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Tiger surface code[1]

Description

A tiger-code variant of the Kitaev surface code that is constructed from a hypergraph product of two repetition codes over the integers. The code is conjectured to realize phases of \(U(1)\) gauge theory.

Protection

Both loss and Euclidean distances scale as the square root of the number of modes for particular rectangular geometries. The Euclidean distance goes to zero for the case of a square lattice.

Cousins

  • Compactified \(\mathbb{R}\) gauge theory code— Both the compactified \(\mathbb{R}\) gauge theory and tiger surface code are constructed from a hypergraph product of two repetition codes over the integers.
  • Abelian topological code— The tiger surface code is conjectured to realize phases of \(U(1)\) gauge theory.
  • Modular-qudit surface code— The tiger surface code can be thought of as a realization of the \(q\to\infty\) \(U(1)\) rotor limit [2] of the qudit surface code as a tiger code.
  • Hypergraph product (HGP) code— The tiger surface code is constructed from a hypergraph product of two repetition codes over the integers.
  • Repetition code— The tiger surface code is constructed from a hypergraph product of two repetition codes over the integers.

Member of code lists

Primary Hierarchy

Parents
The tiger surface code is constructed from a hypergraph product of two repetition codes over the integers.
Tiger surface code

References

[1]
Y. Xu, Y. Wang, C. Vuillot, and V. V. Albert, “Letting the tiger out of its cage: bosonic coding without concatenation”, (2024) arXiv:2411.09668
[2]
V. V. Albert, S. Pascazio, and M. H. Devoret, “General phase spaces: from discrete variables to rotor and continuum limits”, Journal of Physics A: Mathematical and Theoretical 50, 504002 (2017) arXiv:1709.04460 DOI
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Zoo Code ID: tiger_surface

Cite as:
“Tiger surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/tiger_surface
BibTeX:
@incollection{eczoo_tiger_surface, title={Tiger surface code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/tiger_surface} }
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Permanent link:
https://errorcorrectionzoo.org/c/tiger_surface

Cite as:

“Tiger surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/tiger_surface

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/tiger/tiger_surface.yml.