Quantum computing has emerged as a promising field with the potential to revolutionize various domains by harnessing the principles of quantum mechanics. As quantum hardware and algorithms continue to advance, developing high-quality quantum software has become crucial. However, testing quantum programs poses unique challenges due to the distinctive characteristics of quantum systems and the complexity of multi-subroutine programs. This article addresses the specific testing requirements of multi-subroutine quantum programs. We begin by investigating critical properties by surveying existing quantum libraries and providing insights into the challenges of testing these programs. Building upon this understanding, we focus on testing criteria and techniques based on the whole testing process perspective, spanning from unit testing to integration testing. We delve into various aspects, including IO analysis, quantum relation checking, structural testing, behavior testing, integration of subroutine pairs, and test case generation. We also introduce novel testing principles and criteria to guide the testing process. We conduct comprehensive testing on typical quantum subroutines, including diverse mutants and randomized inputs, to evaluate our proposed approach. The analysis of failures provides valuable insights into the effectiveness of our testing methodology. Additionally, we present case studies on representative multi-subroutine quantum programs, demonstrating the practical application and effectiveness of our proposed testing principles and criteria.

Estimating the unitarity of an unknown quantum channel$\mathcal {E}$provides information on how much it is unitary, which is a basic and important problem in quantum device certification and benchmarking. Unitarity estimation can be performed with either coherent or incoherent access, where the former in general leads to better query complexity while the latter allows more practical implementations. In this paper, we provide a unified framework for unitarity estimation, which induces ancilla-efficient algorithms that use$O(\epsilon ^{-2})$and$O(\sqrt {d}\cdot \epsilon ^{-2})$calls to$\mathcal {E}$with coherent and incoherent accesses, respectively, where$d$is the dimension of the system that$\mathcal {E}$acts on and$\epsilon $is the required precision. We further show that both the$d$-dependence and$\epsilon $-dependence of our algorithms are optimal. As part of our results, we settle the query complexity of the distinguishing problem for depolarizing and unitary channels with incoherent access by giving a matching lower bound$\Omega (\sqrt {d})$, improving the prior best lower bound$\Omega (\sqrt [{3}]{d})$by (Aharonov et al., 2022) and (Chen et al., FOCS 2021).