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@INPROCEEDINGS{Hizzani:1021223,
      author       = {Hizzani, Mohammad and Dobrynin, Dmitri and Van Vaerenbergh,
                      Thomas and Hutchinson, George and Strukov, Dmitri and
                      Strachan, John Paul},
      title        = {{M}apping {NP}-{C}omplete {P}roblems to {P}hysics-{B}ased
                      {QUBO} {S}olvers: {Q}uantitative {C}omparison and
                      {U}nderstanding},
      school       = {RWTH Aachen},
      reportid     = {FZJ-2024-00664},
      year         = {2023},
      abstract     = {NP-complete problems like 3-SAT can be mapped and solved by
                      emerging physics-based hardware such as Ising systems,
                      quantum annealers, or Hopfield neural networks. Such systems
                      natively handle quadratic unconstrained binary optimization
                      (QUBO) problems, while higher order and constrained problem
                      classes can be transformed into these simpler QUBO
                      formulations. However, there are often multiple possible
                      mappings for such transformations, with substantial
                      performance differences. Here, we compared several different
                      mappings from 3-SAT to a QUBO solver and quantified the
                      differences in resources required (additional auxiliary
                      variables) and final time-to-solution. Notably, while the
                      global minimum of the 3-SAT problem matches the global
                      minimum of the QUBO problem, we find stark differences in
                      other portions of the landscape in terms of gradient
                      directions. We attempt to explain the observed differences
                      between the mappings utilizing a simplified under-sampling
                      metric and showed good predictive capability. Our chosen
                      platform was a Hopfield neural network, with different
                      annealing techniques and neuron update rules compared.},
      month         = {Oct},
      date          = {2023-10-25},
      organization  = {International conference on
                       neuromorphic, natural and physical
                       computing, Hannover (Germany), 25 Oct
                       2023 - 27 Oct 2023},
      subtyp        = {Other},
      cin          = {PGI-14},
      cid          = {I:(DE-Juel1)PGI-14-20210412},
      pnm          = {5234 - Emerging NC Architectures (POF4-523) / 5312 -
                      Devices and Applications (POF4-531) / BMBF 16ME0398K -
                      Verbundprojekt: Neuro-inspirierte Technologien der
                      künstlichen Intelligenz für die Elektronik der Zukunft -
                      NEUROTEC II - (BMBF-16ME0398K)},
      pid          = {G:(DE-HGF)POF4-5234 / G:(DE-HGF)POF4-5312 /
                      G:(DE-82)BMBF-16ME0398K},
      typ          = {PUB:(DE-HGF)24},
      doi          = {10.34734/FZJ-2024-00664},
      url          = {https://juser.fz-juelich.de/record/1021223},
}