Quantum annealers are specialized quantum computers for solving combinatorial optimization problems with special quantum computing characteristics, e.g., superposition and entanglement. Theoretically, quantum annealers can outperform classic computers. However, current quantum annealers are constrained by a limited number of qubits and cannot demonstrate quantum advantages. Nonetheless, research is needed to develop novel mechanisms to formulate combinatorial optimization problems for quantum annealing (QA). However, QA applications in software engineering remain unexplored. Thus, we propose BootQA , the very first effort at solving test case minimization (TCM) problems on classical software with QA. We provide a novel TCM formulation for QA and utilize bootstrap sampling to optimize the qubit usage. We also implemented our TCM formulation in three other optimization processes: simulated annealing (SA), QA without problem decomposition, and QA with an existing D-Wave problem decomposition strategy, and conducted an empirical evaluation with three real-world TCM datasets. Results show that BootQA outperforms QA without problem decomposition and QA with the existing decomposition strategy regarding effectiveness. Moreover, BootQA ’s effectiveness is similar to SA. Finally, BootQA has higher efficiency in terms of time when solving large TCM problems than the other three optimization processes.

The most promising applications of quantum computing are centered around solving search and optimization tasks, particularly in fields such as physics simulations, quantum chemistry, and finance. However, the current quantum software testing methods face practical limitations when applied in industrial contexts: (i) they do not apply to quantum programs most relevant to the industry, (ii) they require a full program specification, which is usually not available for these programs, and (iii) they are incompatible with error mitigation methods currently adopted by main industry actors like IBM. To address these challenges, we present QOPS, a novel quantum software testing approach. QOPS introduces a new definition of test cases based on Pauli strings to improve compatibility with different quantum programs. QOPS also introduces a new test oracle that can be directly integrated with industrial APIs such as IBM's Estimator API and can utilize error mitigation methods for testing on real noisy quantum computers. We also leverage the commuting property of Pauli strings to relax the requirement of having complete program specifications, making QOPS practical for testing complex quantum programs in industrial settings. We empirically evaluate QOPS on 194,982 real quantum programs, demonstrating effective performance in test assessment compared to the state-of-the-art with a perfect F1-score, precision, and recall. Furthermore, we validate the industrial applicability of QOPS by assessing its performance on IBM's three real quantum computers, incorporating both industrial and open-source error mitigation methods.

Quantum Computing (QC) promises computational speedup over classic computing. However, noise exists in near-term quantum computers. Quantum software testing (for gaining confidence in quantum software's correctness) is inevitably impacted by noise, i.e., it is impossible to know if a test case failed due to noise or real faults. Existing testing techniques test quantum programs without considering noise, i.e., by executing tests on ideal quantum computer simulators. Consequently, they are not directly applicable to test quantum software on real quantum computers or noisy simulators. Thus, we propose a noise-aware approach (named$\mathit{QOIN}$) to alleviate the noise effect on test results of quantum programs.$\mathit{QOIN}$employs machine learning techniques (e.g., transfer learning) to learn the noise effect of a quantum computer and filter it from a program's outputs. Such filtered outputs are then used as the input to perform test case assessments (determining the passing or failing of a test case execution against a test oracle). We evaluated$\mathit{QOIN}$on IBM's 23 noise models, Google's two available noise models, and Rigetti's Quantum Virtual Machine, with six real-world and 800 artificial programs. We also generated faulty versions of these programs to check if a failing test case execution can be determined under noise. Results show that$\mathit{QOIN}$can reduce the noise effect by more than$80\%$on most noise models. We used an existing test oracle to evaluate$\mathit{QOIN}$'s effectiveness in quantum software testing. The results showed that$\mathit{QOIN}$attained scores of$99\%$,$75\%$, and$86\%$for precision, recall, and F1-score, respectively, for the test oracle across six real-world programs. For artificial programs,$\mathit{QOIN}$achieved scores of$93\%$,$79\%$, and$86\%$for precision, recall, and F1-score respectively. This highlights$\mathit{QOIN}$'s effectiveness in learning noise patterns for noise-aware quantum software testing.