Optimization and Performance Analysis of Shor's Algorithm in Qiskit

Shor's algorithm is widely renowned in the field of quantum computing due to its potential to efficiently break RSA encryption in polynomial time. In this paper, we optimized an end-to-end library-based implementation of Shor's algorithm using the IBM Qiskit quantum library and derived a speed-of-light (i.e., theoretical peak) performance model that calculates the minimum runtime required for executing Shor's algorithm with input size $N$ on a certain machine by counting the total operations as a function of different numbers of gates. We evaluated our model by running Shor's algorithm on CPUs and GPUs, and simulated the factorization of a number up to 4,757. Comparing the speed-of-light runtime to our real-world measurement, we are able to quantify the margin for future quantum library improvements.