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arXiv:2307.01481

Equivalence, Identity, and Unitarity Checking in Black-Box Testing of Quantum Programs

Peixun Long, Jianjun Zhao

Published Jul 4, 2023• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2307.01481

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•Mar 22, 2018•0 citations
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.
Oracle quantum programs are a fundamental class of quantum programs that serve as a critical bridge between quantum computing and classical 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 proposes a black-box testing framework designed for general oracle quantum programs. We formally define these programs, establish the foundational theory for their testing, and propose a detailed testing framework. We develop a prototype tool and conduct extensive experimental evaluations to evaluate the effectiveness of the 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 the potential to solve a wide variety of classically intractable problems. However, the inherent complexity, probabilistic behavior, and fragility of quantum systems pose significant challenges to ensuring the correctness and reliability of quantum programs. In this survey, we present a comprehensive overview of functional testing and validation techniques aimed at addressing these challenges for quantum circuits. We begin by outlining the unique characteristics of quantum systems that complicate traditional testing methodologies, including the absence of classical oracles, non-determinism due to quantum measurement, and the exponential growth of the state space. We then categorize and analyze a wide range of functional testing and validation techniques that have emerged to meet these challenges, including mutation testing, fuzz testing, and coverage testing. We further explore advanced semantic and white-box methods such as property-based testing, metamorphic testing, equivalence checking, fault testing, assertions, and concolic testing. Specifically, we discuss the applicability of these testing techniques to quantum circuits and examine their limitations in the current NISQ (Noisy Intermediate-Scale Quantum) era.
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.
Quantum state discrimination is one of the most fundamental tasks in quantum information since it describes the read-out process of classical information from quantum states in quantum communications.In quantum state discrimination, a given test state is guaranteed to be identical to one of a set of candidate quantum states.The task is to determine the identity of the test state by performing an appropriate quantum measurement based on the classical descriptions of the candidate states.Quantum state discrimination also has several connections to the principles of quantum mechanics such as the no-cloning theorem and the no-signaling principle.One of fundamental properties of quantum mechanics is that the exact classical description of unknown quantum states cannot be retrieved from a single copy of the physical state.Quantum state discrimination in the case that the candidate states are given as two unknown physical states (reference states) but their classical descriptions are not given, has been investigated.The two reference states are labeled one and two, respectively.The task is to determine which of the two reference states is equivalent to the test state, whereas the descriptions of the states are not of interest.We call such a task as equivalence determination of quantum states.Discrimination of quantum operations has been also investigated and it has been shown that there is an intrinsic difference between discrimination of quantum state and discrimination of quantum operations.We analyze a unitary operation version of the equivalence determination task by using the concept of higher-order quantum computation to investigate properties of discrimination of other quantum objects.We consider three black-boxes (test box and reference boxes) implementing unknown unitary operations given as physical systems.The test box is guaranteed to implement one of the two unitary operations given by the reference boxes.Equivalence determination of unitary operations is a task to determine the reference box implementing the same unitary operation as the one by the test box.We assume that the unitary operations of the reference boxes are randomly sampled from the Haar measure of SU(2).We first consider the case that each of three black-boxes can be used only once both in parallel and ordered uses of the black-boxes.We show that the optimal success probability for equivalence determination is 7/8 by obtaining analytical solutions of the corresponding semidefinite programmings (SDPs) both in the parallel and ordered strategies.The optimal success probability can be achieved even without using one of the reference boxes.We also showed that entanglement of an initial state across the systems on which the reference boxes act and the test box acts is necessary to achieve the optimal success probability.We then consider the case that the multiple uses of the reference boxes are allowed.We consider the parallel strategies up to four uses of each of the reference boxes and obtain the optimal success probabilities by numerically solving the semidefinite programmings.We numerically show that the ordered strategies give improvement over the parallel strategies and the optimal success probability varies depending on the order of the black-boxes when one reference box is used once and the other reference box is used twice.This result indicates that an appropriate order of the black-boxes under the ordered strategies is necessary to obtain improvement over the parallel strategies. Chapter 1 Introduction Notations• H i , K j : Hilbert spaces labeled with i and j.• L(H): The set of linear operators on H.• L(H, K): The set of linear operators from H to K.• S(H) : The set of positive semidefinite linear operation of unit trace on H • Tr H : The partial trace over H • U † : The conjugate transpose of U • {Π i }: The positive operator-valued measure • { Π i }: The quantum tester • δ ij : The Kronecker delta, equal to 1 if i = j and 0 otherwise • dµ(•) : The Haar measure, the uniform distribution of the space of unitary operations • |I⟩⟩ : Unnormalized maximally entangled vector defined as |I⟩⟩ = i |i⟩|i⟩ • M : A quantum channel • M : Choi operator of a quantum channel M• U j : The irreducible subspace of the total angular momentum j.