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.

17 pages

References in corpus (15)

• Local stabilizer codes in three dimensions without string logical operators
• Fracton Phases of Matter
• Fracton hydrodynamics
• Fracton topological phases from strongly coupled spin chains
• Topological Defect Networks for Fractons of all Types
• Correlation function diagnostics for type-I fracton phases
• A systematic construction of gapped non-liquid states
• A Generalization of Non-Abelian Anyons in Three Dimensions
• Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
• Compactifying fracton stabilizer models
• Subsystem symmetry enriched topological order in three dimensions
• Type-II fractons from coupled spin chains and layers
• Fractonic order and emergent fermionic gauge theory
• Correcting spanning errors with a fractal code
• Vortices and Fractons

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