Six-qubit-tensor holographic code[1] 

Description

Holographic tensor-network code constructed out of a network of encoding isometries of the \([[6,1,3]]\) six-qubit stabilizer code. The structure of the isometry is similar to that of the heptagon holographic code since both isometries are rank-six tensors, but the isometry in this case is neither a perfect tensor nor a planar-perfect tensor.

Code Capacity Threshold

\(18.8\%\) under depolarizing noise using tensor-network decoder [1].

Parents

Child

  • \([[6,1,3]]\) Six-qubit stabilizer code — The \([[6,1,3]]\) six-qubit stabilizer code is the smallest six-qubit-tensor holographic code. The encoding of more general SCF holographic codes is a holographic tensor network consisting of the encoding isometry for the \([[6,1,3]]\) six-qubit stabilizer code.

References

[1]
T. Farrelly et al., “Tensor-Network Codes”, Physical Review Letters 127, (2021) arXiv:2009.10329 DOI
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Zoo Code ID: holographic_6_1_3

Cite as:
“Six-qubit-tensor holographic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/holographic_6_1_3
BibTeX:
@incollection{eczoo_holographic_6_1_3, title={Six-qubit-tensor holographic code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/holographic_6_1_3} }
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https://errorcorrectionzoo.org/c/holographic_6_1_3

Cite as:

“Six-qubit-tensor holographic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/holographic_6_1_3

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/holographic/holographic_6_1_3.yml.