Hybrid quantum-classical circuit simplification with the ZX-calculus

• URL: http://arxiv.org/abs/2109.06071v1
• Date: Mon, 13 Sep 2021 15:45:56 GMT
• Title: Hybrid quantum-classical circuit simplification with the ZX-calculus
• Authors: Agust\'in Borgna, Simon Perdrix, Beno\^it Valiron
• Abstract summary: This work uses an extension of the formal graphical ZX-calculus called ZX-ground as an intermediary representation of the hybrid circuits. We derive a number of gFlow-preserving optimization rules for ZX-ground diagrams that reduce the size of the graph. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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