2D lattice stabilizer code 

Description

Lattice stabilizer code in two spatial dimensions.

Any prime-qudit code can be converted to several copies of the prime-qudit 2D surface code along with some trivial codes [1].

Decoding

Tensor-network based decoder for 2D codes subject to correlated noise [2].Standard stabilizer-based error correction can be performed even in the presence of perturbations to the codespace [3].

Parent

Children

Cousins

  • Kitaev surface code — Translation-invariant 2D qubit lattice stabilizer codes are equivalent to several copies of the Kitaev surface code via a local constant-depth Clifford circuit [57]. There exists an algorithm with which one can determine the fusion and braiding rules of a 2D translationally invariant qubit code, and decompose the given code into copies of the surface code [8].
  • Abelian quantum-double stabilizer code — Translation-invariant 2D prime-qudit lattice stabilizer codes are equivalent to several copies of the prime-qudit surface code via a local constant-depth Clifford circuit [1].
  • Holographic code — 2D lattice stabilizer codes admit a bulk-boundary correspondence similar to that of holographic codes, namely, the boundary Hilbert space of the former cannot be realized via local degrees of freedom [9].

References

[1]
J. Haah, “Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices”, Journal of Mathematical Physics 62, (2021) arXiv:1812.11193 DOI
[2]
C. T. Chubb and S. T. Flammia, “Statistical mechanical models for quantum codes with correlated noise”, Annales de l’Institut Henri Poincaré D 8, 269 (2021) arXiv:1809.10704 DOI
[3]
W. Zhong, O. Shtanko, and R. Movassagh, “Advantage of Quantum Neural Networks as Quantum Information Decoders”, (2024) arXiv:2401.06300
[4]
T. D. Ellison et al., “Pauli Stabilizer Models of Twisted Quantum Doubles”, PRX Quantum 3, (2022) arXiv:2112.11394 DOI
[5]
H. Bombin, G. Duclos-Cianci, and D. Poulin, “Universal topological phase of two-dimensional stabilizer codes”, New Journal of Physics 14, 073048 (2012) arXiv:1103.4606 DOI
[6]
H. Bombín, “Structure of 2D Topological Stabilizer Codes”, Communications in Mathematical Physics 327, 387 (2014) arXiv:1107.2707 DOI
[7]
J. Haah, “Algebraic Methods for Quantum Codes on Lattices”, Revista Colombiana de Matemáticas 50, 299 (2017) arXiv:1607.01387 DOI
[8]
Z. Liang et al., “Extracting topological orders of generalized Pauli stabilizer codes in two dimensions”, (2023) arXiv:2312.11170
[9]
T. Schuster et al., “A holographic view of topological stabilizer codes”, (2023) arXiv:2312.04617
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Zoo Code ID: 2d_stabilizer

Cite as:
“2D lattice stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/2d_stabilizer
BibTeX:
@incollection{eczoo_2d_stabilizer, title={2D lattice stabilizer code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/2d_stabilizer} }
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Cite as:

“2D lattice stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/2d_stabilizer

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/properties/stabilizer/topological_stabilizer/2d_stabilizer.yml.