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@ARTICLE{Neuhaus:14076,
      author       = {Neuhaus, T. and Peschina, M. and Michielsen, K. and De
                      Raedt, H.},
      title        = {{C}lassical and quantum annealing in the median of
                      three-satisfiability},
      journal      = {Physical review / A},
      volume       = {83},
      number       = {1},
      issn         = {1050-2947},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {PreJuSER-14076},
      pages        = {012309},
      year         = {2011},
      note         = {T.N. thanks the Theory Department at Bielefeld University
                      for extended hospitality. Calculations were performed on the
                      JUMP and JUROPA supercomputers at JSC and on the NICOLE
                      workstation cluster of NIC (VSR Grant No. JJSC02). This work
                      is partially supported by NCF, the Netherlands.},
      abstract     = {We determine the classical and quantum complexities of a
                      specific ensemble of three-satisfiability problems with a
                      unique satisfying assignment for up to N = 100 and 80
                      variables, respectively. In the classical limit, we employ
                      generalized ensemble techniques and measure the time that a
                      Markovian Monte Carlo process spends in searching classical
                      ground states. In the quantum limit, we determine the
                      maximum finite correlation length along a quantum adiabatic
                      trajectory determined by the linear sweep of the adiabatic
                      control parameter in the Hamiltonian composed of the problem
                      Hamiltonian and the constant transverse field Hamiltonian.
                      In the median of our ensemble, both complexities diverge
                      exponentially with the number of variables. Hence, standard,
                      conventional adiabatic quantum computation fails to reduce
                      the computational complexity to polynomial. Moreover, the
                      growth-rate constant in the quantum limit is 3.8 times as
                      large as the one in the classical limit, making classical
                      fluctuations more beneficial than quantum fluctuations in
                      ground-state searches.},
      keywords     = {J (WoSType)},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {Scientific Computing (FUEK411) / 411 - Computational
                      Science and Mathematical Methods (POF2-411)},
      pid          = {G:(DE-Juel1)FUEK411 / G:(DE-HGF)POF2-411},
      shelfmark    = {Optics / Physics, Atomic, Molecular $\&$ Chemical},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000286738100007},
      doi          = {10.1103/PhysRevA.83.012309},
      url          = {https://juser.fz-juelich.de/record/14076},
}