Hybrid quantum-classical circuit simplification with the ZX-calculus

TL;DR

This paper introduces a comprehensive optimization method for hybrid quantum-classical circuits using ZX-calculus, enabling granular reductions and classical gate integration, with implementation in the PyZX library.

Contribution

It extends the ZX-calculus framework to optimize hybrid circuits, including classical logic, with a novel diagram rewriting strategy and circuit extraction process.

Findings

Reduces hybrid circuit size through ZX-ground diagram optimizations.

Effectively integrates classical gates into quantum circuits.

Implemented as an extension to the PyZX library.

Abstract

We present a complete optimization procedure for hybrid quantum-classical circuits with classical parity logic. While common optimization techniques for quantum algorithms focus on rewriting solely the pure quantum segments, there is interest in applying a global optimization process for applications such as quantum error correction and quantum assertions. This work, based on the pure-quantum circuit optimization procedure by Duncan et al., uses an extension of the formal graphical ZX-calculus called ZX-ground as an intermediary representation of the hybrid circuits to allow for granular optimizations below the quantum-gate level. We define a translation from hybrid circuits into diagrams that admit the graph-theoretical focused-gFlow property, needed for the final extraction back into a circuit. We then derive a number of gFlow-preserving optimization rules for ZX-ground diagrams that reduce the size of the graph, and devise an strategy to find optimization opportunities by rewriting the diagram guided by a Gauss elimination process. Then, after extracting the circuit, we present a general procedure for detecting segments of circuit-like ZX-ground diagrams which can be implemented with classical gates in the extracted circuit. We have implemented our optimization procedure as an extension to the open-source python library PyZX.