Exploiting Geometric Degrees of Freedom in Topological Quantum Computing

TL;DR

This paper proposes leveraging redundant geometric degrees of freedom in topological quantum computing to enhance gate accuracy, demonstrated through explicit Fibonacci model constructions and comparisons with existing algorithms.

Contribution

It introduces a novel method to exploit geometric redundancies for improved quantum gate fidelity in topological quantum computing.

Findings

Redundant geometric degrees of freedom can improve gate accuracy.

Explicit constructions in the Fibonacci model validate the approach.

Comparison shows efficiency gains over the Solovay-Kitaev algorithm.

Abstract

In a topological quantum computer, braids of non-Abelian anyons in a (2+1)-dimensional space-time form quantum gates, whose fault tolerance relies on the topological, rather than geometric, properties of the braids. Here we propose to create and exploit redundant geometric degrees of freedom to improve the theoretical accuracy of topological single- and two-qubit quantum gates. We demonstrate the power of the idea using explicit constructions in the Fibonacci model. We compare its efficiency with that of the Solovay-Kitaev algorithm and explain its connection to the leakage errors reduction in an earlier construction [Phys. Rev. A 78, 042325 (2008)].