Duality between string and computational order in symmetry-enriched topological phases

TL;DR

This paper introduces a new framework for analyzing the computational potential of topological phases of matter, demonstrating models that serve as universal resources for measurement-based quantum computation with symmetry protection.

Contribution

It develops a more general framework beyond short-range entangled phases and presents new topological models with protected computational universality.

Findings

Ground states of the toric code under magnetic fields are non-universal for MBQC.

A new topological model with universal MBQC resources is proposed.

Subsystem symmetries protect the computational power of the models.

Abstract

We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation. This is possible thanks to a new framework for analyzing the computational properties of phases of matter that is more general than previous constructions, which were limited to short-range entangled phases in one dimension. We show that ground states of the toric code in an anisotropic magnetic field yield a natural, albeit non-computationally-universal, application of our framework. We then present a new model with topological order whose ground states are universal resources for MBQC. Both topological models are enriched by subsystem symmetries, and these symmetries protect their computational power. Our framework greatly expands the range of physical models that can be analyzed from the computational perspective.