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This chapter presents a method for equivalence checking of parameterized quantum circuits, which is crucial for verifying the compilation of variational quantum algorithms. The proposed multi-stage method first attempts to prove the equivalence of two parameterized circuits using the ZX-calculus. If this fails, it instantiates the parameters and employs a conventional complete equivalence checker. The chapter also introduces an instantiation scheme that simplifies most parameterized gates, ensuring a complete equivalence checking procedure for parameterized quantum circuits.

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Equivalence Checking of Parameterized Quantum Circuits: Verifying the Compilation ofVariational Quantum Algorithms

  • 章节

  • 发表日期：

    2026年

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  • Lukas Burgholzer,
  • Robert Wille

摘要

This chapter presents a method for equivalence checking of parameterized quantum circuits, which is crucial for verifying the compilation of variational quantum algorithms. The proposed multi-stage method first attempts to prove the equivalence of two parameterized circuits using the ZX-calculus. If this fails, it instantiates the parameters and employs a conventional complete equivalence checker. The chapter also introduces an instantiation scheme that simplifies most parameterized gates, ensuring a complete equivalence checking procedure for parameterized quantum circuits.