リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「<講義ノート>量子アニーリングやイジングマシンの基礎と応用」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

<講義ノート>量子アニーリングやイジングマシンの基礎と応用

田中, 宗 京都大学

2022.03

概要

本原稿では, 近年, 産学両面から注目されている新しい計算技術である量子アニーリングやイジングマシンの基礎と応用について紹介する. これらの計算技術は組合せ最適化問題(膨大な選択肢から, 制約条件を満たし, ベストな選択肢を探索する問題)に対する高効率解法として期待されている. これらの計算技術は物理学の概念を取り込んだアルゴリズムを基盤としており, 統計力学による理論構築や, ハードウェア開発, ソフトウェア開発, アプリケーション探索といった幅広い領域の研究開発が同時進行で進められている. 量子アニーリングやイジングマシン分野の研究は, 物理学と情報科学・情報工学の境界領域分野の研究に位置づけられ, これからますます幅広い分野の研究者・技術者の参入が必要不可欠である.

この論文で使われている画像

参考文献

[1] 梅谷俊治. しっかり学ぶ数理最適化 モデルからアルゴリズムまで. 講談社サイ

エンティフィク, 2020.

[2] Tadashi Kadowaki and Hidetoshi Nishimori. Quantum annealing in the

transverse Ising model. Phys. Rev. E, Vol. 58, pp. 5355–5363, Nov 1998.

[3] Tadashi Kadowaki. Study of optimization problems by quantum annealing. Ph.D. thesis, Department of Physics, Tokyo Institute of Technology,

1998.

[4] Scott Kirkpatrick, C Daniel Gelatt, and Mario P Vecchi. Optimization by

simulated annealing. science, Vol. 220, No. 4598, pp. 671–680, 1983.

[5] David S Johnson, Cecilia R Aragon, Lyle A McGeoch, and Catherine

《講義ノート》

物性研究・電子版 Vol. 10, No. 1, 101206(2022年3月号)

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

Schevon. Optimization by simulated annealing: An experimental evaluation; part i, graph partitioning. Operations research, Vol. 37, No. 6, pp.

865–892, 1989.

David S Johnson, Cecilia R Aragon, Lyle A McGeoch, and Catherine

Schevon. Optimization by simulated annealing: an experimental evaluation; part ii, graph coloring and number partitioning. Operations research,

Vol. 39, No. 3, pp. 378–406, 1991.

Stuart Geman and Donald Geman. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on

pattern analysis and machine intelligence, No. 6, pp. 721–741, 1984.

M. W. Johnson, M. H. S. Amin, S. Gildert, T. Lanting, F. Hamze, N. Dickson, R. Harris, A. J. Berkley, J. Johansson, P. Bunyk, and et al. Quantum

annealing with manufactured spins. Nature, Vol. 473, No. 7346, pp. 194–

198, 2011.

Satoshi Morita and Hidetoshi Nishimori. Convergence theorems for quantum annealing. Journal of Physics A: Mathematical and General, Vol. 39,

No. 45, p. 13903, 2006.

Arnab Das and Bikas K Chakrabarti. Quantum annealing and related

optimization methods, Vol. 679. Springer Science & Business Media, 2005.

Arnab Das and Bikas K Chakrabarti. Colloquium: Quantum annealing

and analog quantum computation. Reviews of Modern Physics, Vol. 80,

No. 3, p. 1061, 2008.

Shu Tanaka, Ryo Tamura, and Bikas K Chakrabarti. Quantum spin

glasses, annealing and computation. Cambridge University Press, 2017.

西森秀稔, 大関真之. 量子アニーリングの基礎. 共立出版, 2018.

Masanao Yamaoka, Chihiro Yoshimura, Masato Hayashi, Takuya

Okuyama, Hidetaka Aoki, and Hiroyuki Mizuno. A 20k-spin Ising chip to

solve combinatorial optimization problems with CMOS annealing. IEEE

Journal of Solid-State Circuits, Vol. 51, No. 1, pp. 303–309, 2016.

Takahiro Inagaki, Yoshitaka Haribara, Koji Igarashi, Tomohiro Sonobe,

Shuhei Tamate, Toshimori Honjo, Alireza Marandi, Peter L. McMahon, Takeshi Umeki, Koji Enbutsu, Osamu Tadanaga, Hirokazu Takenouchi, Kazuyuki Aihara, Ken-ichi Kawarabayashi, Kyo Inoue, Shoko Utsunomiya, and Hiroki Takesue. A coherent Ising machine for 2000-node

optimization problems. Science, Vol. 354, No. 6312, pp. 603–606, 2016.

Takuya Okuyama, Masato Hayashi, and Masanao Yamaoka. An Ising

computer based on simulated quantum annealing by path integral Monte

Carlo method. 2017 IEEE International Conference on Rebooting Computing, ICRC 2017 - Proceedings, Vol. 2017-Janua, pp. 1–6, 2017.

Chihiro Yoshimura, Masato Hayashi, Takuya Okuyama, and Masanao Ya-

《講義ノート》

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]

物性研究・電子版 Vol. 10, No. 1, 101206(2022年3月号)

maoka. Implementation and Evaluation of FPGA-based Annealing Processor for Ising Model by use of Resource Sharing. International Journal

of Networking and Computing, Vol. 7, No. 2, pp. 154–172, 2017.

Maliheh Aramon, Gili Rosenberg, Elisabetta Valiante, Toshiyuki

Miyazawa, Hirotaka Tamura, and Helmut G. Katzgraber. Physics-inspired

optimization for quadratic unconstrained problems using a digital annealer. Frontiers in Physics, Vol. 7, No. 48, pp. 1–14, 2019.

Hayato Goto, Kosuke Tatsumura, and Alexander R. Dixon. Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems. Science Advances, Vol. 5, No. 4, pp. 1–9, 2019.

Fixstars Amplify Annealing Engine: Fixstars Amplify. https://amplify.

fixstars.com.

M Maezawa, K Imafuku, M Hidaka, H Koike, and S Kawabata. Design

of quantum annealing machine for prime factoring. In 2017 16th International Superconductive Electronics Conference (ISEC), pp. 1–3. IEEE,

2017.

Masaaki Maezawa, Go Fujii, Mutsuo Hidaka, Kentaro Imafuku, Katsuya

Kikuchi, Hanpei Koike, Kazumasa Makise, Shuichi Nagasawa, Hiroshi

Nakagawa, Masahiro Ukibe, et al. Toward practical-scale quantum annealing machine for prime factoring. Journal of the Physical Society of

Japan, Vol. 88, No. 6, p. 061012, 2019.

Yuya Seki and Hidetoshi Nishimori. Quantum annealing with antiferromagnetic fluctuations. Physical Review E, Vol. 85, No. 5, p. 051112, 2012.

Yuya Seki and Hidetoshi Nishimori. Quantum annealing with antiferromagnetic transverse interactions for the hopfield model. Journal of Physics

A: Mathematical and Theoretical, Vol. 48, No. 33, p. 335301, 2015.

Yuki Susa, Johann F Jadebeck, and Hidetoshi Nishimori. Relation between quantum fluctuations and the performance enhancement of quantum annealing in a nonstoquastic hamiltonian. Physical Review A, Vol. 95,

No. 4, p. 042321, 2017.

Layla Hormozi, Ethan W Brown, Giuseppe Carleo, and Matthias Troyer.

Nonstoquastic Hamiltonians and quantum annealing of an Ising spin glass.

Physical review B, Vol. 95, No. 18, p. 184416, 2017.

Yuya Seki, Shu Tanaka, and Shiro Kawabata. Quantum phase transition

in fully connected quantum Wajnflasz–Pick model. Journal of the Physical

Society of Japan, Vol. 88, No. 5, p. 054006, 2019.

Neil G Dickson, MW Johnson, MH Amin, R Harris, F Altomare,

AJ Berkley, P Bunyk, J Cai, EM Chapple, P Chavez, et al. Thermally assisted quantum annealing of a 16-qubit problem. Nature communications,

Vol. 4, No. 1, pp. 1–6, 2013.

《講義ノート》

物性研究・電子版 Vol. 10, No. 1, 101206(2022年3月号)

[29] Andrew Lucas. Ising formulations of many np problems. Frontiers in

Physics, Vol. 2, p. 5, 2014.

[30] 組合せ最適化問題のイジング模型定式化. https://quantum.fixstars.com/

techresources/research/ising-model-formulation/.

[31] T-Wave. https://qard.is.tohoku.ac.jp/T-Wave/.

[32] Kotaro Tanahashi, Shinichi Takayanagi, Tomomitsu Motohashi, and Shu

Tanaka. Application of Ising machines and a software development for

Ising machines. Journal of the Physical Society of Japan, Vol. 88, No. 6,

p. 061010, 2019.

[33] Harry Markowitz. Portfolio selection. Journal of Finance, Vol. 7, pp.

77–91, 1952.

[34] 今野浩. 理財工学〈1〉―平均・分散モデルとその拡張. 日科技連出版社, 1995.

[35] Gili Rosenberg, Poya Haghnegahdar, Phil Goddard, Peter Carr, Kesheng

Wu, and Marcos L´

opez De Prado. Solving the optimal trading trajectory

problem using a quantum annealer. IEEE Journal of Selected Topics in

Signal Processing, Vol. 10, No. 6, pp. 1053–1060, 2016.

[36] Florian Neukart, Gabriele Compostella, Christian Seidel, David

Von Dollen, Sheir Yarkoni, and Bob Parney. Traffic flow optimization

using a quantum annealer. Frontiers in ICT, Vol. 4, p. 29, 2017.

[37] Masayuki Ohzeki, Akira Miki, Masamichi J Miyama, and Masayoshi Terabe. Control of automated guided vehicles without collision by quantum

annealer and digital devices. Frontiers in Computer Science, Vol. 1, p. 9,

2019.

[38] Kotaro Terada, Daisuke Oku, Sho Kanamaru, Shu Tanaka, Masato

Hayashi, Masanao Yamaoka, Masao Yanagisawa, and Nozomu Togawa.

An Ising model mapping to solve rectangle packing problem. In 2018

International Symposium on VLSI Design, Automation and Test (VLSIDAT), pp. 1–4, 2018.

[39] Sho Kanamaru, Daisuke Oku, Masashi Tawada, Shu Tanaka, Masato

Hayashi, Masanao Yamaoka, Masao Yanagisawa, and Nozomu Togawa.

Efficient Ising model mapping to solving slot placement problem. In 2019

IEEE International Conference on Consumer Electronics (ICCE), pp. 1–

6, 2019.

[40] Natsuhito Yoshimura, Masashi Tawada, Shu Tanaka, Junya Arai, Satoshi

Yagi, Hiroyuki Uchiyama, and Nozomu Togawa. Efficient Ising model

mapping for induced subgraph isomorphism problems using Ising machines. In 2019 IEEE 9th International Conference on Consumer Electronics (ICCE-Berlin), pp. 227–232, 2019.

[41] Yosuke Mukasa, Tomoya Wakaizumi, Shu Tanaka, and Nozomu Togawa.

Visiting-route recommendation in amusement parks and its evaluations by

《講義ノート》

[42]

[43]

[44]

[45]

[46]

[47]

[48]

[49]

[50]

[51]

[52]

物性研究・電子版 Vol. 10, No. 1, 101206(2022年3月号)

an Ising machine. In 2021 IEEE International Conference on Consumer

Electronics (ICCE), pp. 1–6, 2021.

Harmut Neven, Vasil S Denchev, Marshall Drew-Brook, Jiayong Zhang,

William G Macready, and Geordie Rose. Nips 2009 demonstration: Binary classification using hardware implementation of quantum annealing.

Quantum, pp. 1–17, 2009.

Daniel O’Malley, Velimir V Vesselinov, Boian S Alexandrov, and Ludmil B Alexandrov. Nonnegative/binary matrix factorization with a DWave quantum annealer. PloS one, Vol. 13, No. 12, p. e0206653, 2018.

Koki Kitai, Jiang Guo, Shenghong Ju, Shu Tanaka, Koji Tsuda, Junichiro

Shiomi, and Ryo Tamura. Designing metamaterials with quantum annealing and factorization machines. Physical Review Research, Vol. 2, No. 1,

p. 013319, 2020.

Steffen Rendle. Factorization machines. In 2010 IEEE International Conference on Data Mining, pp. 995–1000. IEEE, 2010.

Rongxin Xia, Teng Bian, and Sabre Kais. Electronic structure calculations

and the Ising Hamiltonian. The Journal of Physical Chemistry B, Vol. 122,

No. 13, pp. 3384–3395, 2017.

Michael Streif, Florian Neukart, and Martin Leib. Solving quantum chemistry problems with a D-Wave quantum annealer. In International Workshop on Quantum Technology and Optimization Problems, pp. 111–122.

Springer, 2019.

R Harris, Y Sato, AJ Berkley, M Reis, F Altomare, MH Amin, K Boothby,

P Bunyk, C Deng, C Enderud, et al. Phase transitions in a programmable

quantum spin glass simulator. Science, Vol. 361, No. 6398, pp. 162–165,

2018.

Andrew D King, Juan Carrasquilla, Jack Raymond, Isil Ozfidan, Evgeny

Andriyash, Andrew Berkley, Mauricio Reis, Trevor Lanting, Richard Harris, Fabio Altomare, et al. Observation of topological phenomena in a

programmable lattice of 1,800 qubits. Nature, Vol. 560, No. 7719, pp.

456–460, 2018.

Andrew D King, Jack Raymond, Trevor Lanting, Sergei V Isakov, Masoud

Mohseni, Gabriel Poulin-Lamarre, Sara Ejtemaee, William Bernoudy, Isil

Ozfidan, Anatoly Yu Smirnov, et al. Scaling advantage over path-integral

monte carlo in quantum simulation of geometrically frustrated magnets.

Nature communications, Vol. 12, No. 1, pp. 1–6, 2021.

YouTube Channel (D-Wave Systems). https://www.youtube.com/user/

dwavesystems.

D-Wave Ocean Software Documentation.

https://docs.ocean.

dwavesys.com/en/stable/.

《講義ノート》

物性研究・電子版 Vol. 10, No. 1, 101206(2022年3月号)

[53] OpenJij Tutorial 0.3.0 documentation. https://openjij.github.io/

OpenJijTutorial/build/html/ja/004-DWaveOceanSDK.html.

[54] PyQUBO. https://pyqubo.readthedocs.io/en/latest/.

[55] Mashiyat Zaman, Kotaro Tanahashi, and Shu Tanaka. PyQUBO: Python

library for QUBO creation. IEEE Transactions on Computers, pp. 1–1,

2021.

[56] OpenJij. https://openjij.github.io/OpenJijTutorial/build/html/

index.html.

[57] Fixstars Amplify. https://amplify.fixstars.com/.

...

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文

一発検索!

この論文の関連論文を見る