The paper supplies a rigorous dictionary between GKP codes and polarized abelian varieties, proving asymptotic isometry of the encoding, Gaussian realization of all logical Cliffords, and first-order noise failure governed by a systolic invariant of the polarization isogeny.
Analysis of loss correction with the gottesman-kitaev-preskill code.arXiv preprint arXiv:2112.01425, 2021
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Complex abelian varieties and quantum error correction: a mathematical framework for GKP codes
The paper supplies a rigorous dictionary between GKP codes and polarized abelian varieties, proving asymptotic isometry of the encoding, Gaussian realization of all logical Cliffords, and first-order noise failure governed by a systolic invariant of the polarization isogeny.