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Hyperinvariant tensor-network (HTN) code[1]

Alternative names: Evenbly code.

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.

Code Capacity Threshold

\(19.1\%\) under depolarizing noise and \(50\%\) under erasure noise for a \(\{5,4\}\) tiling [3].\(40\%\) under erasure noise for constant-rate version of the code [3].

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Parents
Qubit stabilizer code
Holographic tensor-network codeHQECC QECC Quantum
The encoding of an HTN code is a hyperinvariant tensor network.
Hyperinvariant tensor-network (HTN) code

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
[3]
M. Steinberg, J. Fan, R. J. Harris, D. Elkouss, S. Feld, and A. Jahn, “Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes”, (2024) arXiv:2407.11926
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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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Permanent link:
https://errorcorrectionzoo.org/c/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

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