Precision Analysis and Hardware Acceleration for Large-Scale Quantum Fourier Transformation on Modern FPGAS

With the development of quantum algorithms and practical quantum computing devices, how to efficiently simulate emerging quantum algorithms via quantum circuit simulators on classical parallel-computing hardware platforms has raised more and more interest. The superior customized parallelism and pipeline efficiency over general-purpose processors make FPGAs ideal for large scale quantum algorithms/circuits simulation. Since the quantum Fourier transform (QFT) has been used in many quantum algorithms, such as quantum linear algebra, quantum phase estimation and quantum machine leaning, this paper presented a novel precision analysis and an efficient customized-precision QFT simulator accelerated on AMD Alveo U55C FPGAs. Customized-precision representations via high-level synthesis are employed for QFT implementation with up to 16 qubits, demonstrating up-to 8.3× speedup versus implementations in floating-point arithmetic within an error tolerance of 0.1%.