Search-Based Quantum Program Testing via Commuting Pauli String

Abstract: Quantum software testing is important for reliable quantum software engineering. Despite recent advances, existing quantum software testing approaches rely on simple test inputs and statistical oracles, costly program specifications, and limited validation on real quantum computers. To address these challenges, we propose SB-QOPS, a search-based quantum program testing approach via commuting Pauli strings. SB-QOPS, as a direct extension to a previously proposed QOPS approach, redefines test cases in terms of Pauli strings and introduces a measurement-centric oracle that exploits their commutation properties, enabling effective testing of quantum programs while reducing the need for full program specifications. By systematically exploring the search space through an expectation-value-based fitness function, SB-QOPS improves test budget utilization and increases the likelihood of uncovering subtle faults. We conduct a large-scale empirical evaluation on quantum circuits of up to 29 qubits on real quantum computers and emulators. We assess three search strategies: Genetic Algorithm, Hill Climbing, and the (1+1) Evolutionary Algorithm, and evaluate SB-QOPS under both simulated and real noisy conditions. Experiments span three quantum computing platforms: IBM, IQM, and Quantinuum. Results show that SB-QOPS significantly outperforms QOPS, achieving a fault-detection score of 100% for circuits up to 29 qubits, and demonstrating portability across quantum platforms.