Quantum computational capability of a 2D valence bond solid phase

Journal Article · Fri Jul 15 04:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.03.006· OSTI ID:21583307

Miyake, Akimasa ^[1]

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1. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo Ontario, N2L 2Y5 (Canada)

Highlights: > Our model is the 2D valence bond solid phase of a quantum antiferromagnet. > Universal quantum computation is processed by measurements of quantum correlations. > An intrinsic complexity of strongly-correlated quantum systems could be a resource. - Abstract: Quantum phases of naturally-occurring systems exhibit distinctive collective phenomena as manifestation of their many-body correlations, in contrast to our persistent technological challenge to engineer at will such strong correlations artificially. Here we show theoretically that quantum correlations exhibited in the 2D valence bond solid phase of a quantum antiferromagnet, modeled by Affleck, Kennedy, Lieb, and Tasaki (AKLT) as a precursor of spin liquids and topological orders, are sufficiently complex yet structured enough to simulate universal quantum computation when every single spin can be measured individually. This unveils that an intrinsic complexity of naturally-occurring 2D quantum systems-which has been a long-standing challenge for traditional computers-could be tamed as a computationally valuable resource, even if we are limited not to create newly entanglement during computation. Our constructive protocol leverages a novel way to herald the correlations suitable for deterministic quantum computation through a random sampling, and may be extensible to other ground states of various 2D valence bond phases beyond the AKLT state.

• OSTI ID: 21583307
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 7 Vol. 326; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
CALCULATION METHODS
COMPUTERS
CORRELATIONS
ENERGY LEVELS
FLUIDS
GROUND STATES
LIQUIDS
MANY-BODY PROBLEM
MATHEMATICS
PARTICLE PROPERTIES
QUANTUM COMPUTERS
QUANTUM ENTANGLEMENT
RANDOMNESS
SOLIDS
SPIN
TOPOLOGY
TWO-DIMENSIONAL CALCULATIONS
VALENCE