A comment on "Factoring integers with sublinear resources on a superconducting quantum processor"

TL;DR

This paper critically evaluates a recent quantum algorithm proposal for factoring RSA 2048, demonstrating that its claimed efficiency is not achievable with current or perfect quantum optimizers, and providing an open-source implementation for community testing.

Contribution

The authors provide an open-source implementation of Yan et al.'s quantum-assisted lattice factoring algorithm and empirically show its limitations in factoring large integers, challenging previous claims.

Findings

Successfully factors up to 70-bit integers

Fails to factor 80-bit integers with the proposed method

Provides a tool for community testing of quantum-classical factoring algorithms

Abstract

Quantum computing has the potential to revolutionize cryptography by breaking classical public-key cryptography schemes, such as RSA and Diffie-Hellman. However, breaking the widely used 2048-bit RSA using Shor's quantum factoring algorithm is expected to require millions of noisy physical qubits and is well beyond the capabilities of present day quantum computers. A recent proposal by Yan et. al. tries to improve the widely debated Schnorr's lattice-based integer factorization algorithm using a quantum optimizer (QAOA), and further claim that one can break RSA 2048 using only 372 qubits. In this work, we present an open-source implementation of the algorithm proposed by Yan et. al. and show that, even if we had a perfect quantum optimizer (instead of a heuristic like QAOA), the proposed claims don't hold true. Specifically, our implementation shows that the claimed sublinear lattice dimension for the Hybrid quantum+classical version of Schnorr's algorithm successfully factors integers only up to 70 bits and fails to find enough factoring relations for random 80 bit integers and beyond. We further hope that our implementation serves as a playground for the community to easily test other hybrid quantum + classical integer factorization algorithm ideas using lattice based reductions.