Heptagon holographic code[1] 

Also known as Holographic Steane code.

Description

Holographic tensor-network code constructed out of a network of encoding isometries of the Steane code. Depending on how the isometry tensors are contracted, there is a zero-rate and a finite-rate code family.

Decoding

Optimal erasure decoder [1].

Threshold

\(~33\%\) under erasures using optimal erasure decoder for the finite-rate family, and \(50\%\) for the zero-rate family [1].Depolarizing noise: \(9.4\%\) using tensor-network decoder, and \(\sim 7\%\) using integer optimization decoder [2].

Parents

Child

  • Concatenated Steane code — A recursively concatenated Steane code is a heptagon holographic code on a tree tensor network.

Cousin

References

[1]
R. J. Harris et al., “Calderbank-Shor-Steane holographic quantum error-correcting codes”, Physical Review A 98, (2018) arXiv:1806.06472 DOI
[2]
T. Farrelly et al., “Parallel decoding of multiple logical qubits in tensor-network codes”, (2020) arXiv:2012.07317
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Zoo Code ID: holographic_steane

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

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

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