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.