TY - JOUR
T1 - Statistical-mechanical analysis of compressed sensing for hamiltonian estimation of ising spin glass
AU - Takahashi, Chako
AU - Ohzeki, Masayuki
AU - Okada, Shuntaro
AU - Terabe, Masayoshi
AU - Taguchi, Shinichiro
AU - Tanaka, Kazuyuki
N1 - Funding Information:
Acknowledgments The authors would like to thank Shu Tanaka, Shun Kataoka, and Yuya Seki for insightful comments and suggestions. One of the authors (CT) was partially supported by Grants-in-Aid for JSPS Fellows from the Japan Society for the Promotion of Science (No. JP17J03081) and JST-CREST for Japan Science and Technology Agency (No. JPMJCR1402). One of the authors (MO) was partially supported by Inamori Foundation, KAKENHI Nos. 15H03699, 16H04382, and 16K13849, the ImPACT Program of the Council for Science, Technology and Innovation (Cabinet Office, Government of Japan), and JST-START.
Publisher Copyright:
©2018 The Physical Society of Japan.
PY - 2018
Y1 - 2018
N2 - Several powerful machines, such as the D-Wave 2000Q, dedicated to solving combinatorial optimization problems through the Ising-model formulation have been developed. To input problems into the machines, the unknown parameters of the Ising model must be determined, and this is a nontrivial task. It may be beneficial to construct a method to estimate the parameters of the Ising model from several pairs of values of the energy and spin configurations. In the present paper, we propose a simple method employing L1-norm minimization, which is based on the concept of compressed sensing. Moreover, we analyze the typical performance of our proposed method of Hamiltonian estimation by using the replica method. We also compare our analytical results through several numerical experiments using the alternating direction method of multipliers.
AB - Several powerful machines, such as the D-Wave 2000Q, dedicated to solving combinatorial optimization problems through the Ising-model formulation have been developed. To input problems into the machines, the unknown parameters of the Ising model must be determined, and this is a nontrivial task. It may be beneficial to construct a method to estimate the parameters of the Ising model from several pairs of values of the energy and spin configurations. In the present paper, we propose a simple method employing L1-norm minimization, which is based on the concept of compressed sensing. Moreover, we analyze the typical performance of our proposed method of Hamiltonian estimation by using the replica method. We also compare our analytical results through several numerical experiments using the alternating direction method of multipliers.
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U2 - 10.7566/JPSJ.87.074001
DO - 10.7566/JPSJ.87.074001
M3 - Article
AN - SCOPUS:85048952730
SN - 0031-9015
VL - 87
JO - Journal of the Physical Society of Japan
JF - Journal of the Physical Society of Japan
IS - 7
M1 - 074001
ER -