Factorizing numbers with classical interference: several implementations in optics

TL;DR

This paper demonstrates how classical optical interference can be used to factorize numbers by employing superpositions of light waves, providing practical implementations of the mathematical sums used in factorization.

Contribution

It introduces optical implementations of number factorization algorithms based on classical interference patterns, bridging mathematical sums and physical optics.

Findings

Optical superpositions can realize Fourier, Gauss, Kummer, and exponential sums for factorization.

The paper presents several simple optical setups for number factorization.

Classical light interference can effectively perform number factorization tasks.

Abstract

Truncated Fourier, Gauss, Kummer and exponential sums can be used to factorize numbers: for a factor these sums equal unity in absolute value, whereas they nearly vanish for any other number. We show how this factorization algorithm can emerge from superpositions of classical light waves and we present a number of simple implementations in optics.