Add identity removal pass to presets

[mtreinish]

Summary

This commit adds the newly added RemoveIdentityEquivalent transpiler
pass to the preset pass managers for optimization levels 2 and 3. The
pass is added to the init and optimization stages. For the init stage
the pass is run after 3 or more qubit decomposition. While the pass
works fine with 3 qubit gates, the thinking behind this placement was
it seems less likely for a multi qubit identity equivalent gate to be
added while components of it's decomposition are more likely to be
equivalent to an identity. For the optimization stage it is added to
the optimization loop.

One test needed to be updated because the additional pass changes the
decomposition outcome in that test. Although the output circuit is
different it is equivalent to the other decomposition and the original
circuit. A unitary equivalence check is added to the test to verify
that.

Details and comments

This PR is based on top of #12384 and will need to be rebased after it merges. You can see the contents of this PR by looking at the head commit:

be36b59

[qiskit-bot]

One or more of the following people are relevant to this code:

• @Qiskit/terra-core

[coveralls]

Pull Request Test Coverage Report for Build 11712056331

Details

• 1 of 1 (100.0%) changed or added relevant line in 1 file are covered.
• 16 unchanged lines in 2 files lost coverage.
• Overall coverage increased (+0.005%) to 88.805%

---

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	4	91.98%
crates/qasm2/src/parse.rs	12	96.69%

Totals
Change from base Build 11710853769:	0.005%
Covered Lines:	77556
Relevant Lines:	87333

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💛 - Coveralls

[Cryoris]

I think I would expect the transpiler to remove Ry(0) & co even as a very basic optimization, should we also include this target-free run in optimization level 1?

[mtreinish]

My concern with doing it for level 1 was more about small angles like Ry(1e-8) will be removed and I was worried that might be surprising to people especially at level 1. But I don't feel super strongly about it, it's easy enough to add it to level 1 if you think that's better.

[Cryoris]

Hm you're right, I didn't think that these angles are already removed already... as rule we should maybe not increase the level of approximation that is already happening (e.g. cutoffs that unitary re-synthesis does). On level 1 we don't do re-synthesis, right? So then I agree we shouldn't add it one 1 yet 🙂

[mtreinish]

Level 1 will run 1q re-synthesis, but via Optikize1qGatesDecomposition not UnitarySynthesis. I can't remember how that pass handles tolerances, I'll have to check.

[Cryoris]

This is slightly unexpected, I guess at some point a gate is now removed and Optimize1qGatesDecomposition optimizes the sequence differently? Or why do you think this happens?

[mtreinish]

That was my assumption, I don't remember the exact details though. Let me run it with a callback and see what's going on exactly.

[mtreinish]

Looking through each pass it looks like RemoveIdentityEquivalent changes:

global phase: 4.6124
   ┌──────┐┌────┐┌───────────┐┌────┐┌───────┐
q: ┤ P(0) ├┤ √X ├┤ P(3.3416) ├┤ √X ├┤ P(3π) ├
   └──────┘└────┘└───────────┘└────┘└───────┘

to:

global phase: 4.6124
   ┌────┐┌───────────┐┌────┐┌───────┐
q: ┤ √X ├┤ P(3.3416) ├┤ √X ├┤ P(3π) ├
   └────┘└───────────┘└────┘└───────┘

This changes the output of Optimize1qGatesDecomposition which runs immediately after from:

global phase: 4.8124
   ┌───────┐┌────┐┌───────────┐┌────┐
q: ┤ P(-π) ├┤ √X ├┤ P(2.9416) ├┤ √X ├
   └───────┘└────┘└───────────┘└────┘

which is the output on calling the pass on the circuit with P(0)

to:

global phase: 4.6124
   ┌────┐┌───────────┐┌────┐┌───────┐
q: ┤ √X ├┤ P(3.3416) ├┤ √X ├┤ P(3π) ├
   └────┘└───────────┘└────┘└───────┘

which is the pass's output with P(0) removed. What this is coming down to is the preference for Optimize1qGatesDecomposition to defer to the input circuit if it doesn't think the synthesis output is any better. Since the gate counts of either output are the same, the pass views them as equivalent (in the absence of error rates in the target) and prefer to not modify the circuit instead of use the synthesis output. While in the case of without the removal pass being run there is an extra 1q gate in the sequence the pass views the synthesis output as being more efficient because it has 1 fewer gate.

[Cryoris]

Ahh that makes sense -- thanks for checking, better to be sure! 🙂