An Efficient Quantum Factoring Algorithm

We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3\mathrm{/}2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm relies on a number-theoretic heuristic assumption reminiscent of those used in subexponential classical factorization algorithms. It is currently not clear if the algorithm can lead to improved physical implementations in practice.