Fibonacci topological phase in arrays of anyonic chains

TL;DR

This paper presents a method to realize a Fibonacci topological phase using arrays of anyonic chains derived from an $SU(2)_4$ topological phase, advancing quantum computing research.

Contribution

It introduces a novel construction of Fibonacci topological phases from $SU(2)_4$ phases via anyonic chain arrays, extending the understanding of topological quantum states.

Findings

Fibonacci topological phase can be constructed from $SU(2)_4$ topological phase.

Arrays of anyonic chains lead to the Fibonacci phase.

The approach can be generalized to other topological phases.

Abstract

Fibonacci anyon, an exotic quasi-particle excitation, plays a pivotal role in realization of a quantum computer. Starting from a $SU(2)_4$ topological phase, in this paper we demonstrate a way to construct a Fibonacci topological phase which has only one non-trivial excitation described by the Fibonacci anyon. We show that arrays of anyonic chains created by excitations of the $SU(2)_4$ phase leads to the Fibonacci phase. We further demonstrate that our theoretical propositions can be extended to other topological phases.