Quasitriangular Hopf algebras, braid groups and quantum entanglement

TL;DR

This paper presents a method to derive braid group representations from quasitriangular Hopf algebras, enabling the construction of quantum gates that preserve entanglement, with potential applications in quantum computing.

Contribution

It introduces a novel approach to obtain braid group representations from specific Hopf algebras, linking algebraic structures to quantum entanglement preservation.

Findings

Constructed R-matrices as quantum logic gates

Demonstrated preservation of quantum entanglement

Linked algebraic structures to quantum computational elements

Abstract

The aim of the paper is to provide an method to obtain representations of the braid group through a set of quasitriangular Hopf algebras. In particular, these algebras may be derived from group algebras of cyclic groups with additional algebraic structures. In this context, by using the flip operator, it is possible to construct R-matrices that can be regarded as quantum logic gates capable of preserving quantum entanglement.