# A Low-Resource Quantum Factoring Algorithm

Conference paper

First Online:

## 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 \(q=\root 3 \of {8/3}\approx 1.387\). 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.

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