Discussion: Add a Conjugate meta-bloq

[anurudhp]

This captures the pattern Conjugate(A, B) $= A^\dagger \cdot B \cdot A$. This has an efficient controlled version: C-Conjugate(A, B) = Conjugate(A, C-B) $= A^\dagger \cdot C\text{-}B \cdot A$.

Some bloqs which have custom controlled version to support the above optimization:

• QubitizationWalkOperator
• ReflectionUsingPrepare
• MeanEstimationOperator
  etc.

This would require carefully wiring up the registers, though. Especially when the registers of A and B don't match.
See LCUBlockEncodingZeroState for a similar decomposition.

Ref. https://dl.acm.org/doi/pdf/10.1145/3656397, Fig 14 (b). "Conditional Narrowing".

cc @charlesyuan314