Analogue algorithm for parallel factorization of an exponential number of large integers I. Theoretical description

TL;DR

This paper introduces a theoretical analogue algorithm capable of simultaneously factoring an exponential number of large integers using interference patterns, with potential scalability improvements via quantum correlations.

Contribution

It presents a novel theoretical framework for an analogue factoring algorithm leveraging interference, extending to quantum correlations for improved scalability.

Findings

Algorithm can factor many integers simultaneously

Interference patterns reveal factors of integers

Potential scalability with quantum correlations

Abstract

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].