swap-test implementation

This work addresses the challenge of designing high-fidelity quantum circuits, which often suffer from limited generality and suboptimal performance. The authors propose modeling the design problem as differentiable logic programming, uniquely integrating continuous logic with quantum unitary evolution. They develop an optimization framework based on T-norm fuzzy logic and geodesic interpolation, augmented with bias-aware initialization to mitigate barren plateaus. The approach enables users to specify custom differentiable logical axioms—such as correctness, simplicity, and robustness—and automatically discovers a 4-qubit quantum Fourier transform (QFT) circuit from a space of 21 candidate gates. Validated on the IBM Torino processor for local routing tasks, the method achieves a 59.3-percentage-point fidelity improvement over baselines and demonstrates resilience to hardware faults.

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.

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.

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.

This work addresses the long-standing oracle problem in quantum software stack (QSS) testing—the lack of reliable reference outputs for expected behavior—by introducing QEMI, the first testing methodology to adapt Equivalence Modulo Inputs (EMI), a technique from classical compiler testing, to the quantum domain. QEMI generates random quantum programs containing dead code and constructs semantically equivalent variants, then detects QSS bugs by comparing their execution outcomes across different platforms. Unlike conventional approaches that rely on syntactic or structural transformations, QEMI enables semantic-preserving program mutation and analysis. Empirical evaluation on Qiskit, Q#, and Cirq uncovered 11 crash-inducing bugs and one behavioral inconsistency, substantially enhancing the effectiveness of quantum software stack testing.

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.

This work addresses the challenge of reliably testing variational quantum eigensolvers (VQE) in the absence of known ground-state energies, a scenario where conventional testing methods suffer from high false-positive rates. The authors propose a metamorphic testing framework grounded in quantum mechanical invariants, uniquely integrating physical symmetries and algebraic properties into quantum software validation. By exploiting intrinsic invariants arising from parameterized rotation gates and diagonal Hamiltonians, the approach verifies circuit correctness without requiring oracle knowledge of the true ground-state energy. Demonstrated on 500 benchmark circuits—including those generated by humans and large language models—the method achieves zero false positives and substantially outperforms convergence-based testing, with a Youden’s J statistic of 0.57 compared to 0.02.

Existing quantum program testing approaches rely on simplistic inputs, statistical oracles, or costly complete specifications, and exhibit limited validation capabilities on real hardware. This work proposes SB-QOPS, the first method to integrate commuting Pauli strings with search-based testing, leveraging Pauli measurements to construct a lightweight oracle. It introduces an expectation-value-based fitness function to guide the search without requiring a full program specification. Implemented across IBM, IQM, and Quantinuum platforms, SB-QOPS achieves 100% fault detection on circuits with up to 29 qubits, significantly outperforming QOPS. The approach demonstrates excellent portability, maintaining high effectiveness in both simulated and real noisy environments.

This work addresses the lack of reproducible and fairly comparable benchmarks in quantum software testing, which has largely relied on small, hard-coded circuits that poorly reflect real-world development practices. To bridge this gap, the authors introduce Qolumbina—the first scalable benchmark suite for quantum software testing—systematically curated from 40 representative programs sourced from open-source repositories and rigorously refactored with standardized interfaces, test cases, and formal specifications. The study further proposes a novel taxonomy of testing characteristics specific to quantum programs and employs program complexity modeling to enable scalability analysis and systematic evaluation. Covering a diverse range of testing attributes, Qolumbina has already facilitated empirical studies on execution overhead and fault detection capability, revealing the critical influence of backend dependencies on the interpretation of testing outcomes.