We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ 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.

翻译：我们证明，通过独立运行一个具有$\tilde{O}(n^{3/2})$个量子门的量子电路$\sqrt{n}+4$次，然后进行多项式时间的经典后处理，可以对$n$位整数进行因式分解。该算法的正确性依赖于一个数论启发式假设，该假设类似于亚指数经典因式分解算法中所使用的假设。目前尚不清楚该算法能否在实践中带来改进的物理实现。