Schuch, Norbert (2011) Complexity of commuting Hamiltonians on a square lattice of qubits. Quantum Information and Computation, 11 (11-12). pp. 901-912. ISSN 1533-7146. doi:10.48550/arXiv.arXiv:1105.2843. https://resolver.caltech.edu/CaltechAUTHORS:20111031-112554680
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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.
| Item Type: | Article | |||||||||
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| 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. | |||||||||
| Group: | Institute for Quantum Information and Matter | |||||||||
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| Subject Keywords: | Quantum complexity, Hamiltonian complexity, commuting Hamiltonians | |||||||||
| Issue or Number: | 11-12 | |||||||||
| DOI: | 10.48550/arXiv.arXiv:1105.2843 | |||||||||
| Record Number: | CaltechAUTHORS:20111031-112554680 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20111031-112554680 | |||||||||
| Official Citation: | Complexity of commuting Hamiltonians on a square lattice of qubits (pp0901-0912) Norbert Schuch | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 27523 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 31 Oct 2011 20:17 | |||||||||
| Last Modified: | 02 Jun 2023 01:32 |
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