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arXiv · 2405.03645

Calculating HOMFLY-PT polynomials on a photonic processor

Ivan Dyakonov·Ilya Kondratyev·Sergey Mironov·Andrey Morozov
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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.

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Ivan Dyakonov, Ilya Kondratyev, Sergey Mironov, Andrey Morozov. 2024-05-06. Calculating HOMFLY-PT polynomials on a photonic processor. https://arxiv.org/abs/2405.03645

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