Factoring integers with sublinear resources on a superconducting quantum processor

TL;DR

This paper presents a novel quantum algorithm that significantly reduces qubit requirements for integer factorization, demonstrating its effectiveness by factoring 48-bit integers with only 10 superconducting qubits, and discusses its potential to challenge RSA-2048.

Contribution

The authors introduce a quantum algorithm combining classical lattice reduction with QAOA that requires sublinear qubits, enabling more practical factorization on near-term quantum devices.

Findings

Factored 48-bit integers with 10 qubits

Estimated 372 qubits needed to challenge RSA-2048

Algorithm is the most qubit-efficient to date

Abstract

Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities. Here, we report a universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm (QAOA). The number of qubits required is O(logN/loglog N), which is sublinear in the bit length of the integer $N$, making it the most qubit-saving factorization algorithm to date. We demonstrate the algorithm experimentally by factoring integers up to 48 bits with 10 superconducting qubits, the largest integer factored on a quantum device. We estimate that a quantum circuit with 372 physical qubits and a depth of thousands is necessary to challenge RSA-2048 using our algorithm. Our study shows great promise in expediting the application of current noisy quantum computers, and paves the way to factor large integers of realistic cryptographic significance.