Paper 2017/352

A low-resource quantum factoring algorithm

Daniel J. Bernstein, Jean-François Biasse, and Michele Mosca

Abstract

In this paper, we present a factoring algorithm that, assuming standard heuristics, uses just $(\log N)^{2/3+o(1)}$ qubits to factor an integer $N$ in time $L^{q+o(1)}$ where $L = \exp((\log N)^{1/3}(\log\log N)^{2/3})$ and $q=\sqrt[3]{8/3}\approx 1.387$. For comparison, the lowest asymptotic time complexity for known pre-quantum factoring algorithms, assuming standard heuristics, is $L^{p+o(1)}$ where $p>1.9$. The new time complexity is asymptotically worse than Shor's algorithm, but the qubit requirements are asymptotically better, so it may be possible to physically implement it sooner.