Add equivalences from CR<Pauli> to R<Paulis>

[Cryoris]

Summary

Add equivalences from controlled Pauli rotations to 2-Pauli rotations. This is particularly interesting e.g. for QPD applications where cuts are usually defined for 2-Pauli rotations or for compiling to the RZX gate and using a pulse-efficient decomposition. This could e.g. be used to compile a CRY gate to an efficient pulse sequence instead of 2 CX gates.

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[mtreinish]

It's not really related to this PR, as a standalone these equivalences are fine on their own. But one thing we are missing in the equivalence lib (it came up on slack) is targeting a CR<Pauli> basis. I think to fix it we can just define a rules from cx to crx, etc to fix that.

[coveralls]

Pull Request Test Coverage Report for Build 4066536314

• 64 of 64 (100.0%) changed or added relevant lines in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage remained the same at 85.244%

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Totals
Change from base Build 4065741968:	0%
Covered Lines:	67097
Relevant Lines:	78712

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💛 - Coveralls

[jakelishman]

(For posterity: the correctness of the standard equivalence library is tested automatically, without needing to modify the suite.)

[jakelishman]

If this is correct then I don't like our naming convention for RZXGate - to me, that reads as a ZX bitstring interaction, i.e. the Z is on qubit 1. But whatever, even if it mattered what I thought, the ship's long since sailed.

[Cryoris]

Tbh I never know which order it is and just end up trying until it fits 😅 but I agree that RZX should implement e^{i theta * ZX} and in our tensor order that would be Z on q_1..

[jakelishman]

I think the argument is that it implements what our documentation calls $Z \otimes X$, where I think there's some conflation of the general tensor product $\otimes$ with the Kronecker product ordering we use to make concrete matrix representations.

But anyway, the ship's sailed, and it's unrelated to this PR!

[jakelishman]

Ah - Wikipedia explains:

the Kronecker product, sometimes denoted by $\otimes$

as opposed to:

the tensor product $V\otimes W$

I've never used \otimes to refer to the Kronecker product, and wasn't aware that was something people did - to me, it's always meant the arbitrary tensor product, which isn't tied to any particular representation of linear algebra.

[Cryoris]

@mtreinish I opened an issue to keep track of these missing equivalences: #9511