Realizing an exact entangling gate using Fibonacci anyons

TL;DR

This paper introduces a method combining braiding and measurement operations to implement an exact entangling gate on Fibonacci anyons, overcoming previous limitations of leakage during braiding-based quantum gates.

Contribution

It presents the first exact entangling gate for Fibonacci anyons by integrating measurement with braiding, enabling precise quantum operations.

Findings

Achieved an exact controlled rotation gate using combined braiding and measurement.

Demonstrated the feasibility of leakage-free entangling gates in topological quantum computation.

Provided a practical approach to improve quantum gate precision with Fibonacci anyons.

Abstract

Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However there is no known braid that entangles two qubits without leaving the space spanned by the two qubits. In other words, there is no known "leakage-free" entangling gate made by braiding. In this paper, we provide a remedy to this problem by supplementing braiding with measurement operations in order to produce an exact controlled rotation gate on two qubits.