dc.contributor.author | Temme, Kristan | |
dc.date.accessioned | 2014-09-12T15:10:25Z | |
dc.date.available | 2014-09-12T15:10:25Z | |
dc.date.issued | 2014-08 | |
dc.date.submitted | 2014-05 | |
dc.identifier.issn | 1050-2947 | |
dc.identifier.issn | 1094-1622 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/89459 | |
dc.description.abstract | We show that it is impossible to obtain a quantum speedup for a faulty Hamiltonian oracle. The effect of dephasing noise to this continuous-time oracle model has first been investigated by Shenvi, Brown, and Whaley [Phys. Rev. A 68, 052313 (2003).]. The authors consider a faulty oracle described by a continuous-time master equation that acts as dephasing noise in the basis determined by the marked item. The analysis focuses on the implementation with a particular driving Hamiltonian. A universal lower bound for this oracle model, which rules out a better performance with a different driving Hamiltonian, has so far been lacking. Here, we derive an adversary-type lower bound which shows that the evolution time T has to be at least in the order of N, i.e., the size of the search space, when the error rate of the oracle is constant. This means that quadratic quantum speedup vanishes and the runtime assumes again the classical scaling. For the standard quantum oracle model this result was first proven by Regev and Schiff [in Automata, Languages and Programming, Lecture Notes in Computer Science Vol. 5125 (Springer, Berlin, 2008), pp. 773–781]. Here, we extend this result to the continuous-time setting. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (Physics Frontiers Center, Institute for Quantum Information and Matter) | en_US |
dc.description.sponsorship | Gordon and Betty Moore Foundation (Grant No. PHY-0803371) | en_US |
dc.description.sponsorship | Gordon and Betty Moore Foundation (Grant No. PHY-1125565) | en_US |
dc.description.sponsorship | Austrian Science Fund (Erwin Schrodinger Fellowship, J3219-N16) | en_US |
dc.publisher | American Physical Society | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1103/PhysRevA.90.022310 | en_US |
dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
dc.source | American Physical Society | en_US |
dc.title | Runtime of unstructured search with a faulty Hamiltonian oracle | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Temme, Kristan. “Runtime of Unstructured Search with a Faulty Hamiltonian Oracle.” Phys. Rev. A 90, no. 2 (August 2014). © 2014 American Physical Society. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Center for Theoretical Physics | en_US |
dc.contributor.mitauthor | Temme, Kristan | en_US |
dc.relation.journal | Physical Review A | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2014-08-11T22:00:04Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | American Physical Society | |
dspace.orderedauthors | Temme, Kristan | en_US |
mit.license | PUBLISHER_POLICY | en_US |
mit.metadata.status | Complete | |