Quantum Error Correction in the Lowest Landau Level

TL;DR

This paper introduces finite-dimensional quantum error-correcting codes based on Landau levels on spherical geometries, offering potentially easier state preparation and extending previous continuous-variable code frameworks.

Contribution

It develops finite-dimensional versions of ACP codes using Landau levels on spherical geometries, expanding the types of quantum error correction schemes available.

Findings

Codes can be realized on spherical Landau levels or spin coherent states

The scheme is inherently approximate, potentially simplifying state preparation

Extends continuous-variable quantum error correction to finite dimensions

Abstract

We develop finite-dimensional versions of the quantum error-correcting codes proposed by Albert, Covey, and Preskill (ACP) for continuous-variable quantum computation on configuration spaces with nonabelian symmetry groups. Our codes can be realized by a charged particle in a Landau level on a spherical geometry -- in contrast to the planar Landau level realization of the qudit codes of Gottesman, Kitaev, and Preskill (GKP) -- or more generally by spin coherent states. Our quantum error-correction scheme is inherently approximate, and the encoded states may be easier to prepare than those of GKP or ACP.