Entangling gates for the SU(N) anyons

TL;DR

This paper explores the generalization of braiding-based two-qubit operations from SU(2) to SU(N) anyons in topological quantum computing, addressing new challenges and differences.

Contribution

It extends previous SU(2) braiding methods to SU(N), analyzing the differences and new problems in implementing two-qubit gates.

Findings

Generalization of braiding techniques to SU(N) anyons.

Identification of new problems in SU(N) topological quantum gates.

Comparison between SU(2) and SU(N) braiding approaches.

Abstract

The model of a topological quantum computer is a promising one due to its natural resistance to noise and other errors. Operations in such a computer are implemented by braiding the trajectories of anyons. While it is easy to understand how to build one-qubit operations, two-qubit operations are more difficult. In arXiv:2412.20931 we suggested an approach to build such operations for a topological quantum computer based on SU(2) Chern-Simons theory with arbitrary level using cabling of knots. In this paper we discuss how this approach should be generalized to the SU(N) case, what the differences are, and which new problems arise.