Subsystem hyperbolic surface code[1] 

Description

Subsystem generalization of the surface code on a 2D hyperbolic tesselation with gauge-group generators of weight at most three. An \(\{r,s\}\) hyperbolic tesselation with \(E\) edges yields a \([[3E/2,(1/2-2/r)E+2,(1-2/r)E,d]]\) subsystem code.

Protection

Distance \(d\) is bounded between \(d_X/2\) and \(d_X\), where \(d_X\) is the \(X\) distance of the subspace hyperbolic surface code derived from the same tesselation [1; Appx. F].

Parent

Cousin

References

[1]
O. Higgott and N. P. Breuckmann, “Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead”, Physical Review X 11, (2021) arXiv:2010.09626 DOI
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Zoo Code ID: subsystem_hyperbolic_surface

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

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/subsystem/topological/surface/subsystem_hyperbolic_surface.yml.