Peixun Long

Oracle quantum programs are a fundamental class of quantum programs that enable developers to embed classical logic into quantum computing. Many important quantum algorithms are built upon oracle quantum programs, making it essential to ensure their correctness during development. Although software testing is a well-established approach for improving program reliability, no systematic method has been developed to test oracle quantum programs. This paper aims to build an equivalence-class-partition-based testing framework to complete the testing tasks for general oracle quantum programs. Our research methods involve both theoretical analysis and experimental evaluations. In the theoretical analysis, we first give the formal definition of general oracle quantum programs. Then we establish the foundational theory for the testing approaches. We propose an equivalence-class-partition-based testing framework, involving 4 testing criteria and 3 propositions about the selection of parameters in testing execution. In experimental evaluations, we select 10 original oracle quantum programs and their 132 mutants to evaluate the correctness of our theory and the effectiveness of our testing framework. Our results demonstrate that the proposed framework significantly aids developers in testing oracle quantum programs, providing insights to enhance the reliability of quantum software.

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.

We introduce isQ, a new software stack for quantum programming in an imperative programming language, also named isQ. The aim of isQ is to make programmers write quantum programs as conveniently as possible. In particular: 1)The isQ language and its compiler contain many useful features, including but not limited to: classical control flow, such as recursion; decomposition of self-defined unitary gates; and oracle programming and its circuit realization. 2)To make it flexible, an isQ program can be compiled into several different kinds of intermediate representation and assemblies, including QIR, eQASM, OpenQASM 3.0, and QCIS (specially tailored for the superconducting quantum hardware at USTC). 3)Besides interfacing isQ with real superconducting hardware, a QIR simulator is also developed for the demonstration and testing of isQ programs. isQ software stack encompasses abundant compiler optimizations of high-level quantum programs. To realize it, a distinct MLIR dialect name isQ-IR is proposed.

Estimating the unitarity of an unknown quantum channel 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 (ϵ ^–2 ) and O ( √ d ∙ϵ ^–2 ) calls to E with coherent and incoherent accesses, respectively, where d is the dimension of the system that E acts on and ϵ is the required precision. We further show that both the d -dependence and ϵ-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 Ω( √ d ), improving the prior best lower bound Ω( ∛ d ) by Aharonov et al. (Nat. Commun. 2022) and Chen et al. (FOCS 2021).