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001021223 0247_ $$2datacite_doi$$a10.34734/FZJ-2024-00664
001021223 037__ $$aFZJ-2024-00664
001021223 041__ $$aEnglish
001021223 1001_ $$0P:(DE-Juel1)190961$$aHizzani, Mohammad$$b0$$eCorresponding author
001021223 1112_ $$aInternational conference on neuromorphic, natural and physical computing$$cHannover$$d2023-10-25 - 2023-10-27$$gNNPC2023$$wGermany
001021223 245__ $$aMapping NP-Complete Problems to Physics-Based QUBO Solvers: Quantitative Comparison and Understanding
001021223 260__ $$c2023
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001021223 502__ $$cRWTH Aachen
001021223 520__ $$aNP-complete problems like 3-SAT can be mapped and solved by emerging physics-based hardware such as Ising systems, quantum annealers, or Hopfield neural networks. Such systems natively handle quadratic unconstrained binary optimization (QUBO) problems, while higher order and constrained problem classes can be transformed into these simpler QUBO formulations.  However, there are often multiple possible mappings for such transformations, with substantial performance differences.  Here, we compared several different mappings from 3-SAT to a QUBO solver and quantified the differences in resources required (additional auxiliary variables) and final time-to-solution. Notably, while the global minimum of the 3-SAT problem matches the global minimum of the QUBO problem, we find stark differences in other portions of the landscape in terms of gradient directions. We attempt to explain the observed differences between the mappings utilizing a simplified under-sampling metric and showed good predictive capability. Our chosen platform was a Hopfield neural network, with different annealing techniques and neuron update rules compared.
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001021223 7001_ $$0P:(DE-Juel1)188725$$aDobrynin, Dmitri$$b1
001021223 7001_ $$0P:(DE-HGF)0$$aVan Vaerenbergh, Thomas$$b2
001021223 7001_ $$0P:(DE-HGF)0$$aHutchinson, George$$b3
001021223 7001_ $$0P:(DE-HGF)0$$aStrukov, Dmitri$$b4
001021223 7001_ $$0P:(DE-Juel1)188145$$aStrachan, John Paul$$b5
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001021223 9141_ $$y2024
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