Quantum computing has emerged as a revolutionary paradigm with the potential to solve complex problems that are practically intractable for classical computers. Central to quantum computing is the concept of qubits, which can exist in superposition and entangled states, enabling the execution of quantum algorithms that outperform classical counterparts. However, the inherent challenges in building and maintaining quantum hardware have prompted the exploration of alternative approaches. This study investigates the utilization of Field-Programmable Gate Arrays (FPGAs) for quantum gate implementation, focusing on accelerating quantum operations through FPGA-based simulation. In this research, we have developed a Python-based quantum gate simulator and harnessed FPGA technology to achieve a significant 1.38-fold acceleration in quantum gate simulations. Our innovative approach involved seamlessly integrating this simulator with the Ultra96 evaluation board and implementing dataflow designs to optimize quantum gate execution. This finding demonstrates the potential of FPGA-based acceleration for quantum computing simulations, offering practical implications for quantum computing research and applications.