Realistic benchmarks of reproducible bugs and fixes are vital to good experimental evaluation of debugging and testing approaches. However, there is no suitable benchmark suite that can systematically evaluate the debugging and testing methods of quantum programs until now. This paper proposes Bugs4Q, a benchmark of thirty-six real, manually validated Qiskit bugs from four popular Qiskit elements (Terra, Aer, Ignis, and Aqua), supplemented with the test cases for reproducing buggy behaviors. Bugs4Q also provides interfaces for accessing the buggy and fixed versions of the Qiskit programs and executing the corresponding test cases, facilitating the reproducible empirical studies and comparisons of Qiskit program debugging and testing tools. Bugs4Q is publicly available at https://github.com/Z-928/Bugs4Q.