A low-resource quantum factoring algorithm

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 Lq+o(1) where L = exp((log N)1/3 (log log N)2/3) and q =3√8/3 ≈ 1.387. For comparison, the lowest asymptotic time complexity for known pre-quantum factoring algorithms, assuming standard heuristics, is Lp+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.