大整数指数数并行因式分解的一种新算法I。理论描述
Analogue algorithm for parallel factorization of an exponential number of large integers I. Theoretical description
摘要：
我们描述了一种新的模拟算法，允许同时因式分解的指数数量的大整数与多项式数量的实验运行。它是在模拟计算机的输出处测量的“因子分解”干涉图的干涉引起的周期性，其允许选择每个整数的因子[1，2，3，4]。在现阶段，该算法表现出指数缩放，这可以通过将该方法扩展到从n阶量子相关测量中出现的相关量子比特来克服。我们描述了一个通用的物理系统计算这样的模拟算法的条件。在本系列的第二篇论文中将讨论基于光干涉的“光计算机”给出的一个特殊例子。
英文摘要：
We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring" interferograms measured at the output of an analogue computer that allows the selection of the factors of each integer [1,2,3,4]. At the present stage the algorithm manifests an exponential scaling which may be overcome by an extension of this method to correlated qubits emerging from n-order quantum correlations measurements. We describe the conditions for a generic physical system to compute such an analogue algorithm. A particular example given by an "optical computer" based on optical interference will be addressed in the second paper of this series [5].
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