  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.
