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A FullyConnected Ising Model Embedding Method and Its Evaluation for CMOS Annealing Machines
Daisuke OKU Kotaro TERADA Masato HAYASHI Masanao YAMAOKA Shu TANAKA Nozomu TOGAWA
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E102D
No.9
pp.16961706 Publication Date: 2019/09/01
Online ISSN: 17451361
DOI: 10.1587/transinf.2018EDP7411
Type of Manuscript: PAPER Category: Fundamentals of Information Systems Keyword: CMOS annealing, Ising model, Ising computing, graph embedding, combinatorial optimization,
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Summary:
Combinatorial optimization problems with a large solution space are difficult to solve just using von Neumann computers. Ising machines or annealing machines have been developed to tackle these problems as a promising Nonvon Neumann computer. In order to use these annealing machines, every combinatorial optimization problem is mapped onto the physical Ising model, which consists of spins, interactions between them, and their external magnetic fields. Then the annealing machines operate so as to search the ground state of the physical Ising model, which corresponds to the optimal solution of the original combinatorial optimization problem. A combinatorial optimization problem can be firstly described by an ideal fullyconnected Ising model but it is very hard to embed it onto the physical Ising model topology of a particular annealing machine, which causes one of the largest issues in annealing machines. In this paper, we propose a fullyconnected Ising model embedding method targeting for CMOS annealing machine. The key idea is that the proposed method replicates every logical spin in a fullyconnected Ising model and embeds each logical spin onto the physical spins with the same chain length. Experimental results through an actual combinatorial problem show that the proposed method obtains spin embeddings superior to the conventional de facto standard method, in terms of the embedding time and the probability of obtaining a feasible solution.

