Generalize spacetime fractalization to non-CSS codes

Establish a generalization of the spacetime fractalization framework to quantum error-correcting codes that are not CSS codes, with the aim of enabling the discovery of further exotic spacetime topological phases of matter.

Background

The paper develops spacetime fractalization primarily for CSS stabilizer codes, using the Raussendorf–Bravyi–Harrington cluster state and adaptive measurement-based quantum-computing circuits. This construction produces Floquet codes with fracton excitations that are immobile in both space and time.

The authors explicitly identify extending the framework beyond CSS codes as unresolved. Such a generalization could expand the range of realizable spacetime topological phases beyond those accessible through the CSS-based constructions studied in the paper.