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This chapter reviews the state of the art in equivalence checking of quantum circuits with the ZX-calculus. It discusses how the method can be augmented to handle inaccuracies in complex number representations, different qubit mappings, and ancillary qubits. The completeness of the method is established for Clifford circuits, and a case study is presented to establish a baseline for the current state of the art in equivalence checking.

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Equivalence Checking of Quantum Circuits with the ZX-Calculus

  • 章节

  • 发表日期：

    2026年

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  • Lukas Burgholzer,
  • Robert Wille

摘要

This chapter reviews the state of the art in equivalence checking of quantum circuits with the ZX-calculus. It discusses how the method can be augmented to handle inaccuracies in complex number representations, different qubit mappings, and ancillary qubits. The completeness of the method is established for Clifford circuits, and a case study is presented to establish a baseline for the current state of the art in equivalence checking.