Fractalizing quantum codes

TL;DR

The paper introduces a 'fractalization' method to extend spin models into higher dimensions, enabling new insights into fracton phases and quantum codes, and constructs novel fractal spin models and codes.

Contribution

It presents a new 'fractalization' procedure to derive higher-dimensional spin models and quantum codes from lower-dimensional ones, linking fracton phases with well-understood models.

Findings

Constructed higher-dimensional fracton models with fractal excitations.

Developed 3D subsystem codes from 2D codes that may saturate quantum storage bounds.

Provided a framework connecting fracton phases to lower-dimensional models.

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.