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 certain Pauli noise [2].
Code Capacity Threshold
\(18.8\%\) under depolarizing noise using tensor-network decoder [1].
Parents
- Qubit stabilizer code
- Holographic tensor-network code — 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.
Child
- \([[6,1,3]]\) Six-qubit stabilizer code — 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 et al., “Tensor-Network Codes”, Physical Review Letters 127, (2021) arXiv:2009.10329 DOI
- [2]
- J. Fan et al., “Overcoming the Zero-Rate Hashing Bound with Holographic Quantum Error Correction”, (2024) arXiv:2408.06232
Page edit log
- Victor V. Albert (2024-07-01) — most recent
Cite as:
“Six-qubit-tensor holographic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/holographic_6_1_3