quantum hypothesis testing

This study addresses the dominance of classical testing methods and the limited adoption of cutting-edge quantum verification techniques in quantum algorithm testing—particularly within the Qiskit Algorithms library. Employing empirical software engineering methodologies, we systematically identify and categorize seven prevalent testing patterns: fixed-seed testing, deterministic oracles, exact/approximate assertions, data-driven testing, functional testing, intermediate-state verification, and quantum circuit equivalence checking. Through large-scale empirical analysis, we reveal a significant gap between industry and academia: despite numerous quantum-native verification approaches proposed in research, current engineering practice remains heavily reliant on classical testing paradigms. Our work provides a foundational empirical basis and a structured taxonomy to bridge the theory–practice divide and advance standardization in quantum software engineering.

As quantum software grows increasingly complex, traditional quality assurance approaches relying on classical simulation have become infeasible to scale. This work addresses this challenge by systematically introducing classical software testing principles into the quantum computing domain from a software engineering perspective, thereby breaking dependence on simulation and establishing a testing paradigm tailored for real quantum hardware. By integrating quantum program analysis, error model identification, and hardware-aware modeling, the study proposes a deployable testing strategy and quality assurance framework suitable for actual quantum devices. It clearly articulates the core challenges of large-scale quantum software testing and offers a practical engineering pathway toward developing highly reliable quantum software.

In the rapidly advancing field of quantum computing, measurement-based output verification faces fundamental limitations due to the probabilistic nature of quantum states, hindering rigorous validation of complex quantum program behavior. Method: We systematically classify existing measurement-based verification techniques and empirically analyze their shortcomings—particularly their inability to adequately characterize distribution-level and value-level correctness, especially for programs exhibiting nontrivial quantum phenomena. We then comparatively evaluate state-vector–based verification, conducting an empirical study across diverse quantum programs. Contribution/Results: Our results demonstrate that measurement-based verification is only suitable for rudimentary existential checks, whereas state-vector–based verification precisely captures superposition, entanglement, and other core quantum behaviors, significantly enhancing test depth and reliability. This work advances quantum program testing from a “result-oriented” paradigm toward a “process-traceable” one, providing both theoretical foundations and methodological guidance for building robust quantum software quality assurance frameworks.

Traditional test case generation for safety-critical cyber-physical systems (CPS) suffers from low efficiency and poor coverage of deep-seated faults. Method: This paper pioneers the systematic application of quantum annealing to mutation-based test generation. It formulates test mutation as a binary optimization problem and leverages the D-Wave quantum annealer to identify and optimize critical test regions, thereby tightly integrating quantum-heuristic search with classical testing objectives. Contribution/Results: Experiments demonstrate that the proposed approach significantly outperforms classical optimization algorithms in test case generation speed while achieving fault detection rates comparable to state-of-the-art methods. Moreover, it empirically characterizes the relationships among problem scale, current quantum hardware limitations, and testing effectiveness. This work validates the feasibility and efficiency advantages of quantum annealing in practical CPS testing engineering and establishes a novel paradigm for quantum-enhanced software testing.

To address challenges in quantum program testing—including the difficulty of quantum state quantification, absence of symbolic modeling, inefficient path exploration, and insufficient branch coverage—this paper proposes the first concolic (combined concrete and symbolic) testing framework tailored for quantum programs. Methodologically, it introduces a novel constraint modeling mechanism for quantum control statements, designs symbolic representations for quantum variables, and develops a dedicated quantum constraint-solving strategy; it further integrates Qiskit to enable quantum-state quantification and constraint-driven path guidance. Experimental evaluation on programs with up to five qubits achieves a branch coverage of 74.27%, substantially outperforming baseline approaches. Moreover, the framework generates higher-quality quantum input samples, effectively exposing logical errors and quantum gate sequence defects. This work establishes a scalable symbolic execution paradigm and provides a practical toolset for quantum software testing.

This study addresses the lack of a unified methodology in empirical research on quantum software testing, which has hindered result interpretability and reproducibility. To this end, the work proposes a systematic analytical framework encompassing ten critical dimensions—including test subjects, baseline comparisons, and experimental configurations—and conducts a comprehensive literature review of 59 empirical studies coupled with multidimensional cross-analysis. The analysis reveals prevalent methodological flaws and inconsistencies in current practices. Beyond identifying common issues, the study formulates actionable methodological guidelines and concrete recommendations for improvement, thereby establishing both theoretical grounding and practical benchmarks to guide future empirical research in quantum software testing.

This study addresses the lack of effective metrics for analyzability in quantum-classical hybrid software, a key barrier to its maintainability and industrial adoption. Building upon the ISO/IEC 25010 standard, the authors propose a novel analyzability model for quantum software and empirically validate its ability to differentiate analyzability across diverse quantum algorithms through four controlled experiments involving multiple scenarios and participant groups. Complementing these experiments with user surveys on perceived complexity, the study demonstrates a strong alignment between the model’s outputs and human subjective judgments. The findings indicate that the proposed model not only provides an effective means to quantify analyzability in quantum software but also establishes a meaningful correspondence between objective measurement and human cognition, thereby offering a reliable tool for quantum software quality assessment.

Quantum software testing presents unique challenges not addressed by classical software engineering practices, yet its professional scope and competency requirements remain poorly defined. Method: This study systematically analyzes job postings from 110 quantum hardware and software enterprises, integrating semantic role labeling, latent Dirichlet allocation (LDA)-based topic modeling, and cross-domain skill mapping to empirically characterize the profession. Contribution/Results: We propose the first empirically grounded occupational definition of quantum software testing, formalized as a three-dimensional competency framework—“calibration, control, and hybrid verification.” The framework identifies three core competencies: programming automation, quantum device literacy, and interdisciplinary collaboration. This work bridges the epistemic gap between industry demand and academic training, providing empirically validated foundations for curriculum design, workforce standardization, and career pathway development in quantum software engineering.

Quantum programs produce probabilistic outputs, rendering traditional testing methods with fixed sampling budgets both costly on real hardware and statistically inadequate. This work proposes the first Bayesian sequential verification framework tailored for quantum programs, formulating verification as a Bayesian hypothesis test against a reference source—such as an ideal state vector or finite-sample outcomes. The approach dynamically updates the posterior distribution through batched observations to make pass/fail decisions, unifying statistical rigor with measurement-budget awareness. Implemented in Qiskit, the method significantly reduces measurement overhead on benchmark tasks including Bell state preparation and QAOA for MaxCut, outperforming fixed-budget baselines and demonstrating both efficiency and practicality.

Quantum program verification on early fault-tolerant hardware faces critical challenges due to scarce measurement resources and tight measurement budgets. Method: We propose the first unified, program-level measurement budgeting framework that systematically links theoretical error bounds—based on trace distance, fidelity, error probability, and the quantum Chernoff bound—with practical testing strategies: inversion testing, swap testing, and chi-square testing. The framework supports scalable analysis, from single-gate verification to full-program validation. Contribution/Results: We quantify substantial measurement overhead differences among strategies: inversion testing is optimal; swap testing incurs roughly 2× overhead; chi-square testing is simple but costly. Noise and fine-grained circuit decomposition further escalate costs. To address this, we introduce coarse-grained partitioning and weighted budget allocation, achieving superior trade-offs between verification accuracy and hardware resource consumption. Our framework establishes a computationally tractable, deployable paradigm for quantifying and allocating measurement resources in quantum software verification.