implement swap test

Quantum software complexity poses significant challenges to the detection of state discrepancies and reliability in unit testing. To address this, we propose a quantum-centric unit testing framework specifically designed for quantum circuits, featuring a novel inverse test technique integrated with statevector testing and SWAP testing—yielding a hybrid verification methodology compatible with both classical simulation and quantum hardware execution. Empirical evaluation across over 1.79 million mutated circuits demonstrates that our approach substantially reduces both false positive and false negative rates compared to conventional statistical testing. Moreover, statevector and inverse tests achieve high-confidence verification with significantly fewer measurements and markedly improved fault detection capability. This work establishes a new unit testing paradigm for quantum software that offers superior accuracy and efficiency in verification.

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.

This work systematically addresses the verifiability and quantifiability of quantum “magic”—a fundamental resource underpinning quantum computational advantage. We propose a scalable stabilizer verification protocol based on quantum convolution and swap testing, reducing the verification complexity for quantum states and gates to polynomial time. We introduce the novel concept of “magic entropy,” the first experimentally measurable magic monotone that is both monotonic under Clifford operations and convex—overcoming the long-standing limitation that magic cannot be directly observed. Through theoretical analysis, design of universal circuits (for both qubits and qudits), and numerical simulations, we demonstrate that magic entropy exhibits high sensitivity to deviations from the Clifford group. Our framework establishes a new paradigm for benchmarking and hardware validation of magic resources in near-term quantum devices.

The absence of systematic benchmarks hampers rigorous evaluation of quantum software testing techniques. Method: We conduct a large-scale empirical study, generating over 700,000 faulty mutants from 382 real-world quantum circuits, and systematically analyze how circuit characteristics (e.g., depth, gate count), algorithm classes (e.g., QAOA), and mutation operators influence fault detection capability. Contribution/Results: We present the first quantitative characterization of the relationship between quantum circuit features and mutation detection difficulty; propose a configurable, cost-benefit–driven paradigm for constructing fault benchmarks; and release QFaultBench—an open-source tool that intelligently recommends mutants based on algorithm category and detection difficulty. Our work delivers a standardized benchmark suite, highly discriminative mutation operator combinations, and empirically grounded recommendation strategies, significantly enhancing the scientific rigor and efficiency of quantum testing benchmark construction.

Synthesis of reversible Boolean functions as multi-controlled Toffoli (MCT) quantum circuits, with the objective of minimizing the actual gate count under physical constraints. Method: We propose the first end-to-end integer optimization model that directly minimizes the number of physical quantum gates. The model integrates constraint programming (CP), integer nonlinear modeling, symmetry analysis, and custom symmetry-breaking constraints to drastically improve computational efficiency. Contribution/Results: Our approach achieves up to two orders of magnitude speedup over prior methods. For 7-qubit benchmarks with at most 15 gates, it delivers the first provably optimal solutions for multiple classical benchmarks, establishing new records for minimal MCT circuits. Unlike heuristic approaches, our method provides mathematically verifiable optimality guarantees and yields strictly smaller circuits. The key innovation lies in embedding the physical gate-count objective into a compact, rigorous optimization framework while systematically exploiting symmetries for pruning—thereby unifying theoretical soundness with computational tractability.

Quantum circuits are inherently difficult to debug and monitor at runtime due to the no-cloning theorem and wavefunction collapse upon measurement. This paper introduces the first runtime monitoring framework that jointly ensures high fidelity and observability: it enables localized error localization by inserting lightweight monitoring operators, performing mid-circuit measurements, and resetting qubits—without perturbing the original circuit behavior, including entanglement and other essential quantum properties. The framework continuously compares the expected quantum state with the empirically measured probability distribution, introducing negligible disturbance. Evaluated on 154 benchmark circuits, the approach achieves zero functional degradation, high error detection rates, and practical levels of coverage and robustness.

This work addresses the challenge of effectively detecting implementation faults in quantum neural networks by proposing an efficient mutation testing approach. The method introduces novel quantum circuit mutation operators and a targeted mutation generation strategy, which collectively reduce redundant mutants while enhancing the precision of fault injection. By generating mutants with greater diversity and representativeness, the approach significantly strengthens the ability of test suites to validate quantum neural network implementations, uncovering defects that are often missed by conventional testing techniques. Experimental results demonstrate the effectiveness of the proposed method in improving the reliability of quantum machine learning models.

Existing approaches to quantum program testing struggle to adequately explore the quantum state space, limiting software reliability. This work proposes a test circuit generation framework based on Brick-Circuit architectures that constructs hardware-compatible gates to approximate ideal random states, thereby enhancing coverage of the state space. The method introduces a novel diversity scoring mechanism that jointly accounts for amplitude, phase, and entanglement, integrating local and global perspectives. Furthermore, it designs a shallow yet highly expressive generator for test inputs. Experimental results demonstrate that, compared to existing techniques, the proposed generator achieves more uniform coverage of quantum states and stronger entanglement capabilities at significantly reduced circuit depths.

This study addresses the significant challenge of verifying the correctness of quantum compiler transformations, which is inherently difficult due to high computational complexity. To overcome the limitations of conventional unit testing, this work proposes RetroQ, a framework that integrates the principles of retrosynthetic back-testing and the Hadamard test to enable automated verification of both semantic preservation and structural modifications within quantum compilation pipelines. Implemented through the integration of PennyLane and Qiskit, the proposed approach not only successfully reproduces known defects but also detects latent bugs related to parameter handling and logical errors. By facilitating rigorous and automated validation of compilation passes, RetroQ substantially enhances the reliability of the quantum software stack.

This work addresses the lack of fault-injected benchmark programs in quantum software testing, which hinders effective evaluation of test cases. To bridge this gap, the authors propose and construct QMutBench, a large-scale benchmark dataset comprising over 700,000 mutated quantum circuits that encompass diverse fault types. QMutBench is the first dataset to enable flexible filtering along multiple dimensions—including original circuit, mutation operator type, and mutant survival rate—and is publicly accessible via an online interface. By providing a customizable and reproducible evaluation infrastructure for mutation-based quantum software testing, QMutBench significantly advances both research and practical applications in this emerging field.