A Novel Quantum Circuit for Integer Factorization: Evaluation via Simulation and Real Quantum Hardware

This work tests the hypothesis that a Quantum Number Theoretic Transform (QNTT) circuit, here named Jesse-Victor-Gharabaghi (JVG) algorithm, can perform better than the Shor’s algorithm, in terms of number of required gates and qubits. This methodology replaces the Quantum Fourier Transform (QFT) with a Quantum Number Theoretic Transform (QNTT) circuit to predict periodicity in the number theory and factor integer numbers, which serve as keys in cryptographic methods, like RSA and ECC. Several composite numbers were evaluated through both simulation and real quantum hardware to verify feasibility and performance. Performance was assessed across runtime, memory consumption, and gate counts. Simulation results showed that the JVG can reduce the growth in CX gates by 30.3%, circuit depth by 33.5%, memory by 9.6%, and runtime by 14.7% relative to the Shor’s algorithm. On quantum hardware, JVG reduces growth in runtime by 26% and X-gate counts by 44.4%, achieving consistently lower coefficients of variation across metrics. Projection curves derived from the fitted trends predict the eventual JVG advantage, over Shor ,in runtime, gates, and depth as the number of qubits increases, including RSA-scale configurations. These results support JVG as a more hardware-compatible and robust noise-tolerant substitute for the Shor’s framework, offering a viable path toward practical quantum integer factorization on near-term Noisy Intermediate-Scale Quantum (NISQ) devices.