Gottesman-Kitaev-Preskill codes: A lattice perspective

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.

Automated summary

The study examines the application of general Gottesman-Kitaev-Preskill (GKP) codes in continuous-variable quantum error correction using lattice theory. It proposes new methods to obtain GKP codes and identifies potential resource savings. The general findings are illustrated through examples from different classes of codes.