Factoring numbers with a single interferogram

TL;DR

This paper presents an optical interferometry method to factor large integers by encoding hyperbolic functions into light interference patterns, enabling prime decomposition of large numbers with potential for scalable computation.

Contribution

The authors introduce a novel analog optical computing approach that uses light interference to factor numbers, expanding the capabilities of physical computation methods.

Findings

Successfully factored seven-digit numbers using optical interference.

Demonstrated encoding of hyperbolic functions into interferograms.

Provided estimates for the maximum size of numbers that can be factored with this method.

Abstract

We construct an analog computer based on light interference to encode the hyperbolic function f({\zeta}) = 1/{\zeta} into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the prime number decompositions of integers. We implement this idea exploiting polychromatic optical interference in a multipath interferometer and factor seven-digit numbers. We give an estimate for the largest number that can be factored by this scheme.