Complexity of the XY antiferromagnet at fixed magnetization
Andrew M. Childs, David Gosset, Zak Webb
TL;DR
This paper proves that calculating the ground energy of the XY antiferromagnet at fixed magnetization is computationally hard (QMA-complete), by linking it to the Bose-Hubbard model's complexity.
Contribution
It establishes QMA-completeness for the XY model's ground energy approximation, extending previous results through a novel connection to the Bose-Hubbard model.
Findings
Proves QMA-completeness for the XY antiferromagnetic model at fixed magnetization.
Strengthens previous results by establishing QMA-completeness for the Bose-Hubbard model.
Links the complexity of the XY model to that of the Bose-Hubbard model.
Abstract
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.
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