Test case optimization (TCO) reduces the software testing cost while preserving its effectiveness. However, to solve TCO problems for large-scale and complex software systems, substantial computational resources are required. Quantum approximate optimization algorithms (QAOAs) are promising combinatorial optimization algorithms that rely on quantum computational resources, with the potential to offer increased efficiency compared to classical approaches. Several proof-of-concept applications of QAOAs for solving combinatorial problems, such as portfolio optimization, energy optimization in power systems, and job scheduling, have been proposed. Given the lack of investigation into QAOA’s application for TCO problems, and motivated by the computational challenges of TCO problems and the potential of QAOAs, we present IGDec-QAOA to formulate a TCO problem as a QAOA problem and solve it on both ideal and noisy quantum computer simulators, as well as on a real quantum computer. To solve bigger TCO problems that require many qubits, which are unavailable these days, we integrate a problem decomposition strategy with the QAOA. We performed an empirical evaluation with five TCO problems and four publicly available industrial datasets from ABB, Google, and Orona to compare various configurations of IGDec-QAOA, assess its decomposition strategy of handling large datasets, and compare its performance with classical algorithms (i.e., Genetic Algorithm (GA) and Random Search). Based on the evaluation results achieved on an ideal simulator, we recommend the best configuration of our approach for TCO problems. Also, we demonstrate that our approach can reach the same effectiveness as GA and outperform GA in two out of five test case optimization problems we conducted. In addition, we observe that, on the noisy simulator, IGDec-QAOA achieved similar performance to that from the ideal simulator. Finally, we also demonstrate the feasibility of IGDec-QAOA on a real quantum computer in the presence of noise.