Fractalizing quantum codes

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.

arXiv comment17 pages

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Cited by in corpus (9)

• Quantum Low-Density Parity-Check Codes
• Subsystem Non-Invertible Symmetry Operators and Defects
• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• No Strings Attached: Boundaries and Defects in the Cubic Code
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• Wire Codes