├──■────────────────────────■──┤ X ├
     └───┘┌─┴─┐                    ┌─┴─┐└───┘
q_3: ─────┤ X ├───────■─────────■──┤ X ├─────
     ┌───┐└───┘     ┌─┴─┐┌───┐┌─┴─┐├───┤     
q_4: ┤ X ├───────■──┤ X ├┤ X ├┤ X ├┤ X ├─────
     └─┬─┘┌───┐┌─┴─┐└───┘└─┬─┘├───┤└─┬─┘     
q_5: ──■──┤ X ├┤ X ├──■────■──┤ X ├──■───────
          └─┬─┘└───┘┌─┴─┐     └─┬─┘┌───┐     
q_6: ───────■───────┤ X ├──■────■──┤ X ├──■──
                    └───┘┌─┴─┐     └─┬─┘┌─┴─┐
q_7: ────────────────────┤ X ├───────■──┤ X ├
                         └───┘          └───┘
Circuit transpiled with opt level 2 :                                              
q_0: ────────────────────────────────────────
                                             
q_1: ────────────────────────────────────────
                                             
q_2: ────────────────────────────────────────
                                             
q_3: ────────────────────────────────────────
     ┌───┐               ┌───┐     ┌───┐     
q_4: ┤ X ├───────■───────┤ X ├─────┤ X ├─────
     └─┬─┘┌───┐┌─┴─┐     └─┬─┘┌───┐└─┬─┘     
q_5: ──■──┤ X ├┤ X ├──■────■──┤ X ├──■───────
          └─┬─┘└───┘┌─┴─┐     └─┬─┘┌───┐     
q_6: ───────■───────┤ X ├──■────■──┤ X ├──■──
                    └───┘┌─┴─┐     └─┬─┘┌─┴─┐
q_7: ────────────────────┤ X ├───────■──┤ X ├
                         └───┘          └───┘

[coveralls]

Pull Request Test Coverage Report for Build 2007200649

• 14 of 14 (100.0%) changed or added relevant lines in 3 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.01%) to 83.504%

---

Totals
Change from base Build 2007186808:	0.01%
Covered Lines:	52465
Relevant Lines:	62829

---

💛 - Coveralls

[jakelishman]

Is there a reason to limit this to level 2? The same iteration happens in levels 1 and 3 as well.

The tests of the preset pass managers are in test/python/transpiler/test_preset_passmanagers.py, but this would be fairly tricky to write a targetted test for, I think. In principle, we could construct one by making a circuit with two disjoint sets of qubits, where the first set has an operation that cancels down to a size of 0, but only after 3 loops, while the second collapses down in only 1 loop to a depth of more than first set has after the first loop. Finding those operations would be tricky, though; it would be easy for unrelated improvements in other transpiler passes to stymie the test by immediately reducing both paths to their smallest size.

At the very least, we could add a regression test of the case in #7386 to ensure that two subsequent calls to transpile don't change the size or depth.

[TheGupta2012]

@jakelishman would this PR require any more changes? I had updated the issue with some benchmarks which caught my eye.

[jakelishman]

I put some comments in #7386 about the benchmarking we'd want to do in advance, and the possibility of new benchmarks, but I'll have to pass final review to @kdk (or to whomever he delegates) because I'm going to be away from work for a while. It looks sensible to me on a quick glance, though.

[kdk]

Thanks for the updates here @TheGupta2012 , this LGTM!