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Open Quantum Systems: Effects in Interferometry, Quantum Computation, and Adiabatic Evolution
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Kemiska sektionen, Fysikalisk-kemiska institutionen, Avdelningen för kvantkemi.
2005 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

The effects of open system evolution on single particle interferometry, quantum computation, and the adiabatic approximation are investigated.

Single particle interferometry: Three concepts concerning completely positive maps (CPMs) and trace preserving CPMs (channels), named subspace preserving (SP) CPMs, subspace local channels, and gluing of CPMs, are introduced. SP channels preserve probability weights on given orthogonal sum decompositions of the Hilbert space of a quantum system. Subspace locality determines what channels act locally with respect to such decompositions. Gluings are the possible total channels obtainable if two evolution devices, characterized by channels, act jointly on a superposition of a particle in their inputs. It is shown that gluings are not uniquely determined by the two channels. We determine all possible interference patterns in single particle interferometry for given channels acting in the interferometer paths. It is shown that the standard interferometric setup cannot distinguish all gluings, but a generalized setup can.

Quantum computing: The robustness of local and global adiabatic quantum search subject to decoherence in the instantaneous eigenbasis of the search Hamiltonian, is examined. In both the global and local search case the asymptotic time-complexity of the ideal closed case is preserved, as long as the Hamiltonian dynamics is present. In the case of pure decoherence, where the environment monitors the search Hamiltonian, it is shown that the local adiabatic quantum search performs as the classical search with scaling N, and that the global search scales like N3/2 , where N is the list length. We consider success probabilities p<1 and prove bounds on the run-time with the same scaling as in the conditions for the p → 1 limit.

Adiabatic evolution: We generalize the adiabatic approximation to the case of open quantum systems in the joint limit of slow change and weak open system disturbances.

Ort, förlag, år, upplaga, sidor
Uppsala: Acta Universitatis Upsaliensis , 2005. , s. vii + 52
Serie
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 77
Nyckelord [en]
Physics, Open Systems, Completely Positive Maps, Channels, Decoherence, Quantum Information, Quantum Computing, Adiabatic Approximation, Quantum Search, Time-Complexity
Nyckelord [sv]
Fysik
Nationell ämneskategori
Fysik
Identifikatorer
URN: urn:nbn:se:uu:diva-5893ISBN: 91-554-6307-X (tryckt)OAI: oai:DiVA.org:uu-5893DiVA, id: diva2:166767
Disputation
2005-09-22, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 10:15
Opponent
Handledare
Tillgänglig från: 2005-09-01 Skapad: 2005-09-01Bibliografiskt granskad
Delarbeten
1. Subspace preservation, subspace locality, and gluing of completely positive maps
Öppna denna publikation i ny flik eller fönster >>Subspace preservation, subspace locality, and gluing of completely positive maps
2004 Ingår i: Annals of Physics, ISSN 0003-4916, Vol. 313, s. 326-367Artikel i tidskrift (Refereegranskat) Published
Identifikatorer
urn:nbn:se:uu:diva-93318 (URN)
Tillgänglig från: 2005-09-01 Skapad: 2005-09-01Bibliografiskt granskad
2. Operations and single-particle interferometry
Öppna denna publikation i ny flik eller fönster >>Operations and single-particle interferometry
2004 Ingår i: Physical Review A, ISSN 1050-2947, Vol. 70, s. 012103-Artikel i tidskrift (Refereegranskat) Published
Identifikatorer
urn:nbn:se:uu:diva-93319 (URN)
Tillgänglig från: 2005-09-01 Skapad: 2005-09-01Bibliografiskt granskad
3. Robustness of the adiabatic quantum search
Öppna denna publikation i ny flik eller fönster >>Robustness of the adiabatic quantum search
2005 (Engelska)Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 71, nr 6, s. 060312(R)-Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

The robustness of the local adiabatic quantum search to decoherence in the instantaneous eigenbasis of the search Hamiltonian is examined. We demonstrate that the asymptotic time complexity of the ideal closed case is preserved, as long as the Hamiltonian dynamics is present. In the special case of pure decoherence where the environment monitors the search Hamiltonian, it is shown that the local adiabatic quantum search performs as the classical search.

Nyckelord
Quantum computation, adiabatic quantum evolution, search algorithm
Nationell ämneskategori
Fysik
Forskningsämne
Fysik
Identifikatorer
urn:nbn:se:uu:diva-93320 (URN)10.1103/PhysRevA.71.060312 (DOI)000230275200013 ()
Anmärkning
Also in Virtual Journal of Nanoscale Science and Technology, July 11 issue 2005 and Virtual Journal of Quantum Information, July issue 2005.Tillgänglig från: 2005-09-01 Skapad: 2005-09-01 Senast uppdaterad: 2017-12-14
4. Quantum adiabatic search with decoherence in the instantaneous energy eigenbasis
Öppna denna publikation i ny flik eller fönster >>Quantum adiabatic search with decoherence in the instantaneous energy eigenbasis
2005 (Engelska)Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 72, nr 4, s. 042317-Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

In Phys. Rev. A 71, 060312(R) (2005), the robustness of the local adiabatic quantum search to decoherence in the instantaneous eigenbasis of the search Hamiltonian was examined. We expand this analysis to include the case of the global adiabatic quantum search. As in the case of the local search the asymptotic time complexity for the global search is the same as for the ideal closed case, as long as the Hamiltonian dynamics is present. In the case of pure decoherence, where the environment monitors the search Hamiltonian, we find that the time complexity of the global quantum adiabatic search scales like N3∕2, where N is the list length. We moreover extend the analysis to include success probabilities p<1 and prove bounds on the run time with the same scaling as in the conditions for the p→1 limit. We supplement the analytical results by numerical simulations of the global and local search.

Nyckelord
Quantum computation, adiabatic approximation, search algorithm, open quantum systems
Nationell ämneskategori
Fysik
Forskningsämne
Fysik
Identifikatorer
urn:nbn:se:uu:diva-93321 (URN)10.1103/PhysRevA.72.042317 (DOI)000232931800051 ()
Anmärkning
Also in Virtual Journal of Nanoscale Science and Technology, October 31 issue 2005 and Virtual Journal of Quantum Information, November issue 2005. Tillgänglig från: 2005-09-01 Skapad: 2005-09-01 Senast uppdaterad: 2017-12-14
5. Adiabatic approximation for weakly open systems
Öppna denna publikation i ny flik eller fönster >>Adiabatic approximation for weakly open systems
2005 (Engelska)Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. A72, nr 022328, s. 022328-1-022328-13Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is “physically reasonable” as under wide conditions it leads to a completely positive evolution, if the original master equation can be written on a time-dependent Lindblad form. We demonstrate the approximation for a non-Abelian holonomic implementation of the Hadamard gate, disturbed by a decoherence process. We compare the resulting approximate evolution with numerical simulations of the exact equation.

Nyckelord
Adiabatic approximation, open quantum systems, quantum computation
Nationell ämneskategori
Fysik
Forskningsämne
Fysik
Identifikatorer
urn:nbn:se:uu:diva-93322 (URN)10.1103/PhysRevA.72.022328 (DOI)000231564200060 ()
Tillgänglig från: 2005-09-01 Skapad: 2005-09-01 Senast uppdaterad: 2017-12-14Bibliografiskt granskad

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