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@PHDTHESIS{Willsch:886007,
      author       = {Willsch, Madita},
      title        = {{S}tudy of quantum annealing by simulating the time
                      evolution of flux qubits},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      publisher    = {RWTH Aachen University},
      reportid     = {FZJ-2020-04228},
      pages        = {VIII, 163 pages},
      year         = {2020},
      note         = {DOI: 10.18154/RWTH-2020-08026; Dissertation, RWTH Aachen
                      University, 2020},
      abstract     = {In this thesis, we study the operation of existing quantum
                      annealers by simulating the real-time dynamics of two
                      coupled flux qubits based on SQUIDs (superconducting quantum
                      interference devices) during quantum annealing processes. We
                      investigate two aspects. First, we study the influence of
                      the higher energy levels which are neglected when deriving
                      the qubit Hamiltonian from the superconducting circuit model
                      including the tunable coupler. Second, we investigate the
                      influence of an environment on the qubit system during
                      quantum annealing. For the latter, we examine two different
                      models for the environment, a generic spin bath and
                      non-interacting two-level systems. For simulating the
                      dynamics, we use the Suzuki-Trotter product-formula
                      algorithm to solve the time-dependent Schrödinger equation
                      numerically. We find that the higher energy levels as well
                      as the presence of the tunable coupler have little influence
                      on the performance of the quantum annealing process for most
                      of the investigated problem instances, suggesting that the
                      two-level approximation works very well. However, we find
                      that for a particular class of instances, the results of the
                      SQUID model and the qubit model show certain deviations.
                      Additionally, we perform experiments on the D-Wave 2000Q
                      quantum annealer. Our study of the two models for the
                      environment suggests that the model of non-interacting
                      two-level systems is better suited to describe the data
                      obtained from the real device than the generic spin bath
                      model.},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / PhD no Grant - Doktorand ohne besondere
                      Förderung (PHD-NO-GRANT-20170405)},
      pid          = {G:(DE-HGF)POF3-511 / G:(DE-Juel1)PHD-NO-GRANT-20170405},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2020-08026},
      url          = {https://juser.fz-juelich.de/record/886007},
}