Surface-code-fragment (SCF) holographic code[1] 

Description

Holographic tensor-network code constructed out of a network of encoding isometries of the \([[5,1,2]]\) rotated surface code. The structure of the isometry is similar to that of the HaPPY code since both isometries are rank-six tensors. In the case of the SCF holographic code, the isometry is only a planar-perfect tensor (as opposed to a perfect tensor).

Code Capacity Threshold

\(7.1\%\) and \(8.2\%\) for even and odd raddi reduced-rate codes, respectively, under depolarizing using the integer optimization decoder [1].

Parents

Child

  • \([[5,1,2]]\) rotated surface code — The \([[5,1,2]]\) rotated surface code is the smallest SCF holographic code. The encoding of more general SCF holographic codes is a holographic tensor network consisting of the encoding isometry for the \([[5,1,2]]\) rotated surface code, which is a planar-perfect tensor.

Cousin

References

[1]
R. J. Harris et al., “Decoding holographic codes with an integer optimization decoder”, Physical Review A 102, (2020) arXiv:2008.10206 DOI
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Zoo Code ID: holographic_5_1_2

Cite as:
“Surface-code-fragment (SCF) holographic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/holographic_5_1_2
BibTeX:
@incollection{eczoo_holographic_5_1_2, title={Surface-code-fragment (SCF) holographic code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/holographic_5_1_2} }
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“Surface-code-fragment (SCF) holographic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/holographic_5_1_2

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/holographic/holographic_5_1_2.yml.