Add ResetAfterMeasureSimplification transpiler pass

[mtreinish]

Summary

This commit adds a new transpiler pass to simplify resets after a
measurement. This pass when run will replace any reset after a
measurement with a conditional X gate. This is because the reset
operation on IBM backends is implemented by performing a conditional x
gate after a reset. So doing this simplification will improve the
fidelity of the circuit because we're removing a duplicate measurement
which was implicit in the reset. This pass is based on the marz library:
https://github.com/Qiskit-Partners/marz which did the same thing but at
the QuantumCircuit level.

One note is that this pass is basically specific to IBM backends so it's
not added to the preset pass managers. Ideally we'd be able to have the
IBM backends run this as part of the init stage or something to do the
logical transformation early in the compilation. But right now there is
no mechanism to do this (see #8329), so for now having the pass and
letting users specify it in the pass manager directly is the best
option. After #8329 is implemented we can look at adding this pass to
that hook interface in the ibm provider's backends directly so that they
can leverage this optimization whenever they're the compilation target.

Details and comments

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[coveralls]

Pull Request Test Coverage Report for Build 2975962918

• 24 of 24 (100.0%) changed or added relevant lines in 3 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.009%) to 84.201%

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Totals
Change from base Build 2975949685:	0.009%
Covered Lines:	57040
Relevant Lines:	67743

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💛 - Coveralls

[taalexander]

Not all IBM backends implement reset with a conditional gate. Furthermore, as only IBM dynamic circuit backends are capable of applying the conditional operations and exploiting for performance I would recommend adding this pass to the IBM provider as in Qiskit/qiskit-ibm-provider#367

[nonhermitian]

Not all IBM backends implement reset with a conditional gate

I do not think that that actually matters here provided that conditional x gates are more efficient then whatever you use for reset. But it is an interesting point that I was unaware of.

As it turns out, @mtreinish and myself were talking in parallel about transpiler passes in the IBM provider.

[nonhermitian]

I think this is good from my end, but of course I am biased. The substitute_node_with_dag is nice, and I wish I thought of that when I was hacking around with the DAG.

I would say though that this is not 100% IBM specific, but the applicability to other platforms depends on the details; If your measurement does project into the computational basis states and your conditional-x gate (provided you can do them) is lower in error than whatever reset mechanism your using then you should win. That being said, I would agree that this is a likely candidate for the IBM provider / the notion of a staged passmanager

[jakelishman]

I think it can still be reasonable to include the pass in Terra, even if it was originally designed for certain IBM-specific backends. If nothing else, it's a nice example of a simple optimisation pass, but I do also think it's going to be a reasonable optimisation that quite a few backends will want to include in their backend-specific "codegen" transpiler stages. I'd have a problem with it if we added it to the default pass managers (which this PR doesn't do), because then we'd be making unfair assumptions about backends.

[jakelishman]

This looks fine to me. Did we decide to move forwards with including it in Terra as an example (especially now there's more extensibility in the preset pass managers), or did we decide it's too IBM specific?

(My vote, as above, is that it's fine to include as a possible plugin, just not in the preset pass managers.)

[nonhermitian]

I vote for adding it.