Quantum computational capability of a 2D valence bond solid phase

TL;DR

This paper demonstrates that the naturally occurring 2D valence bond solid phase in quantum antiferromagnets can be used as a resource for universal quantum computation through local measurements, revealing intrinsic computational complexity.

Contribution

It shows that naturally occurring 2D quantum phases possess structured correlations capable of universal quantum computation without creating additional entanglement.

Findings

Quantum correlations in 2D valence bond solid phases enable universal quantum computation.

A constructive protocol for deterministic quantum computation via local measurements.

Potential extensibility to other 2D valence bond phases.

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 two-dimensional valence bond solid phase of a quantum antiferromagnet, modeled by Affleck, Kennedy, Lieb, and Tasaki 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.