New series of multi-parametric solutions to GYBE: quantum gates and integrability

TL;DR

This paper introduces two new series of spectral parameter dependent solutions to the generalized Yang-Baxter equations, expanding the set of integrable models and quantum gates with potential applications in quantum information.

Contribution

It presents novel multi-parametric solutions to GYBE for matrices of arbitrary dimensions, including extensions for inhomogeneous cases and connections to quantum information theory.

Findings

Two series of solutions to GYBE are constructed.

Examples include integrable models and generalized Bell matrices.

Solutions encompass known braiding matrices as special cases.

Abstract

We obtain two series of spectral parameter dependent solutions to the generalized Yang-Baxter equations (GYBE), for definite types of $N_1^2\times N_2^2$ matrices with general dimensions $N_1$ and $N_2$. Appropriate extensions are presented for the inhomogeneous GYBEs. The first series of the solutions includes as particular cases the $X$-shaped trigonometric braiding matrices. For construction of the second series the colored and graded permutation operators are defined, and multi-spectral parameter Yang-Baxterization is performed. For some examples the corresponding integrable models are discussed. The unitary solutions existing in these two series can be considered as generalizations of the multipartite Bell matrices in the quantum information theory.