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@PHDTHESIS{Jattana:1010673,
      author       = {Jattana, Manpreet Singh},
      title        = {{A}pplications of variational methods for quantum
                      computers},
      volume       = {53},
      school       = {RWTH Aachen},
      type         = {Dissertation},
      address      = {Jülich},
      publisher    = {Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag},
      reportid     = {FZJ-2023-03182},
      isbn         = {978-3-95806-700-4},
      series       = {Schriften des Forschungszentrums Jülich IAS Series},
      pages        = {vii, 160},
      year         = {2023},
      note         = {Dissertation, RWTH Aachen, 2022},
      abstract     = {The primary subject of this dissertation is the analysis
                      and improvement of variational methods that combine the use
                      of classical and gate based quantum computers. The secondary
                      subject is the development of matrix based error mitigation
                      and benchmarking protocols fornoisy quantum computers.
                      Variational methods run on quantum computer emulators are
                      used to find the ground state energies of the Heisenberg and
                      Hubbard models and selected molecules in chemistry. An
                      algorithm is developed and deployed to automate the creation
                      of variational circuits. The theory and overview of
                      variational methods and gradient based optimisation
                      algorithms are presented. We learn that while variational
                      methods make it possible to use current generation quantum
                      computers, guarantees of always finding the ground state
                      energy are elusive.We introduce noise in our emulations and
                      adapt the optimisation algorithms to withstand it. We
                      observe the emergence of local minima and barren plateaus
                      which hinder variational methods from finding the ground
                      state energies. It is discerned that clever choices of
                      initial states and parameters are necessary ingredients for
                      success. We develop the technique of quasi-dynamical
                      evolution inspired by quantum annealing. It overcomes the
                      limitations of standard variational algorithms by
                      systematically improving the ground state energy estimate.
                      Our tests show that the heuristic improves the energy
                      estimate even in facile settings. We introduce seven
                      criteria for ideal error mitigation protocols. A new
                      protocol is developedon its basis. Our tests on IBM Q
                      quantum computers show noticeable error mitigation.The
                      matrix generated during the execution of the protocol helps
                      detect and visualise errorsand biases. We invent and use
                      small depth quantum circuits for benchmarking
                      quantumcomputers.},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5111},
      typ          = {PUB:(DE-HGF)3 / PUB:(DE-HGF)11},
      urn          = {urn:nbn:de:0001-20231004085351526-3932686-7},
      doi          = {10.34734/FZJ-2023-03182},
      url          = {https://juser.fz-juelich.de/record/1010673},
}