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@PHDTHESIS{Mehta:1026467,
      author       = {Mehta, Vrinda},
      title        = {{Q}uantum annealing and its variants: {A}pplication to
                      quadratic unconstrained binary optimization},
      volume       = {59},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Jülich},
      publisher    = {Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag},
      reportid     = {FZJ-2024-03411},
      isbn         = {978-3-95806-755-4},
      series       = {Schriften des Forschungszentrums Jülich IAS Series},
      pages        = {iii, 152},
      year         = {2024},
      note         = {Dissertation, RWTH Aachen University, 2023},
      abstract     = {In this thesis, we study the performance of the numerical
                      implementation of quantum annealing, as well as of physical
                      quantum annealing systems from D-Wave Quantum Systems Inc.,
                      for solving 2-Satisfiability (2-SAT) and other quadratic
                      unconstrained binaryoptimization (QUBO) problems. For
                      gauging the suitability of quantum annealing for solving
                      these problems, we use three main metrics: the probability
                      of the algorithm to solve the problem, its ability to find
                      all the solutions to the problem if the problem has more
                      than one solution, and the scaling of the time to solution
                      as a function of the problem size. In doing so, we compare
                      the performance of the numerically simulated ideal quantum
                      annealing with its actual physical realization. We find that
                      the ideal, standard quantum annealing algorithm can solve
                      the sets of 2-SAT problems considered in this work, even if
                      with a low success probability for hard problems, and can
                      sample the degenerate ground states of the 2-SAT problems
                      with multiple satisfying assignments in accordance with
                      perturbation theory. However, in the long annealing time
                      limit, the ideal standard annealing algorithm leads to a
                      scaling of the time to solution that is worse compared to
                      even the simple enumeration of all the possible states. On
                      the other hand, we find noise and temperature effects to
                      play an active role in the evolution of the state of the
                      system on the D-Wave quantum annealers. These systems can
                      solve a majority of the studied problems with a relatively
                      large success probability, and the scaling of the time to
                      solution, though still growing exponentially in the system
                      size, is significantly improved. Next, by means of
                      simulations, we introduce two modifications in the standard
                      quantum annealing algorithm, and gauge the performance of
                      the modified algorithms. These modifications are the
                      addition of a trigger Hamiltonian to the standard quantum
                      annealing Hamiltonian, or a change in the initial
                      Hamiltonian of the annealing Hamiltonian. We choose the
                      trigger Hamiltonian to have either ferromagnetic or
                      antiferromagnetic transverse couplings, while the additional
                      higher-order couplings added to the typically chosen initial
                      Hamiltonian are ferromagnetic. We find that these
                      modifications can lead to significant improvements in the
                      performance of the annealing algorithm, even if the scaling
                      behavior is still exponential.},
      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:0001-20241209125135062-9549579-4},
      doi          = {10.34734/FZJ-2024-03411},
      url          = {https://juser.fz-juelich.de/record/1026467},
}