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arXiv:2106.12989 · PRX Quantum

Quantum Error Correction with the Gottesman-Kitaev-Preskill Code

Arne L. Grimsmo, Shruti Puri

Published Jun 23, 2021• 138 citations
arXivHTMLPDF

Abstract

The Gottesman-Kitaev-Preskill (GKP) code was proposed in 2001 by
DOI
10.1103/prxquantum.2.020101

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We examine general Gottesman-Kitaev-Preskill (GKP) codes for continuous-variable quantum error correction, including concatenated GKP codes, through the lens of lattice theory, in order to better understand the structure of this class of stabilizer codes. We derive formal bounds on code parameters, show how different decoding strategies are precisely related, propose new ways to obtain GKP codes by means of glued lattices and the tensor product of lattices and point to natural resource savings that have remained hidden in recent approaches. We present general results that we illustrate through examples taken from different classes of codes, including scaled self-dual GKP codes and the concatenated surface-GKP code.