Calculating HOMFLY-PT polynomials on a photonic processor

In this paper, we discuss an approach to calculate knot polynomials on a photonic processor. Calculation of knot polynomials is a computationally difficult problem, and therefore it is interesting to use new, to the best of our knowledge, 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.