TY  - JOUR
AU  - Dobrynin, Dmitri
AU  - Renaudineau, Adrien
AU  - Hizzani, Mohammad
AU  - Strukov, Dmitri
AU  - Mohseni, Masoud
AU  - Strachan, John Paul
TI  - Energy landscapes of combinatorial optimization in Ising machines
JO  - Physical review / E
VL  - 110
IS  - 4
SN  - 2470-0045
M1  - FZJ-2025-01037
SP  - 045308
PY  - 2024
AB  - Physics-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.
LB  - PUB:(DE-HGF)16
C6  - 39562922
UR  - <Go to ISI:>//WOS:001340811600004
DO  - DOI:10.1103/PhysRevE.110.045308
UR  - https://juser.fz-juelich.de/record/1037899
ER  -