Identifying phases of quantum many-body systems that are universal for quantum computation

TL;DR

This paper identifies a quantum phase transition in a spin-lattice system that distinguishes a disordered phase from an ordered phase capable of universal quantum computation, using nonlocal correlation functions.

Contribution

It demonstrates that a simple spin-lattice system exhibits a quantum phase transition marking the boundary between non-computational and computationally universal phases.

Findings

Existence of a quantum phase transition in the system.

Ordered 'cluster phase' enables universal quantum gates.

Disordered phase does not support universal quantum computation.

Abstract

Quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state, such as the ground state of an interacting many-body system. We investigate a simple spin-lattice system based on the cluster-state model, and by using nonlocal correlation functions that quantify the fidelity of quantum gates performed between distant qubits, we demonstrate that it possesses a quantum (zero-temperature) phase transition between a disordered phase and an ordered "cluster phase" in which it is possible to perform a universal set of quantum gates.