Factoring integers via Schnorr's algorithm assisted with VQE

TL;DR

This paper analyzes and replicates a quantum-assisted integer factorization method, using Variational Quantum Eigensolver (VQE), successfully factoring the number 1961, and discusses the potential of quantum algorithms to challenge classical cryptography.

Contribution

It introduces a novel approach combining Schnorr's algorithm with VQE for integer factorization and demonstrates its effectiveness on a specific number.

Findings

Successfully factored 1961 using VQE-assisted Schnorr's algorithm

Replicated previous hybrid quantum algorithm experiments

Highlights potential of quantum algorithms to impact cryptography

Abstract

Current asymmetric cryptography is based on the principle that while classical computers can efficiently multiply large integers, the inverse operation, factorization, is significantly more complex. For sufficiently large integers, this factorization process can take in classical computers hundreds or even thousands of years to complete. However, there exist some quantum algorithms that might be able to factor integers theoretically -- the theory works properly, but the hardware requirements are far away from what we can build nowadays -- and, for instance, Yan, B. et al. ([14]) claim to have constructed a hybrid algorithm which could be able even to challenge RSA-2048 in the near future. This work analyses this article and replicates the experiments they carried out, but with a different quantum method (VQE), being able to factor the number 1961.