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.Rate
Zero-rate version of the code surpasses the hashing bound for certain Pauli noise [2].Code Capacity Threshold
\(18.8\%\) under depolarizing noise using tensor-network decoder [1].Primary Hierarchy
Parents
The encoding of the six-qubit-tensor holographic code is a holographic tensor network consisting of the encoding isometry for the \([[6,1,3]]\) six-qubit stabilizer code.
Six-qubit-tensor holographic code
Children
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, R. J. Harris, N. A. McMahon, and T. M. Stace, “Tensor-Network Codes”, Physical Review Letters 127, (2021) arXiv:2009.10329 DOI
- [2]
- J. Fan, M. Steinberg, A. Jahn, C. Cao, and S. Feld, “Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding”, (2025) arXiv:2408.06232
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2024-07-01)
Cite as:
“Six-qubit-tensor holographic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/holographic_6_1_3, arXiv:2606.11484