TY - JOUR

T1 - A fully-connected ising model embedding method and its evaluation for CMOS annealing machines

AU - Oku, Daisuke

AU - Terada, Kotaro

AU - Hayashi, Masato

AU - Yamaoka, Masanao

AU - Tanaka, Shu

AU - Togawa, Nozomu

N1 - Funding Information:
This paper is based on the results obtained from a project commissioned by the New Energy and Industrial Technology Development Organization (NEDO). One of the authors (S. T.) was supported by JST, PRESTO Grant Number JPMJPR1665, Japan and JSPS KAKENHI Grant Numbers 15K17720, 15H03699.
Publisher Copyright:
© 2019 The Institute of Electronics, Information and Communication Engineers.

PY - 2019

Y1 - 2019

N2 - 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 Non-von 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 fully-connected 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 fully-connected Ising model embedding method targeting for CMOS annealing machine. The key idea is that the proposed method replicates every logical spin in a fully-connected 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.

AB - 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 Non-von 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 fully-connected 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 fully-connected Ising model embedding method targeting for CMOS annealing machine. The key idea is that the proposed method replicates every logical spin in a fully-connected 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.

KW - CMOS annealing

KW - Combinatorial optimization

KW - Graph embedding

KW - Ising computing

KW - Ising model

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U2 - 10.1587/transinf.2018EDP7411

DO - 10.1587/transinf.2018EDP7411

M3 - Article

AN - SCOPUS:85071909395

SN - 0916-8532

VL - E102D

SP - 1696

EP - 1706

JO - IEICE Transactions on Information and Systems

JF - IEICE Transactions on Information and Systems

IS - 9

ER -