Fractalizing quantum codes

Trithep Devakul; Dominic J. Williamson

doi:10.22331/q-2021-04-22-438

Fractalizing quantum codes

Trithep Devakul^1,2 and Dominic J. Williamson³

¹Department of Physics, Princeton University, Princeton, NJ 08540, USA
²Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
³Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305, USA

Published:	2021-04-22, volume 5, page 438
Eprint:	arXiv:2009.01252v2
Doi:	https://doi.org/10.22331/q-2021-04-22-438
Citation:	Quantum 5, 438 (2021).

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Abstract

We introduce "fractalization", a procedure by which spin models are extended to higher-dimensional "fractal" spin models. This allows us to interpret type-II fracton phases, fractal symmetry-protected topological phases, and more, in terms of well understood lower-dimensional spin models. Fractalization is also useful for deriving new spin models and quantum codes from known ones. We construct higher dimensional generalizations of fracton models that host extended fractal excitations. Finally, by applying fractalization to a 2D subsystem code, we produce a family of locally generated 3D subsystem codes that are conjectured to saturate a quantum information storage tradeoff bound.

► BibTeX data

@article{Devakul2021fractalizingquantum,
  doi = {10.22331/q-2021-04-22-438},
  url = {https://doi.org/10.22331/q-2021-04-22-438},
  title = {Fractalizing quantum codes},
  author = {Devakul, Trithep and Williamson, Dominic J.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {438},
  month = apr,
  year = {2021}
}

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[4] Cory T. Aitchison, Daniel Bulmash, Arpit Dua, Andrew C. Doherty, and Dominic J. Williamson, "Boundaries and defects in the cubic code", Physical Review B 109 20, 205125 (2024).

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[6] Julia Wildeboer, Thomas Iadecola, and Dominic J. Williamson, "Symmetry-Protected Infinite-Temperature Quantum Memory from Subsystem Codes", PRX Quantum 3 2, 020330 (2022).

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[8] Zheng Zhou, Xue-Feng Zhang, Frank Pollmann, and Yizhi You, "Fractal Quantum Phase Transitions: Critical Phenomena Beyond Renormalization", arXiv:2105.05851, (2021).

[9] Jonathan Francisco San Miguel, Arpit Dua, and Dominic J. Williamson, "Bifurcating subsystem symmetric entanglement renormalization in two dimensions", Physical Review B 103 3, 035148 (2021).

[10] Jason Bennett, "Fractons: gauging spin models and tensor gauge theory", arXiv:2206.14028, (2022).

[11] Po-Shen Hsin, David T. Stephen, Arpit Dua, and Dominic J. Williamson, "Subsystem Symmetry Fractionalization and Foliated Field Theory", arXiv:2403.09098, (2024).

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