Hyperinvariant tensor-network (HTN) code[1] 

Description

Holographic tensor-network error-detecting code constructed out of a hyperinvariant tensor network [2], i.e., a MERA-like network admitting a hyperbolic geometry. The network is defined using two layers A and B, with constituent tensors satisfying isometry conditions (a.k.a. multitensor constraints).

This code produces boundary correlation functions that align with those expected from conformal field theory (CFT) boundary states. HTN codes exhibit state-dependent breakdown of complementary recovery, consistent with quantum gravity corrections in AdS/CFT.

Protection

Certain HTN codes protect against single-site errors.

Parents

References

[1]
M. Steinberg, S. Feld, and A. Jahn, “Holographic codes from hyperinvariant tensor networks”, Nature Communications 14, (2023) arXiv:2304.02732 DOI
[2]
G. Evenbly, “Hyperinvariant Tensor Networks and Holography”, Physical Review Letters 119, (2017) arXiv:1704.04229 DOI
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Zoo Code ID: holographic_hyperinvariant

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

“Hyperinvariant tensor-network (HTN) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/holographic_hyperinvariant

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