Universal quantum computation using fractal symmetry-protected cluster phases

TL;DR

This paper demonstrates that certain 2D fractal symmetry-protected topological phases can be used as universal resources for measurement-based quantum computation, with computational universality persisting throughout these phases.

Contribution

It explicitly shows that two cluster models within fractal SPT phases enable universal quantum computation, highlighting the role of rigid subsystem symmetries.

Findings

Fractal SPT phases serve as universal resources for measurement-based quantum computation.

Universality persists across the entire fractal SPT phases.

One model reduces to a cluster model on the honeycomb lattice.

Abstract

We show that 2D fractal subsystem symmetry-protected topological phases may serve as resources for universal measurement-based quantum computation. This is demonstrated explicitly for two cluster models known to lie within fractal symmetry-protected topological phases, and computational universality is shown to persist throughout those phases. One of the models considered is simply the cluster model on the honeycomb lattice in one limit. We discuss the importance of rigid subsystem symmetries, as opposed to global or $(\text{D}-1)$-form symmetries, in this context.