Implementation and Evaluation of Shor’s Algorithm for RSA Factorization Using QISKIT and IBM Quantum Services

Quantum algorithms that surpass the performance of classical methods are of increasing practical and scientific importance, with Shor’s algorithm remaining a landmark result for integer factorization and cryptanalysis. This work presents a full-stack, reproducible implementation of Shor’s algorithm using Qiskit, incorporating exact permutation-based modular multiplication unitaries, a scalable Quantum Phase Estimation (QPE) pipeline, and hybrid classical post-processing based on continued fractions and number-theoretic verification. The ar- chitecture is designed with modular components that explicitly separate quantum execution, classical analysis, and visualization, enabling detailed introspection of the order-finding procedure. Experimental results show successful factorization of multiple semiprimes using both local Aer simulations and IBM Quantum cloud backends. The cloud-based experiments expose practical constraints such as device noise, circuit-depth limits, and shot availability, while demonstrating portability of the framework to real hardware. The implementation further provides automated circuit-diagram generation, histogram-based phase diagnostics, and optional classical reference routines for comparison. Overall, this work delivers a transparent, educationally oriented, and cloud-deployable platform for studying Shor’s algorithm and benchmarking hybrid quantum–classical computing workflows.