Systematic construction of stabilizer codes via gauging abelian boundary symmetries

Bram Vancraeynest-De Cuiper; José Garre-Rubio

doi:10.22331/q-2025-09-08-1852

Systematic construction of stabilizer codes via gauging abelian boundary symmetries

Bram Vancraeynest-De Cuiper¹ and José Garre-Rubio^2,3

¹Department of Physics and Astronomy, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
²University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
³Instituto de Física Teórica, UAM/CSIC, C. Nicolás Cabrera 13-15, Cantoblanco, 28049 Madrid, Spain

Published:	2025-09-08, volume 9, page 1852
Editor:	Alioscia Hamma
Eprint:	arXiv:2410.09044v2
Doi:	https://doi.org/10.22331/q-2025-09-08-1852
Citation:	Quantum 9, 1852 (2025).

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Abstract

We propose a systematic framework to construct a $(d+1)$-dimensional stabilizer model from an initial generic d-dimensional abelian symmetry. Our approach builds upon the iterative gauging procedure, developed by one of the authors in [J. Garre-Rubio, Nature Commun. 15, 7986 (2024)][12], in which an initial symmetric state is repeatedly gauged to obtain an emergent model in one dimension higher that supports the initial symmetry at its boundary. This method not only enables the construction of emergent states and corresponding commuting stabilizer Hamiltonians of which they are ground states, but it also provides a way to construct gapped boundary conditions for these models that amount to spontaneously breaking part of the boundary symmetry. In a detailed introductory example, we showcase our paradigm by constructing three-dimensional Clifford-deformed surface codes from iteratively gauging a global 0-form symmetry that lives in two dimensions. We then provide a proof of our main result, hereby drawing upon a slight extension of the gauging procedure of Williamson. We additionally provide two more examples in $d=2$ in which different type-I fracton orders emerge from gauging initial linear subsystem and Sierpinski fractal symmetries. En passant, we provide explicit tensor network representations of all of the involved gauging maps and the emergent states.

► BibTeX data

@article{Cuiper2025systematic,
  doi = {10.22331/q-2025-09-08-1852},
  url = {https://doi.org/10.22331/q-2025-09-08-1852},
  title = {Systematic construction of stabilizer codes via gauging abelian boundary symmetries},
  author = {Cuiper, Bram Vancraeynest-De and Garre-Rubio, Jos{\'{e}}},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1852},
  month = sep,
  year = {2025}
}

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Cited by

[1] Bram Vancraeynest-De Cuiper, José Garre-Rubio, Frank Verstraete, Kevin Vervoort, Dominic J. Williamson, and Laurens Lootens, "From gauging to duality in one-dimensional quantum lattice models", SciPost Physics 20 4, 113 (2026).

[2] Bram Vancraeynest-De Cuiper, Weronika Wiesiolek, and Frank Verstraete, "Les Houches lecture notes on tensor networks", SciPost Physics Lecture Notes 128 (2026).

[3] Bram Vancraeynest-De Cuiper, Weronika Wiesiolek, and Frank Verstraete, "Les Houches Lecture Notes on Tensor Networks", arXiv:2512.24390, (2025).

[4] Clay Cordova, Davi B. Costa, and Po-Shen Hsin, "Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories", arXiv:2412.16681, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-10 11:59:21) and SAO/NASA ADS (last updated successfully 2026-08-10 11:59:22). The list may be incomplete as not all publishers provide suitable and complete citation data.

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