[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/.
...