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 dg|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.

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

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: penrose

Cite as:
“Penrose tiling code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/penrose
BibTeX:
@incollection{eczoo_penrose, title={Penrose tiling code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/penrose} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/penrose

Cite as:

“Penrose tiling code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/penrose

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/uncategorized/penrose.yml.