Analogue algorithm for parallel factorization of an exponential number of large integers II. Optical implementation

TL;DR

This paper analyzes an optical analogue algorithm designed for parallel factorization of many large integers, highlighting its potential for exponential to polynomial scaling through quantum interference.

Contribution

It provides a detailed analysis of an optical implementation of an analogue factorization algorithm, exploring its scalability and potential advantages over classical methods.

Findings

Optical implementation enables simultaneous factorization of many integers.

Quantum interference can potentially improve scaling from exponential to polynomial.

The analysis suggests promising future directions for quantum-enhanced factorization.

Abstract

We report a detailed analysis of the optical realization [1, 3, 2, 4] of the analogue algorithm described in the first paper of this series [5] for the simultaneous factorization of an exponential number of integers. Such an analogue procedure, which scales exponentially in the context of first order interference, opens up the horizon to polynomial scaling by exploiting multi-particle quantum interference.