Calculating HOMFLY-PT polynomials on a photonic processor

TL;DR

This paper demonstrates a photonic processor approach to calculating knot polynomials, specifically the trefoil knot, showcasing potential for generalization to more complex knots and quantum computing applications.

Contribution

It introduces a novel photonic method for computing knot polynomials, bridging photonic and quantum computing techniques.

Findings

Successfully calculated the trefoil knot polynomial using photonic processors

The method can be extended to more complex knots and quantum computers

Proof of concept supports future research in knot theory and quantum computation

Abstract

In this paper we discuss an approach to calculate knot polynomials on a photonic processor. Calculations of knot polynomials is a computationally difficult problem and therefore it is interesting to use new advanced calculation methods to find them. Here we present a proof of concept by calculating the simplest knot polynomial of the trefoil knot in fundamental representation. This approach, however, can easily be generalized to more complex knots and representations. Same operators can also be realized on a quantum computer with the same effect.