Symmetry-protected topologically ordered states for universal quantum computation

TL;DR

This paper demonstrates that two-dimensional plaquette states on arbitrary lattices possess nontrivial symmetry-protected topological order and serve as universal resource states for measurement-based quantum computation.

Contribution

It extends the understanding of symmetry-protected topological order to arbitrary 2D lattices and establishes their universality for quantum computation.

Findings

2D plaquette states exhibit nontrivial SPT order on arbitrary lattices.

These states are proven to be universal resources for measurement-based quantum computation.

Extension of previous lattice-specific constructions to more general 2D lattices.

Abstract

Measurement-based quantum computation is a model for quantum information processing utilizing local measurements on suitably entangled resource states for the implementation of quantum gates. A complete characterization for universal resource states is still missing. It has been shown that symmetry-protected topological order in one dimension can be exploited for the protection of certain quantum gates in measurement-based quantum computation. In this paper we show that the two-dimensional plaquette states on arbitrary lattices exhibit nontrivial symmetry-protected topological order in terms of symmetry fractionalization and that they are universal resource states for quantum computation. Our results of the nontrivial symmetry-protected topological order on arbitrary 2D lattices are based on an extension of the recent construction by Chen, Gu, Liu and Wen [Phys. Rev. B \textbf{87}, 155114 (2013)] on the square lattice.