Accelerating Shor's Factorization Algorithm on GPUs

Abstract: Shor's quantum algorithm is very important for cryptography, since it can factor large numbers much faster than classical algorithms. In this study, we implement a simulator for Shor's quantum algorithm on graphic processor units (GPU) and compare our results with Liquid -which is Microsoft quantum simulation platform- and two classical CPU-implementations. We evaluate 10 benchmarks for comparing our GPU implementation with Liquid and single-core implementation. The analysis shows that GPU vector operations is more suitable for Shor's quantum algorithm. Our GPU kernel function is compute-bound, due to all threads in a block reach to the same element of the state vector. Our implementation has $52.5\times$ speedup over single-core algorithm and $20.5\times$ speedup over Liquid.