With the accelerating development of quantum technologies and their growing computational potential, quantum systems are being adapted for simulations and other critical tasks across diverse domains, making the reliability of the corresponding quantum software an essential concern. Although recent efforts have started to incorporate quantum-specific properties such as magnitude, phase, and entanglement under the form of input-coverage criteria into software testing, the unique structure of the quantum state space demands for more comprehensive testing. In particular, the notion of complete state-space exploration has so far received little attention. To address this gap, we propose a framework for evaluating test circuit generators with respect to their coverage of the quantum state space. Our contribution is threefold: we develop a set of diversity scores that capture both local and global indicators of the extent to which the state space is explored; we propose a test circuit generator that produces test input states via a Brick-Circuit (BC) construction designed to approximate ideal random states using hardware-compatible gates; we compare the proposed construction with existing generators based on their ability to generate uniformly distributed random test input states. Our extended diversity scores quantify the local correlations and global spread of magnitude, phase and entanglement. Using these scores, we evaluate the expressibility, defined as the capability to span the quantum state space uniformly, and entangling capabilities of existing generators relative to the BC generator. Our results show that the hardware-compatible BC generator achieves higher expressibility and entanglement performance at shallower depths than existing circuit generators.
With the accelerating development of quantum technologies and their growing computational potential, quantum systems are being adapted for simulations and other critical tasks across diverse domains, making the reliability of the corresponding quantum software an essential concern. Although recent efforts have started to incorporate quantum-specific properties such as magnitude, phase, and entanglement under the form of input-coverage criteria into software testing, the unique structure of the quantum state space demands for more comprehensive testing. In particular, the notion of complete state-space exploration has so far received little attention. To address this gap, we propose a framework for evaluating test circuit generators with respect to their coverage of the quantum state space. Our contribution is threefold: we develop a set of diversity scores that capture both local and global indicators of the extent to which the state space is explored; we propose a test circuit generator that produces test input states via a Brick-Circuit (BC) construction designed to approximate ideal random states using hardware-compatible gates; we compare the proposed construction with existing generators based on their ability to generate uniformly distributed random test input states. Our extended diversity scores quantify the local correlations and global spread of magnitude, phase and entanglement. Using these scores, we evaluate the expressibility, defined as the capability to span the quantum state space uniformly, and entangling capabilities of existing generators relative to the BC generator. Our results show that the hardware-compatible BC generator achieves higher expressibility and entanglement performance at shallower depths than existing circuit generators.
The recent fast development of quantum computers breaks several computation limitations that are difficult for conventional computers. Up to the present, although many approaches and tools have been proposed to test quantum programs, the fundamental features of quantum programs, i.e., magnitude, phase, and entanglement, have been largely overlooked, leading to limited fault detection capability and reduced testing effectiveness. To address this problem, we propose an automated testing framework named QURATEST, equipped with three test case generators (including two newly proposed techniques, UCNOT and IQFT in this paper, as well as one based on Random techniques) to test quantum programs. Overall, the proposed generators enable the generation of diverse test inputs by considering the quantum features of quantum programs. In the experiments, we perform an in-depth evaluation of QURATEST from three aspects: generated test case diversity, output coverage of the program under test, and fault detection capability. The results demonstrate the potential of our newly proposed techniques in that IQFT can generate the most diverse test cases regarding magnitude, phase, and entanglement, with 66% cell coverage. Comparatively, the Random approach only has 10% cell coverage. Regarding the evaluations of the output coverage, IQFT can achieve the highest output coverage in 70.2% (33 out of 47) of all quantum programs. In terms of fault detection, UCNOT outperforms the other two techniques. Specifically, the test cases generated by UCNOT have the best mutation score in 88.4% (23 out of 26) quantum programs.
Quantum programs are designed to run on quantum computers, leveraging quantum circuits to solve problems that are intractable for classical machines. As quantum computing advances, ensuring the reliability of quantum programs has become increasingly important. This paper introduces NovaQ, a diversity-guided testing framework for quantum programs. NovaQ combines a distribution-based test case generator with a novelty-driven evaluation module. The generator produces diverse quantum state inputs by mutating circuit parameters, while the evaluator quantifies behavioral novelty based on internal circuit state metrics, including magnitude, phase, and entanglement. By selecting inputs that map to infrequently covered regions in the metric space, NovaQ effectively explores under-tested program behaviors. We evaluate NovaQ on quantum programs of varying sizes and complexities. Experimental results show that NovaQ consistently achieves higher test input diversity and detects more bugs than existing baseline approaches.
This research paper provides an in-depth examination of verification and testing approaches for quantum circuits, focusing on methodologies essential for ensuring the correctness, reliability and operational efficiency of quantum computing systems. Since quantum circuits function on the fundamental principles of superposition and entanglement, they present verification challenges that cannot be effectively addressed using conventional classical testing techniques. As a result, the development of specialized quantum-specific verification strategies has become critically important. The study highlights simulation-based verification as a foundational technique, wherein the outcomes of quantum circuit simulations are systematically compared with results obtained from physical quantum hardware. This process enables the identification of functional inconsistencies and supports iterative refinement of circuit designs. In addition, randomized benchmarking is examined as a key evaluation method for estimating circuit fidelity and quantifying error rates through the application of random gate sequences and performance comparisons against established benchmarks. To further improve system robustness, the research investigates fault-tolerant mechanisms, particularly quantum error correction codes, which play a vital role in minimizing the effects of noise, decoherence and hardware imperfections. The integration of advanced quantum metrology and characterization techniques is also explored, enabling precise measurement and detailed analysis of quantum system behavior. These techniques provide deeper insights into circuit performance and contribute significantly to validation processes. By combining simulation-based verification, randomized benchmarking, fault-tolerant protocols and quantum metrology, this study proposes a comprehensive and reliable framework for quantum circuit verification and testing. The findings contribute to the advancement of dependable quantum technologies and support their growing applications in areas such as cryptography, materials science and other emerging domains.
Coverage criteria play a central role in assessing test adequacy in classical software, yet their effectiveness for quantum programs remains poorly understood and largely unexplored. In this paper, we propose six quantum-tailored criteria - condition, decision, and path coverage, and their probabilistic variants - adapted from their classical counterparts. We present QaCoCo, a tool that computes these criteria for circuit-based quantum programs. We empirically evaluate these criteria on a large and diverse set of 540 circuits and analyze the coverage achieved. Our results show that while circuits frequently achieve high condition and decision coverage (97.56% and 97.63%, on average), path coverage remains limited (71.84%), particularly in the presence of multi-controlled gates, which induce extreme path explosion and coverage imbalance. Moreover, to account for the probabilistic nature of quantum circuits, we introduce probabilistic coverage, which augments structural coverage with a confidence measure (88.87%, 88.65%, and 37.18% for condition, decision, and path coverage, respectively, on average). Finally, through mutation testing, we find weak or no correlation between fault detection and structural coverage, consistent with observations in classical computing.
Quantum Neural Networks (QNNs) have achieved initial success in various tasks by integrating quantum computing and neural networks. However, growing concerns about their reliability and robustness highlight the need for systematic testing. Unfortunately, current testing methods for QNNs remain underdeveloped, with limited practical utility and insufficient empirical evaluation. As an initial effort, we design a set of superposition-targeted coverage criteria to evaluate QNN state exploration embedded in test suites. To characterize the effectiveness, scalability, and robustness of the criteria, we conduct a comprehensive empirical study using benchmark datasets and QNN architectures. We first evaluate their sensitivity to input diversity under multiple data settings, and analyze their correlation with the number of injected faults. We then assess their scalability to increasing circuit scales. The robustness is further studied under practical quantum constraints including insufficient measurement and quantum noise. The results demonstrate the effectiveness of quantifying test adequacy and the potential applicability to larger-scale circuits and realistic quantum execution, while also revealing some limitations. Finally, we provide insights and recommendations for future QNN testing.
Abstract Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications. Expanding the portfolio of such techniques, we propose a quantum circuit learning algorithm that can be used to assist the characterization of quantum devices and to train shallow circuits for generative tasks. The procedure leverages quantum hardware capabilities to its fullest extent by using native gates and their qubit connectivity. We demonstrate that our approach can learn an optimal preparation of the Greenberger-Horne-Zeilinger states, also known as “cat states”. We further demonstrate that our approach can efficiently prepare approximate representations of coherent thermal states, wave functions that encode Boltzmann probabilities in their amplitudes. Finally, complementing proposals to characterize the power or usefulness of near-term quantum devices, such as IBM’s quantum volume, we provide a new hardware-independent metric called the qBAS score. It is based on the performance yield in a specific sampling task on one of the canonical machine learning data sets known as Bars and Stripes. We show how entanglement is a key ingredient in encoding the patterns of this data set; an ideal benchmark for testing hardware starting at four qubits and up. We provide experimental results and evaluation of this metric to probe the trade off between several architectural circuit designs and circuit depths on an ion-trap quantum computer.