Equivalence, identity, and unitarity checking in black-box testing of quantum programs

Quantum programs exhibit inherent non-deterministic behavior, which poses more significant challenges for error discovery compared to classical programs. While several testing methods have been proposed for quantum programs, they often overlook fundamental questions in black-box testing. In this paper, we bridge this gap by presenting three novel algorithms specifically designed to address the challenges of equivalence, identity, and unitarity checking in black-box testing of quantum programs. We also explore optimization techniques for these algorithms, including specialized versions for equivalence and unitarity checking, and provide valuable insights into parameter selection to maximize performance and effectiveness. To evaluate the effectiveness of our proposed methods, we conducted comprehensive experimental evaluations, which demonstrate that our methods can rigorously perform equivalence, identity, and unitarity checking, offering robust support for black-box testing of quantum programs. •A new theorem about how to check whether a quantum operation is a unitary transform.•Black-box checking algorithms for equivalence, identity, and unitarity relation of quantum programs.•Heuristic optimization for equivalence and unitarity checking algorithms.•Evaluation of the performance of proposed algorithms from theoretical and experimental perspectives.