Compiling single-qubit braiding gate for Fibonacci anyons topological quantum computation

TL;DR

This paper demonstrates a numerical method to compile a single-qubit braiding gate for Fibonacci anyons, advancing topological quantum computation by achieving leakage-free gates with publicly shared algorithms.

Contribution

It introduces a numerical approach to approximate the Hadamard gate via braiding Fibonacci anyons, providing a practical method for topological quantum gate implementation.

Findings

Successfully approximated the Hadamard gate with braiding Fibonacci anyons.

Developed and shared algorithms for gate compilation.

Enhanced the feasibility of topological quantum computing.

Abstract

Topological quantum computation is an implementation of a quantum computer in a way that radically reduces decoherence. Topological qubits are encoded in the topological evolution of two-dimensional quasi-particles called anyons and universal set of quantum gates can be constructed by braiding these anyons yielding to a topologically protected circuit model. In the present study we remind the basics of this emerging quantum computation scheme and illustrate how a topological qubit built with three Fibonacci anyons might be adopted to achieve leakage free braiding gate by exchanging the anyons composing it. A single-qubit braiding gate that approximates the Hadamard quantum gate to a certain accuracy is numerically implemented using a brute force search method. The algorithms utilized for that purpose are explained and the numerical programs are publicly shared for reproduction and further use.