Optimising Clifford circuits with Quantomatic

Fagan, Andrew and Duncan, Ross (2019) Optimising Clifford circuits with Quantomatic. Electronic Proceedings in Theoretical Computer Science, 287. pp. 85-105. ISSN 2075-2180

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    Abstract

    We present a system of equations between Clifford circuits, all derivable in the ZX-calculus, and formalised as rewrite rules in the Quantomatic proof assistant. By combining these rules with some non-trivial simplification procedures defined in the Quantomatic tactic language, we demonstrate the use of Quantomatic as a circuit optimisation tool. We prove that the system always reduces Clifford circuits of one or two qubits to their minimal form, and give numerical results demonstrating its performance on larger Clifford circuits.