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Conference Papers Year : 2021

Hybrid Quantum-Classical Circuit Simplification with the ZX-Calculus


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.

Dates and versions

hal-03539521 , version 1 (21-01-2022)



Agustín Borgna, Simon Perdrix, Benoît Valiron. Hybrid Quantum-Classical Circuit Simplification with the ZX-Calculus. APLAS 2021 - Asian Symposium on Programming Languages and Systems, Oct 2021, Chicago, United States. pp.121-139, ⟨10.1007/978-3-030-89051-3_8⟩. ⟨hal-03539521⟩
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