Variational Quantum Eigensolver Approach to Prime Factorization on IBM's Noisy Intermediate Scale Quantum Computer

TL;DR

This paper introduces a hybrid quantum-classical VQE-based algorithm for prime factorization, demonstrating its ability to factor numbers up to 253 on real IBM quantum hardware and larger numbers on simulators, highlighting near-term quantum computing potential.

Contribution

It presents a novel VQE-based approach for prime factorization tailored for noisy intermediate-scale quantum computers, with empirical validation on IBM hardware.

Findings

Successfully factorized 253 on real quantum hardware

Factored 1048561 on classical simulator

Showed potential for practical quantum factoring applications

Abstract

This paper presents a hybrid quantum-classical approach to prime factorization. The proposed algorithm is based on the Variational Quantum Eigensolver (VQE), which employs a classical optimizer to find the ground state of a given Hamiltonian. A numerical study is presented, evaluating the performance of the proposed method across various instances on both IBM's real quantum computer and its classical simulator. The results demonstrate that the method is capable of successfully factorizing numbers up to 253 on a real quantum computer and up to 1048561 on a classical simulator. These findings show the potential of the approach for practical applications on near-term quantum computers.