Translationally-invariant stabilizer code

Description

Stub.

Parent

Cousins

  • Kitaev surface code — Translation-invariant 2D qubit topological stabilizer codes are equivalent to several copies of the Kitaev surface code via a local constant-depth Clifford circuit [1][2][3].
  • Modular-qudit surface code — Translation-invariant 2D prime-qudit topological stabilizer codes are equivalent to several copies of the qudit surface code via a local constant-depth Clifford circuit [4].
  • Abelian topological code — Translationally-invariant stabilizer codes can realize abelian topological orders. Conversely, abelian topological codes need not be translationally invariant, and can realize multiple topological phases on one lattice.
  • Fracton code — Translationally-invariant stabilizer codes can realize fracton orders. Conversely, fracton codes need not be translationally invariant, and can realize multiple phases on one lattice.

Zoo code information

Internal code ID: translationally_invariant_stabilizer.yml

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Zoo Code ID: translationally_invariant_stabilizer.yml

Cite as:
“Translationally-invariant stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/translationally_invariant_stabilizer.yml
BibTeX:
@incollection{eczoo_translationally_invariant_stabilizer.yml, title={Translationally-invariant stabilizer code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/translationally_invariant_stabilizer.yml} }
Permanent link:
https://errorcorrectionzoo.org/c/translationally_invariant_stabilizer.yml

References

[1]
H. Bombin, G. Duclos-Cianci, and D. Poulin, “Universal topological phase of two-dimensional stabilizer codes”, New Journal of Physics 14, 073048 (2012). DOI; 1103.4606
[2]
H. Bombín, “Structure of 2D Topological Stabilizer Codes”, Communications in Mathematical Physics 327, 387 (2014). DOI; 1107.2707
[3]
J. Haah, “Algebraic Methods for Quantum Codes on Lattices”, Revista Colombiana de Matemáticas 50, 299 (2017). DOI; 1607.01387
[4]
J. Haah, “Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices”, Journal of Mathematical Physics 62, 012201 (2021). DOI; 1812.11193

Cite as:

“Translationally-invariant stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/translationally_invariant_stabilizer.yml

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/properties/qldpc/translationally_invariant_stabilizer.yml.