Systematically generated two-qubit anyon braids

TL;DR

This paper presents a systematic method for generating two-qubit entangling gates using Fibonacci anyon braids, avoiding brute force or numerical searches, and demonstrating their utility in quantum computation.

Contribution

It introduces a new iterative procedure to construct two-qubit entangling gates from Fibonacci anyon braids without numerical optimization.

Findings

Systematic construction of two-qubit entangling gates from Fibonacci anyons.

Avoidance of brute force and numerical search methods.

Demonstration of the method's effectiveness in quantum gate design.

Abstract

Fibonacci anyons are non-Abelian particles for which braiding is universal for quantum computation. Reichardt has shown how to systematically generate nontrivial braids for three Fibonacci anyons which yield unitary operations with off-diagonal matrix elements that can be made arbitrarily small in a particular natural basis through a simple and efficient iterative procedure. This procedure does not require brute force search, the Solovay-Kitaev method, or any other numerical technique, but the phases of the resulting diagonal matrix elements cannot be directly controlled. We show that despite this lack of control the resulting braids can be used to systematically construct entangling gates for two qubits encoded by Fibonacci anyons.