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2015

Complexity of the XY antiferromagnet at fixed magnetization

Childs, Andrew M., Gosset, David, Webb, Zak

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We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete.

To show this, we strengthen a previous result by establishing QMA-completeness for approximating the ground energy of the Bose-Hubbard model on simple graphs.
Using a connection between the XY and Bose-Hubbard models that we exploited in previous work, this establishes QMA-completeness of the XY model.

Complexity of the XY antiferromagnet at fixed magnetization · Around

Built on

Alexei Yu. Kitaev, Alexander H. Shen, and Mikhail N. Vyalyi, Classical and quantum computation , American Mathematical Society, 2002
2002
Earlier work this paper cites.
Ari Mizel, Daniel A. Lidar, and Morgan Mitchell, Simple proof of equivalence between adiabatic quantum computation and the circuit model , Physical Review Letters 99
2007
Earlier work this paper cites.
Robert Alicki, Mark Fannes, and Michał Horodecki, On thermalization in Kitaev’s 2D model , Journal of Physics A 42
Original
2009
Earlier work this paper cites.

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Andrew M. Childs, David Gosset, and Zak Webb, The Bose-Hubbard model is QMA-complete , Proceedings of the 41st International Colloquium on Automata, Languages, and Programming, pp. 308–319, 2014, arXiv:1311.3297
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2014
Cited alongside, same era.

Then

Toby Cubitt and Ashley Montanaro, Complexity classification of local Hamiltonian problems , Proceedings of the 55th IEEE Symposium on Foundations of Computer Science, pp. 120–129, 2014, arXiv:1311.3161
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2014
Later among the works it cites.
Stephen Piddock and Ashley Montanaro, The complexity of antiferromagnetic interactions and 2D lattices , 2015, arXiv:1506.04014
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Closest in time.

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