Quantum Error Correction in the Lowest Landau Level

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.