Penrose tiling code[1]
Description
Encodes quantum information into superpositions of rotated and translated versions of different Penrose tilings of \(\mathbb{R}^n\).
Letting \(|T\rangle\) be a Penrose tiling, the codeword corresponding to this tiling is a superposition of all points in the tiling's orbit under all Euclidean transformations, \begin{align} |\overline{T}\rangle=\int \textnormal{d}g|gT\rangle~, \tag*{(1)}\end{align} where \(g\) is a Euclidean transformation.
Protection
Properties of Pensrose tilings such as local indistinguishability and local recoverability ensure that Penrose tiling codes can correct erasures of any finite region of space.
Notes
Popular summary of Penrose tiling codes in Quanta Magazine.
Parent
- Bosonic code — Penrose tiling codes encode information into Penrose tilings, which are non-periodic tilings of \(\mathbb{R}^n\).
References
- [1]
- Z. Li and L. Boyle, “The Penrose Tiling is a Quantum Error-Correcting Code”, (2024) arXiv:2311.13040
Page edit log
- Victor V. Albert (2023-11-28) — most recent
Cite as:
“Penrose tiling code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/penrose