Optical simulation of the Yang-Baxter equation

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 a four-dimensional 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 degrees of freedom of photon polarization and location are utilized as the qubit basis, in which the unitary Yang-Baxter matrices are decomposed into a combination of actions of basic optical elements.