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@ARTICLE{Mehta:910533,
      author       = {Mehta, Vrinda and Jin, Fengping and De Raedt, Hans and
                      Michielsen, Kristel},
      title        = {{Q}uantum annealing for hard 2-satisfiability problems:
                      {D}istribution and scaling of minimum energy gap and success
                      probability},
      journal      = {Physical review / A},
      volume       = {105},
      number       = {6},
      issn         = {2469-9926},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2022-03915},
      pages        = {062406},
      year         = {2022},
      abstract     = {In recent years, quantum annealing has gained the status of
                      being a promising candidate for solving various optimization
                      problems. Using a set of hard 2-satisfiability (2-SAT)
                      problems, consisting of problems of up to 18 variables, we
                      analyze the scaling complexity of the quantum annealing
                      algorithm and study the distributions of the minimum energy
                      gap and the success probability. We extend the analysis of
                      the standard quantum annealing Hamiltonian by introducing an
                      additional term, the trigger Hamiltonian, which can be of
                      two types: ferromagnetic and antiferromagnetic. We use these
                      trigger Hamiltonians to study their influence on the success
                      probability for solving the selected 2-SAT problems. We find
                      that although the scaling of the runtime is exponential for
                      the standard and modified quantum annealing Hamiltonians,
                      the scaling constant in the case of adding the trigger
                      Hamiltonians can be significantly smaller. Furthermore,
                      certain choices for the trigger Hamiltonian and annealing
                      times can result in a better scaling than that for simulated
                      annealing. Finally, we also use the quantum annealers of
                      D-Wave Systems Inc. to study their performance in solving
                      the 2-SAT problems and compare it with the simulation
                      results.},
      cin          = {JSC},
      ddc          = {530},
      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)16},
      UT           = {WOS:000809499800011},
      doi          = {10.1103/PhysRevA.105.062406},
      url          = {https://juser.fz-juelich.de/record/910533},
}