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A Quantum Version of Schöning's Algorithm Applied to Quantum 2-SAT

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.

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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
Funding AgencyGrant Number
Gordon and Betty Moore FoundationGBMF-2644
Massachusetts Institute of Technology (MIT)UNSPECIFIED
NSF Graduate Research FellowshipDGE-0801525
Erwin Schrödinger FellowshipUNSPECIFIED
FWF Der WissenschaftsfondsUNSPECIFIED
Issue or Number:13-14
Record Number:CaltechAUTHORS:20160622-144606809
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68603
Deposited By: Jacquelyn O'Sullivan
Deposited On:23 Jun 2016 21:40
Last Modified:02 Jun 2023 00:25

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