Protocol for making a $2$-qutrit entangling gate in the Kauffman-Jones version of $SU(2)_4$

TL;DR

This paper presents a protocol to physically implement a 2-qutrit entangling gate within the Kauffman-Jones $SU(2)_4$ topological quantum computing framework, utilizing braiding, measurements, and fusion operations.

Contribution

It introduces a novel protocol for generating a 2-qutrit entangling gate using elementary anyonic operations in the Kauffman-Jones $SU(2)_4$ model.

Findings

Protocol successfully creates entangling gates in the $SU(2)_4$ model.

Uses only braids, measurements, fusions, and ancilla creation.

Provides a practical approach for topological quantum computation.

Abstract

The following paper provides a protocol to physically generate a $2$-qutrit entangling gate in the Kauffman-Jones version of $SU(2)$ Chern-Simons theory at level $4$. The protocol uses elementary operations on anyons consisting of braids, interferometric measurements, fusions and unfusions and ancilla pair creation.