Testing quantum programs requires systematic, automated, and intelligent methods due to their inherent complexity, such as their superposition and entanglement. To this end, we present a search-based approach, called Quantum Search-Based Testing (QuSBT), for automatically generating test suites of a given size depending on available testing budget, with the aim of maximizing the number of failing test cases in the test suite. QuSBT consists of definitions of the problem encoding, failure types, test assessment with statistical tests, fitness function, and test case generation with a Genetic Algorithm (GA). To empirically evaluate QuSBT, we compared it with Random Search (RS) by testing six quantum programs. We assessed the effectiveness of QuSBT and RS with 30 carefully designed faulty versions of the six quantum programs. Results show that QuSBT provides a viable solution for testing quantum programs, and achieved a significant improvement over RS in 87% of the faulty programs, and no significant difference in the rest of 13% of the faulty programs.