Measurement-based quantum computation in a 2D phase of matter

TL;DR

This paper demonstrates that a broad class of disordered quantum ground states, including the AKLT model on a honeycomb lattice, can serve as scalable resources for measurement-based quantum computation through local filtering and measurements.

Contribution

It shows that most states in the disordered phase of certain Hamiltonians can be transformed into graph states suitable for MBQC, revealing a new connection between condensed matter phases and quantum computation.

Findings

Disordered phase states can be reduced to graph states for MBQC.

A phase transition affects the universality of the resource states.

Most ground states in the disordered phase are scalable MBQC resources.

Abstract

Recently it has been shown that the non-local correlations needed for measurement based quantum computation (MBQC) can be revealed in the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model involving nearest neighbor spin-3/2 interactions on a honeycomb lattice. This state is not singular but resides in the disordered phase of ground states of a large family of Hamiltonians characterized by short-range-correlated valence bond solid states. By applying local filtering and adaptive single particle measurements we show that most states in the disordered phase can be reduced to a graph of correlated qubits that is a scalable resource for MBQC. At the transition between the disordered and Neel ordered phases we find a transition from universal to non-universal states as witnessed by the scaling of percolation in the reduced graph state.