# Hyperinvariant tensor-network (HTN) code[1]

Also known as 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].

## Parents

- Qubit stabilizer code
- Holographic tensor-network code — The encoding of an HTN code is a hyperinvariant tensor network.

## 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 et al., “Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes”, (2024) arXiv:2407.11926

## 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