Mid-circuit compilation

[jordandsullivan]

Came across this Intel paper on unitary and non-unitary quantum operations, which would be necessary for doing compilation which could handle mid-circuit measurement.
https://arxiv.org/abs/2305.09843

It is an extension of the PCOAST framework: https://arxiv.org/abs/2305.10966

This paper presents the Pauli-based Circuit Optimization, Analysis, and Synthesis Toolchain (PCOAST), a framework for quantum circuit optimizations based on the commutative properties of Pauli strings. Prior work has demonstrated that commuting Clifford gates past Pauli rotations can expose opportunities for optimization in unitary circuits. PCOAST extends that approach by adapting the technique to mixed unitary and non-unitary circuits via generalized preparation and measurement nodes parameterized by Pauli strings.

I think we should explore this for future implementation.