The State of Factoring on Quantum Computers

TL;DR

This paper reviews the current capabilities and limitations of quantum computers in factoring integers, analyzing digital and analog approaches, their error effects, and future prospects for large-scale factoring.

Contribution

It provides a comprehensive analysis of factoring on quantum computers, including error impacts on digital algorithms and experimental results for analog methods.

Findings

Errors cause Shor's algorithm to fail on digital quantum computers.

Analog quantum methods show exponential scaling, better than random guessing.

Future perspectives highlight ongoing challenges and potential for large integer factoring.

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.