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，通过独立运行一个包含$\tilde{O}(n^{3/2})$个门电路的量子线路$\sqrt{n}+4$次，再结合多项式时间的经典后处理，即可实现对$n$比特整数的因式分解。该算法的正确性依赖于一项数论启发式假设，这与亚指数级经典因式分解算法中使用的假设类似。目前尚不清楚该算法是否能在实际中带来物理实现的改进。