An Efficient Quantum Factoring Algorithm

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Abstract

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We show that n-bit integers can be factorized by independently running a quantum circuit with O(n^3/2) gates for √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. Arxiv: https://arxiv.org/abs/2308.06572