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.

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
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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} }
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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.