Chen-Hsin invertible-order code[1] 

Description

A geometrically local commuting-projector code that realizes beyond-group-cohomology invertible topological phases in arbitrary dimensions. Instances of the code in 4D realize the 3D \(\mathbb{Z}_2\) gauge theory with fermionic charge and either bosonic (FcBl) or fermionic (FcFl) loop excitations at their boundaries [2,3]; see Ref. [4] for a different lattice-model formulation of the FcBl boundary code.

Parents

  • Qubit code
  • Two-gauge theory code — Chen-Hsin invertible-order codes realize beyond-group-cohomology invertible topological phases of order two and four in arbitrary dimensions. These phases are described by invertible two-gauge theories [1; pg. 11].

Cousins

  • Abelian topological code — Instances of the code in 4D realize the 3D \(\mathbb{Z}_2\) gauge theory with fermionic charge and either bosonic (FcBl) or fermionic (FcFl) loop excitations at their boundaries [2,3]; see Ref. [4] for a different lattice-model formulation of the FcBl boundary code.
  • Symmetry-protected topological (SPT) code — Instances of the Chen-Hsin invertible-order code realize beyond-group-cohomology SPTs [1].

References

[1]
Y.-A. Chen and P.-S. Hsin, “Exactly solvable lattice Hamiltonians and gravitational anomalies”, SciPost Physics 14, (2023) arXiv:2110.14644 DOI
[2]
T. Johnson-Freyd, “(3+1)D topological orders with only a \(\mathbb{Z}_2\)-charged particle”, (2020) arXiv:2011.11165
[3]
L. Fidkowski, J. Haah, and M. B. Hastings, “Gravitational anomaly of (3+1) -dimensional Z2 toric code with fermionic charges and fermionic loop self-statistics”, Physical Review B 106, (2022) arXiv:2110.14654 DOI
[4]
L. Fidkowski, J. Haah, and M. B. Hastings, “Exactly solvable model for a 4+1D beyond-cohomology symmetry-protected topological phase”, Physical Review B 101, (2020) arXiv:1912.05565 DOI
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Zoo Code ID: invertible

Cite as:
“Chen-Hsin invertible-order code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/invertible
BibTeX:
@incollection{eczoo_invertible, title={Chen-Hsin invertible-order code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/invertible} }
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Cite as:

“Chen-Hsin invertible-order code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/invertible

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