Quantum computer simulators play a critical role in supporting the development and validation of quantum algorithms and hardware. This study focuses on porting Google's qsim, a quantum computer simulator, to AMD Graphics Processing Units (GPUs). We leverage the existing qsim CUDA backend and harness the HIPIFY tool to provide a qsim HIP backend tailored for AMD GPUs. Our performance analysis centers on evaluating the HIP backend's capabilities, executed on a computing node equipped with the AMD MI250X GPU and the AMD EPYC Trento CPU. We use the Random Quantum Circuit (RQC) sampling benchmark, employing a circuit featuring 30 qubits. The qsim HIP backend on AMD GPU outperforms the CPU version by a remarkable margin, achieving seven to nine times faster speeds. Our investigation also compares qsim's performance on the Nvidia A100 and AMD MI250X GPUs. The Nvidia A100 consistently outperforms the AMD MI250x counterpart, and this performance gap further widens with optimal gate fusion configurations. For instance, a two-gate fusion configuration exhibits a 5% difference, whereas a four-gate fusion setup reveals a large 44% performance gap. Our work highlights the substantial performance advantage of GPU-based quantum simulation over traditional CPU approaches. Despite a performance lag compared to the qsim CUDA backend, the AMD HIP qsim backend emerges as a competitive alternative poised for further optimization.