Heptagon holographic code[1]
Also known as Holographic Steane code.
Description
Holographic tensor-network code constructed out of a network of encoding isometries of the Steane code. Depending on how the isometry tensors are contracted, there is a zero-rate and a finite-rate code family.
Decoding
Optimal erasure decoder [1].
Code Capacity Threshold
\(~33\%\) under erasures using optimal erasure decoder for the finite-rate family, and \(50\%\) for the zero-rate family [1].Depolarizing noise: \(9.4\%\) using tensor-network decoder, and \(\approx 7\%\) using integer optimization decoder [2].\(18.985\%\) against depolarizing noise for zero-rate code under tensor-network decoder [3].
Parents
- Qubit CSS code
- Holographic tensor-network code — The encoding of the heptagon holographic code is a holographic tensor network consisting of the encoding isometry for the Steane code, which is a planar-perfect tensor.
Child
- Concatenated Steane code — A recursively concatenated Steane code is a heptagon holographic code on a tree tensor network.
Cousin
- Planar-perfect-tensor code — The encoding of the heptagon holographic code is a holographic tensor network consisting of the encoding isometry for the Steane code, which is a planar-perfect tensor.
References
- [1]
- R. J. Harris, N. A. McMahon, G. K. Brennen, and T. M. Stace, “Calderbank-Shor-Steane holographic quantum error-correcting codes”, Physical Review A 98, (2018) arXiv:1806.06472 DOI
- [2]
- T. Farrelly, R. J. Harris, N. A. McMahon, and T. M. Stace, “Parallel decoding of multiple logical qubits in tensor-network codes”, (2020) arXiv:2012.07317
- [3]
- J. Fan, M. Steinberg, A. Jahn, C. Cao, and S. Feld, “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:
“Heptagon holographic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/holographic_steane