Optical Simulation of Yang-Baxter Equation

TL;DR

This paper presents a method for simulating the Yang-Baxter equation optically by reducing its dimensionality using algebraic techniques and implementing the resulting matrices with basic optical components.

Contribution

It introduces a novel optical simulation approach for the Yang-Baxter equation using Temperley-Lieb algebra and polarization and location degrees of freedom as qubits.

Findings

Successful decomposition of Yang-Baxter matrices into optical elements

Efficient optical implementation of the two-dimensional Yang-Baxter equation

Utilization of photon polarization and location as qubit bases

Abstract

In this paper, several proposals of optically simulating Yang-Baxter equations have been presented. Motivated by the recent development of anyon theory, we apply Temperley-Lieb algebra as a bridge to recast four-dimentional Yang-Baxter equation into its two-dimensional counterpart. In accordance with both representations, we find the corresponding linear-optical simulations, based on the highly efficient optical elements. Both the freedom degrees of photon polarization and location are utilized as the qubit basis, in which the unitary Yang-Baxter matrices are decomposed into combination of actions of basic optical elements.