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@PHDTHESIS{Lagemann:953773,
      author       = {Lagemann, Hannes Alfred},
      othercontributors = {Michielsen, Kristel Francine and DiVincenzo, David},
      title        = {{R}eal-time simulations of transmon systems with
                      time-dependent {H}amiltonian models},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2023-02693},
      pages        = {1 Online-Ressource : Illustrationen, Diagramme},
      year         = {2023},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2023},
      abstract     = {In this thesis we study aspects of Hamiltonian models which
                      can affect the time evolution of transmon systems. We model
                      the time evolution of various systems as a unitary real-time
                      process by numerically solving the time-dependent
                      Schrödinger equation (TDSE). We denote the corresponding
                      computer models as non-ideal gate-based quantum computer
                      (NIGQC) models since transmons are usually used as transmon
                      qubits in superconducting prototype gate-based quantum
                      computers (PGQCs).We first review the ideal gate-based
                      quantum computer (IGQC) model and provide a distinction
                      between the IGQC, PGQCs and the NIGQC models we consider in
                      this thesis. Then, we derive the circuit Hamiltonians which
                      generate the dynamics of fixed-frequency and flux-tunable
                      transmons. Furthermore, we also provide clear and concise
                      derivations of effective Hamiltonians for both types of
                      transmons. We use the circuit and effective Hamiltonians we
                      derived to define two many-particle Hamiltonians, namely a
                      circuit and an associated effective Hamiltonian. The
                      interactions between the different subsystems are modelled
                      as dipole-dipole interactions. Next, we develop two
                      product-formula algorithms which solve the TDSE for the
                      many-particle Hamiltonians we defined. Afterwards, we use
                      these algorithms to investigate how various frequently
                      applied approximations (assumptions) affect the time
                      evolution of transmon systems modelled with the
                      many-particle effective Hamiltonian when a control pulse is
                      applied. Here we also compare the time evolutions generated
                      by the effective and circuit Hamiltonian. We find that the
                      approximations we investigate can substantially affect the
                      time evolution of the probability amplitudes we model. Next,
                      we investigate how susceptible gate-error quantifiers are to
                      approximations which make up the NIGQC model. We find that
                      the approximations (assumptions) we consider clearly affect
                      gate-error quantifiers like the diamond distance and the
                      average infidelity. Furthermore, we provide clear and
                      concise theoretical explanations for many of the findings we
                      present in this thesis.},
      cin          = {137620 / 130000},
      ddc          = {530},
      cid          = {$I:(DE-82)137620_20140620$ / $I:(DE-82)130000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2023-02693},
      url          = {https://publications.rwth-aachen.de/record/953773},
}