A proposal for factorization using Kerr nonlinearities between three harmonic oscillators

TL;DR

This paper introduces a novel quantum-based method for integer factorization using three coupled harmonic oscillators with Kerr nonlinearities, demonstrating its application to specific numbers and analyzing its limitations.

Contribution

It presents a new factorization technique leveraging Kerr nonlinearities in harmonic oscillators, including analysis of dissipation effects and implementation challenges.

Findings

Successfully factorized N=15 and 35 using the proposed method.

Dissipation impacts the performance and success probability of the factorization.

Probability of finding factors decreases with larger input numbers.

Abstract

We propose an alternative method to factorize an integer by using three harmonic oscillators. These oscillators are coupled together via specific Kerr nonlinear interactions. This method can be applied even if two harmonic oscillators are prepared in mixed states. As simple examples, we show how to factorize N=15 and 35 using this approach. The effect of dissipation of the harmonic oscillators on the performance of this method is studied. We also study the realization of nonlinear interactions between the coupled oscillators. However, the probability of finding the factors of a number is inversely proportional to its input size. The probability becomes low when this number is large. We discuss the limitations of this approach.