Transitions in the computational power of thermal states for measurement-based quantum computation

TL;DR

This paper demonstrates a phase transition in the computational utility of thermal states in a spin-lattice model for measurement-based quantum computing, independent of physical phase transitions.

Contribution

It reveals a novel computational phase transition in thermal states that is decoupled from physical phase transitions in the model.

Findings

Identifies a transition from universal quantum computational resource to classically simulable states.

Shows the transition does not align with any physical phase transition in the model.

Highlights the potential for computational phase transitions separate from physical properties.

Abstract

We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct "phases" - one in which every state is a universal resource for quantum computation, and another in which any local measurement sequence can be simulated efficiently on a classical computer. Remarkably, this transition in computational power does not coincide with any phase transition, classical or quantum, in the underlying spin-lattice model.