Fractalizing quantum codes

Trithep Devakul1,2 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

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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.

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Cited by

[1] Joseph Sullivan, Thomas Iadecola, and Dominic J. Williamson, "Planar p-string condensation: Chiral fracton phases from fractional quantum Hall layers and beyond", arXiv:2010.15127, Physical Review B 103 20, 205301 (2021).

[2] 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).

[3] Nathanan Tantivasadakarn, Wenjie Ji, and Sagar Vijay, "Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases", arXiv:2102.09555.

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