The State of Factoring on Quantum Computers

Abstract

We report on the current state of factoring integers on both digital and analog quantum computers. For digital quantum computers, we study the effect of errors for which one can formally prove that Shor's factoring algorithm fails. For analog quantum computers, we experimentally test three factorisation methods and provide evidence for a scaling performance that is absolutely and asymptotically better than random guessing but still exponential. We conclude with an overview of future perspectives on factoring large integers on quantum computers.

This is an updated version (with an extended footnote on post-processing parameters and a paragraph on Schnorr's lattice-based factoring method) of the article published in https://doi.org/10.34734/FZJ-2025-01965