Add transpiler pass to optimize circuits with annotated operations

[alexanderivrii]

What should we add?

The idea is to add a transpiler pass that optimizes circuits with annotated operations.

Here is the list of possible optimizations that came up in various discussions:

Canonicalize modifiers. Convert the modifiers of an annotated operation into canonical form.
Example: consecutively applying inverse(), control(2), and inverse() is equivalent to applying control(2).

Remove annotations when possible.
Example: AnnotatedOperation(SwapGate(), [InverseModifier(), InverseModifier()]) is equivalent to SwapGate().

Recursively combine annotations.
Example: if g1 = AnnotatedOperation(g2, ControlModifier(2)) and g2 = AnnotatedOperation(SwapGate(), InverseModifier()), then we can replace g1 by AnnotatedOperation(SwapGate(), [InverseModifier(), ControlModifier(2)]).

Remove pairs of consecutive inverse gates.
This has several flavors. SGate() cancels out with SdgGate() but also with AnnotatedOperation(SGate(), InverseModifier) and also with AnnotatedOperation(SdgGate(), []). I am not sure this specific optimization should be a part of this transpiler pass, maybe it should be supported by InverseCancellation or the like.

Perform conjugate reduction.
A great example is a controlled QFT-based adder, which looks as follows: control-(QFT^{-1} -- U -- QFT). We saw in the past that Qiskit produces significantly sub-optimal decompositions. The circuit can be optimized to: QFT^{-1} -- control-U -- QFT, i.e. the control can be moved to the U-part only.

The pass probably needs to be recursive, descending into definitions of various gates.

Suggestions for additional optimizations are highly welcome

[ajavadia]

These are great.

I would add that most (any?) circuit optimizations that we do should be done while the gates are controlled by the same qubits. For example there is a pass to collapse a chain of gates: this should be done when those gates share the same control(s) too.

[mtreinish]

I'm going to close this as #11476 has merged now. If there are additional optimizations we want to enable in the pass, we can open a new issue to track those for future releases.