Constructing Functional Braids for Low-Leakage Topological Quantum Computing

TL;DR

This paper presents a method to significantly reduce leakage errors in topological quantum computing by constructing specialized braids in the Fibonacci anyon model, achieving error rates around 10^{-10}.

Contribution

It introduces a novel braid construction that exchanges anyons while preserving quantum information, substantially lowering leakage errors in topological quantum gates.

Findings

Leakage error reduced to ~10^{-10} with the new braid.

Constructed a functional braid in a six-anyon Hilbert space.

Improved the fidelity of controlled-rotation gates in topological quantum computing.

Abstract

We discuss how to significantly reduce leakage errors in topological quantum computation by introducing an irrelevant error in phase, using the construction of a CNOT gate in the Fibonacci anyon model as a concrete example. To be specific, we construct a functional braid in a six-anyon Hilbert space that exchanges two neighboring anyons while conserving the encoded quantum information. The leakage error is $\sim$$10^{-10}$ for a braid of $\sim$100 interchanges of anyons. Applying the braid greatly reduces the leakage error in the construction of generic controlled-rotation gates.