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@MASTERSTHESIS{Hobl:276310,
      author       = {Hobl, Lukas},
      title        = {{S}imulating on the {D}-{W}ave {T}wo and emulating its
                      behavior on an ordinary computer},
      school       = {RWTH Aachen},
      type         = {MS},
      reportid     = {FZJ-2015-06771},
      pages        = {64 p.},
      year         = {2015},
      note         = {RWTH Aachen, Masterarbeit, 2015},
      abstract     = {This work presents the results of random spanning tree and
                      2-SAT problems, which weresolved using a D-Wave Two
                      processor.Firstly, the results for random spanning tree
                      problems, translated to Ising spin problemsare discussed.
                      The results suggest that the Z2-symmetry of the Ising spin
                      systemimplemented on the D-Wave Two processor is severely
                      broken. It is furthermore shown,that isolated regions of
                      qubits on the D-Wave Two processor behave statistically
                      independent.A date and time dependency of the solution
                      frequency is observed as the solutionfrequency of the same
                      problem on different days differs significantly with respect
                      to thestatistical errors.When starting to operate on a new
                      D-Wave processor, the random spanning tree problemspresented
                      in this work can be used as good test cases that allow
                      obtaining basicinformation on the processor’s
                      characteristics. The results of the random spanning
                      treeproblem also suggest that, in order to get statistically
                      reproducible results, computationson the D-Wave Two
                      processor need to be performed over long time periods and in
                      differentregions of the processor.Secondly, the solving
                      frequencies for 2-SAT problems with very small minimum
                      gapssolved on the D-Wave Two processor are compared to those
                      obtained via emulation i.e.simulation of the actual physical
                      behavior of the D-Wave Two quantum processor on aclassical
                      computer. A comparison of the solving frequencies shows,
                      that 2-SAT problemswith minimum gaps larger than the
                      operating temperature of the D-Wave Two processorare solved
                      by quantum annealing. For problems with minimum gaps
                      significantly smallerthan the operating temperature of the
                      D-Wave Two processor, the results suggest thatfinding a
                      solution is assisted by thermal effects. For problems with
                      minimum gaps close tothe operating temperature of the D-Wave
                      Two processor, a transition between the quantumannealing
                      process and the thermally assisted process can be assumed.In
                      order to gain a more detailed insight into the behavior of
                      the D-Wave Two processor,further studies of the 2-SAT
                      problems are planned. An investigation of additionalproblems
                      in the area of transition is expected to deliver a better
                      understanding of the prevailingprocesses. It should also be
                      of interest to investigate at what point a problem with
                      asmaller minimum gap than the processor’s operating
                      temperature would lead to a decreaserather than an increase
                      of the solution frequency. A decrease of the solution
                      frequency isexpected since the energy barriers between
                      states are so small that the likelihood of thermaloccupation
                      of exited states increases and also that calibration errors
                      of the D-WaveTwo processor become more dominant.},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)19},
      url          = {https://juser.fz-juelich.de/record/276310},
}