Hemicubic code[1]
Description
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- Quantum locally testable code (QLTC) — The hypersphere product code family has asymptotically diminishing soundness that scales as order \(\Omega(1/\log n)\), locality of stabilizer generators scaling as order \(O(\log n)\), and distance \(\Theta(\sqrt{n})\). Application of the generalized distance balancing scheme [2] using an asymptotically good classical code of length \(t\) yields \(O(1/(\log(n) t^2))\) soundness and \(\Theta(\sqrt{n}t)\) distance while maintaining locality scaling and at the expense of a dimension scaling as \(\Theta(t^2)\) [3].
References
- [1]
- A. Leverrier, V. Londe, and G. Zémor, “Towards local testability for quantum coding”, Quantum 6, 661 (2022) arXiv:1911.03069 DOI
- [2]
- S. Evra, T. Kaufman, and G. Zémor, “Decodable quantum LDPC codes beyond the \(\sqrt{n}\) distance barrier using high dimensional expanders”, (2020) arXiv:2004.07935
- [3]
- A. Wills, T.-C. Lin, and M.-H. Hsieh, “General Distance Balancing for Quantum Locally Testable Codes”, (2023) arXiv:2305.00689
Page edit log
- Victor V. Albert (2022-09-26) — most recent
Cite as:
“Hemicubic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/hemicubic