Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State

TL;DR

This paper proposes an experiment to determine the non-Abelian braiding statistics of quasiparticles in the $ u=5/2$ fractional quantum Hall state and discusses its potential for topologically-protected qubits.

Contribution

It introduces a method to measure quasiparticle braiding statistics and demonstrates how non-Abelian anyons can be used to create topologically-protected qubits.

Findings

Estimated error rate of $10^{-30}$ for the qubit operation

Proposed experimental setup for braiding quasiparticles

Potential realization of topologically-protected quantum computation

Abstract

The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at Landau level filling fraction $\nu=5/2$. This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to determine the nature of the $\nu=5/2$ state, one must measure the quasiparticle braiding statistics. Here, we propose an experiment which can simultaneously determine the braiding statistics of quasiparticle excitations and, if they prove to be non-Abelian, produce a topologically-protected qubit on which a logical NOT operation is performed by quasiparticle braiding. Using the measured excitation gap at $\nu=5/2$, we estimate the error rate to be $10^{-30}$ or lower.