Quantum annealers are specialized quantum computers for solving combinatorial optimization problems using special characteristics of quantum computing (QC), such as superposition, entanglement, and quantum tunneling. Theoretically, quantum annealers can outperform classical computers. However, the currently available quantum annealers are small-scale, i.e., they have limited quantum bits (qubits); hence, they currently cannot demonstrate the quantum advantage. Nonetheless, research is warranted to develop novel mechanisms to formulate combinatorial optimization problems for quantum annealing (QA). However, solving combinatorial problems with QA in software engineering remains unexplored. Toward this end, we propose BootQA, the very first effort at solving the test case minimization (TCM) problem with QA. In BootQA, we provide a novel formulation of TCM for QA, followed by devising a mechanism to incorporate bootstrap sampling to QA to optimize the use of qubits. We also implemented our TCM formulation in three other optimization processes: classical 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 in terms of 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.