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Published November 2011 | public
Journal Article

Complexity of commuting Hamiltonians on a square lattice of qubits

Abstract

We consider the computational complexity of Hamiltonians which are sums of commuting terms acting on plaquettes in a square lattice of qubits, and we show that deciding whether the ground state minimizes the energy of each local term individually is in the complexity class NP. That is, if the ground states has this property, this can be proven using a classical certificate which can be efficiently verified on a classical computer. Different to previous results on commuting Hamiltonians, our certificate proves the existence of such a state without giving instructions on how to prepare it.

Additional Information

© 2011 Rinton Press. Submitted on 13 May 2011 (v1), last revised 27 Sep 2011 (this version, v2). Received May 30, 2011. Revised July 29, 2011. Communicated by: R Jozsa & B Terhal. We acknowledge helpful conversations with Dorit Aharonov, Sergey Bravyi, Lior Eldar, Tobias Osborne, and Volkher Scholz. This work has been supported by the Gordon and Betty Moore Foundation through Caltech's Center for the Physics of Information, the NSF Grant No. PHY-0803371, and the ARO Grant No. W911NF-09-1-0442.

Additional details

Created:
August 19, 2023
Modified:
October 24, 2023