Abstract
We propose a novel type of minor-embedding (ME) in simulated-annealing-based Ising machines. The Ising machines can solve combinatorial optimization problems. Many combinatorial optimization problems are mapped to find the ground (lowest-energy) state of the logical Ising model. When connectivity is restricted on Ising machines, ME is required for mapping from the logical Ising model to a physical Ising model, which corresponds to a specific Ising machine. Herein we discuss the guiding principle of ME design to achieve a high performance in Ising machines. We derive the proposed ME based on a theoretical argument of statistical mechanics. The performance of the proposed ME is compared with two existing types of MEs for different benchmarking problems. Simulated annealing shows that the proposed ME outperforms existing MEs for all benchmarking problems, especially when the distribution of the degree in a logical Ising model has a large standard deviation. This study validates the guiding principle of using statistical mechanics for ME to realize fast and high-precision solvers for combinatorial optimization problems.
Highlights
IntroductionCombinatorial optimization problems find the optimal combination of decision variables to minimize or maximize the objective function under given constraints
Where P(sk) is the success probability and k is a label of the logical Ising models
We discussed the guiding principle of ME design to achieve a high performance in SA-based Ising machines from a viewpoint of statistical mechanics
Summary
Combinatorial optimization problems find the optimal combination of decision variables to minimize or maximize the objective function under given constraints. Solving a combinatorial optimization problem with a large number of decision variables is difficult because the number of solution candidates increases exponentially with the number of decision variables. Typical examples of combinatorial optimization problems found in textbooks include the satisfiability problem, the traveling salesman problem, and the knapsack problem. Common examples include the shiftplanning optimization, the logistics optimization, and the traffic route optimization. The development of efficient solvers for combinatorial optimization problems has attracted attention both in academia and in industry
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