PreprintCC BY 4.0arXiv
Bosonic codes from compact phase spaces
Abstract
We present the algebraic structure of bosonic quantum error-correcting codes on genus-two Riemann surfaces. We explicitly construct the code words as automorphic forms and analytically generate the full tower of code spaces at all weights. We prove a fundamental no-go theorem: for any genus greater than one, the stabilizer group is non-amenable, forcing a strictly positive spectral gap in the stabilizer Hamiltonian. Consequently, no normalizable quantum state can satisfy all stabilizer conditions. This sharply contrasts with standard Gottesman-Kitaev-Preskill (GKP) codes, where the amenability of the stabilizer group ℤ2 permits approximate code words with arbitrary precision.
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BibTeX
@misc{roberts2026bosonic,
title = {{Bosonic codes from compact phase spaces}},
author = {David Roberts and Aaron Slipper and Alireza Parhizkar and Victor V. Albert and Mohammad Hafezi},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.31156},
eprint = {2608.31156},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31156},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bosonic codes from compact phase spaces
AU - David Roberts
AU - Aaron Slipper
AU - Alireza Parhizkar
AU - Victor V. Albert
AU - Mohammad Hafezi
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.31156
UR - https://arxiv.org/abs/2608.31156
AB - We present the algebraic structure of bosonic quantum error-correcting codes on genus-two Riemann surfaces. We explicitly construct the code words as automorphic forms and analytically generate the full tower of code spaces at all weights. We prove a fundamental no-go theorem: for any genus greater than one, the stabilizer group is non-amenable, forcing a strictly positive spectral gap in the stabilizer Hamiltonian. Consequently, no normalizable quantum state can satisfy all stabilizer conditions. This sharply contrasts with standard Gottesman-Kitaev-Preskill (GKP) codes, where the amenability of the stabilizer group ℤ^2 permits approximate code words with arbitrary precision.
ER -