Farhi, Edward and Kimmel, Shelby and Temme, Kristan (2016) A Quantum Version of Schöning's Algorithm Applied to Quantum 2-SAT. Quantum Information and Computation, 16 (13-14). pp. 1212-1217. ISSN 1533-7146. doi:10.48550/arXiv.1603.06985. https://resolver.caltech.edu/CaltechAUTHORS:20160622-144606809
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Abstract
We study a quantum algorithm that consists of a simple quantum Markov process, and we analyze its behavior on restricted versions of Quantum 2-SAT. We prove that the algorithm solves these decision problems with high probability for n qubits, L clauses, and promise gap c in time O(n2L2c-2). If the Hamiltonian is additionally polynomially gapped, our algorithm efficiently produces a state that has high overlap with the satisfying subspace. The Markov process we study is a quantum analogue of Schöning's probabilistic algorithm for k-SAT.
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| Additional Information: | © 2016 Rinton Press. We thank Sevag Gharibian for helpful discussions. EF was funded by NSF grant CCF-1218176 and ARO contract W911NF-12-1-0486. SK acknowledges support from the Department of Physics at MIT, iQuISE Igert grant contract number DGE-0801525, and the Department of Defense. KT acknowledges the support from the Erwin Schrödinger fellowship, Austrian Science Fund (FWF): J 3219-N16 and funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NFS Grants PHY-1125565 and PHY-0803371) with support of the Gordon and Betty Moore Foundation (GBMF-12500028). | ||||||||||||||||||
| Group: | Institute for Quantum Information and Matter | ||||||||||||||||||
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| Issue or Number: | 13-14 | ||||||||||||||||||
| DOI: | 10.48550/arXiv.1603.06985 | ||||||||||||||||||
| Record Number: | CaltechAUTHORS:20160622-144606809 | ||||||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160622-144606809 | ||||||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||||
| ID Code: | 68603 | ||||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||||
| Deposited By: | Jacquelyn O'Sullivan | ||||||||||||||||||
| Deposited On: | 23 Jun 2016 21:40 | ||||||||||||||||||
| Last Modified: | 02 Jun 2023 00:25 |
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