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001037899 1001_ $$0P:(DE-Juel1)188725$$aDobrynin, Dmitri$$b0$$ufzj
001037899 245__ $$aEnergy landscapes of combinatorial optimization in Ising machines
001037899 260__ $$c2024
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001037899 520__ $$aPhysics-based Ising machines (IM) have been developed as dedicated processors for solving hard combinatorial optimization problems with higher speed and better energy efficiency. Generally, such systems employ local search heuristics to traverse energy landscapes in searching for optimal solutions. Here, we quantify and address some of the major challenges met by IMs by extending energy-landscape geometry visualization tools known as disconnectivity graphs. Using efficient sampling methods, we visually capture landscapes of problems having diverse structure and hardness manifesting as energetic and entropic barriers for IMs. We investigate energy barriers, local minima, and configuration space clustering effects caused by locality reduction methods when embedding combinatorial problems to the Ising hardware. To this end, we sample disconnectivity graphs of PUBO energy landscapes and their different QUBO mappings accounting for both local minima and saddle regions. We demonstrate that QUBO energy-landscape properties lead to the subpar performance for quadratic IMs and suggest directions for their improvement.
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001037899 7001_ $$0P:(DE-Juel1)198908$$aRenaudineau, Adrien$$b1
001037899 7001_ $$0P:(DE-Juel1)190961$$aHizzani, Mohammad$$b2
001037899 7001_ $$0P:(DE-HGF)0$$aStrukov, Dmitri$$b3
001037899 7001_ $$0P:(DE-HGF)0$$aMohseni, Masoud$$b4
001037899 7001_ $$0P:(DE-Juel1)188145$$aStrachan, John Paul$$b5$$ufzj
001037899 773__ $$0PERI:(DE-600)2844562-4$$a10.1103/PhysRevE.110.045308$$gVol. 110, no. 4, p. 045308$$n4$$p045308$$tPhysical review / E$$v110$$x2470-0045$$y2024
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