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Two-foliated fracton code[1,2]

Alternative names: Anisotropic lineon code.

Description

A type-I fracton code obtained by gauging [211] a topological phase with subsystem symmetry.

Gates

The code admits a cup product structure and admits a logical CZ gate from physical CZ gates [12].

Cousins

  • Plaquette Ising code— The two-foliated fracton code is a hypergraph product of the repetition code and the plaquette Ising code on a square lattice with periodic boundary conditions [12].
  • Repetition code— The two-foliated fracton code is a hypergraph product of the repetition code and the plaquette Ising code on a square lattice with periodic boundary conditions [12].

References

[1]
W. Shirley, K. Slagle, and X. Chen, “Fractional excitations in foliated fracton phases”, Annals of Physics 410, 167922 (2019) arXiv:1806.08625 DOI
[2]
W. Shirley, K. Slagle, and X. Chen, “Foliated fracton order from gauging subsystem symmetries”, SciPost Physics 6, (2019) arXiv:1806.08679 DOI
[3]
M. Levin and Z.-C. Gu, “Braiding statistics approach to symmetry-protected topological phases”, Physical Review B 86, (2012) arXiv:1202.3120 DOI
[4]
J. Haegeman, K. Van Acoleyen, N. Schuch, J. I. Cirac, and F. Verstraete, “Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems”, Physical Review X 5, (2015) arXiv:1407.1025 DOI
[5]
S. Vijay, J. Haah, and L. Fu, “Fracton topological order, generalized lattice gauge theory, and duality”, Physical Review B 94, (2016) arXiv:1603.04442 DOI
[6]
D. J. Williamson, “Fractal symmetries: Ungauging the cubic code”, Physical Review B 94, (2016) arXiv:1603.05182 DOI
[7]
L. Bhardwaj, D. Gaiotto, and A. Kapustin, “State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter”, Journal of High Energy Physics 2017, (2017) arXiv:1605.01640 DOI
[8]
A. Kubica and B. Yoshida, “Ungauging quantum error-correcting codes”, (2018) arXiv:1805.01836
[9]
K. Dolev, V. Calvera, S. S. Cree, and D. J. Williamson, “Gauging the bulk: generalized gauging maps and holographic codes”, Journal of High Energy Physics 2022, (2022) arXiv:2108.11402 DOI
[10]
T. Rakovszky and V. Khemani, “The Physics of (good) LDPC Codes I. Gauging and dualities”, (2023) arXiv:2310.16032
[11]
D. J. Williamson and T. J. Yoder, “Low-overhead fault-tolerant quantum computation by gauging logical operators”, (2024) arXiv:2410.02213
[12]
N. P. Breuckmann, M. Davydova, J. N. Eberhardt, and N. Tantivasadakarn, “Cups and Gates I: Cohomology invariants and logical quantum operations”, (2024) arXiv:2410.16250
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Zoo Code ID: two_foliated

Cite as:
“Two-foliated fracton code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/two_foliated
BibTeX:
@incollection{eczoo_two_foliated, title={Two-foliated fracton code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/two_foliated} }
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Cite as:

“Two-foliated fracton code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/two_foliated

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/fracton/two_foliated.yml.