Hyperinvariant tensor-network (HTN) code[1]
Alternative names: Evenbly code.
Description
Holographic tensor-network 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].Cousin
- \([[4,2,2]]_{G}\) four group-qudit code— The explicit 4-ququart encoding tensor \(A'\) used in the HTN code is a \([[4,1,2]]_{\mathbb{Z}_4}\) subcode of the \([[4,2,2]]_{\mathbb{Z}_4}\) four group-qudit code [1; Sec. IID].
Primary Hierarchy
Parents
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”, Quantum 9, 1826 (2025) arXiv:2407.11926 DOI
Page edit log
- Victor V. Albert (2024-07-01) — most recent
Cite as:
“Hyperinvariant tensor-network (HTN) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/holographic_hyperinvariant