Symmetry-Protected Phases for Measurement-Based Quantum Computation

Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia.
Physical Review Letters (Impact Factor: 7.51). 01/2012; 108(24). DOI: 10.1103/PhysRevLett.108.240505
Source: arXiv


Ground states of spin lattices can serve as a resource for measurement-based
quantum computation. Ideally, the ability to perform quantum gates via
measurements on such states would be insensitive to small variations in the
Hamiltonian. Here, we describe a class of symmetry-protected topological orders
in one-dimensional systems, any one of which ensures the perfect operation of
the identity gate. As a result, measurement-based quantum gates can be a robust
property of an entire phase in a quantum spin lattice, when protected by an
appropriate symmetry.

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    • "However , as of present, there still does not exist a complete characterization of all universal resources. An intriguing connection between the resourcefulness in MBQC and certain phases of matter was discovered in Ref. [20], where the authors show that there exists a property of many-body states, namely symmetry-protected topological (SPT) order in 1D, that can be utilized for * † the protection of certain quantum gates in MBQC, even though 1D quantum states do not accommodate universal quantum computation. "
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    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.
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