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@INPROCEEDINGS{Mehta:1018614,
      author       = {Mehta, Vrinda and Jin, Fengping and Michielsen, Kristel and
                      De Raedt, Hans},
      title        = {{Q}uantum annealing: {S}ampling efficiency for 2-{SAT}
                      problems with multiple solutions},
      reportid     = {FZJ-2023-04929},
      year         = {2023},
      abstract     = {The performance of quantum annealing has been studied well
                      for solving optimization problems with a unique solution.
                      One of the most common metrics of performance is the scaling
                      of the success probability (the probability with which one
                      finds the solution to the problem) or related quantities
                      like time to solution (TTS) [1]. On the other hand, for
                      problems with multiple solutions, another aspect of
                      performance that becomes relevant is the fairness of quantum
                      annealing in sampling the various solutions of the problem,
                      i.e., whether or not it can sample all the solutions of the
                      problem with comparable probabilities [2]. Using both
                      simulations and the D-Wave $Advantage_system5.1$ (DWAdv)
                      quantum annealer we study the sampling efficiency of the
                      standard quantum annealing algorithm as well as the reverse
                      annealing protocol, as implemented by the D-Wave systems,
                      for solving 2-Satisfiability (SAT) problems with four
                      satisfying assignments. We find that while the numerically
                      obtained sampling probabilities using the standard quantum
                      annealing algorithm are not always fair, but in agreement
                      with the perturbation theory in the long annealing time
                      limit, the sampling probabilities of the four ground states
                      from DWAdv are comparable for a majority of the problems,
                      which indicates the presence of noise and temperature
                      effects in the latter. On the other hand, we find that the
                      sampling probabilities for the reverse annealing protocol
                      depend greatly on the choice of annealing times, reversal
                      distance, waiting time, and the initial state.},
      month         = {Aug},
      date          = {2023-08-28},
      organization  = {Nonequilibrium Physics – Current
                       Trends and Future Perspectives, Bad
                       Honnef (Germany), 28 Aug 2023 - 1 Sep
                       2023},
      subtyp        = {Other},
      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)24},
      doi          = {10.34734/FZJ-2023-04929},
      url          = {https://juser.fz-juelich.de/record/1018614},
}