Lattice moments and quantum designs

We show that the ensemble of unimodular Gottesman$-$Kitaev$-$Preskill distributions fails to form a rigged quantum $3$-design and quantify the replica defect that determines this failure. This is established by rederiving a second moment formula for symplectic lattices in a self-contained manner.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.40481
Primary Topic
Quantum Computing Algorithms and Architecture
Type
preprint
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preprint

Lattice moments and quantum designs

Kristian Holm, Jonathan Conrad
arXiv (Cornell University)
Quantum Computing Algorithms and Architecture
preprint

Lattice moments and quantum designs

Kristian Holm, Jonathan Conrad
preprint en

Abstract

We show that the ensemble of unimodular Gottesman$-$Kitaev$-$Preskill distributions fails to form a rigged quantum $3$-design and quantify the replica defect that determines this failure. This is established by rederiving a second moment formula for symplectic lattices in a self-contained manner.

arXiv (Cornell University)
Quantum Computing Algorithms and Architecture
DOIOpen Access PDFOpenAlex
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Lattice moments and quantum designs — Kristian Holm, Jonathan Conrad · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS