Application of Ising Machines and a Software Development for Ising Machines
Open accessAbstract
An online advertisement optimization, which can be represented by a combinatorial optimization problem is performed using D-Wave 2000Q, a quantum annealing machine. To optimize the online advertisement allocation optimization, we introduce a generalized version of the Markowitz mean-variance model which is a basic model of portfolio optimization. The obtained optimization performance using D-Wave 2000Q is higher than that using the greedy method which is a conventional method. Additionally, to conveniently use Ising machines including a quantum annealing machine, new software called PyQUBO is developed. The first half of the paper gives a review of several combinatorial optimization problems and how to represent them using the Ising model or the quadratic unconstrained binary optimization (QUBO) form. We show the results of the online advertisement allocation optimization and the explanation of PyQUBO in the last half of the paper.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Inequality constraints can be mapped to equality constraints, where additional variables have to be introduced.
“Inequality constraints can be mapped to equality constraints, where additional variables have to be introduced [53, 135].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [135]
The equality constraints can be considered in the Hamiltonian as penalty terms.
“The equality constraints can be considered in the Hamiltonian as so-called penalty terms as [135]:”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [135]
If λ is too low, then infeasible states are more likely to occur; if it is too high, then the quality of the obtained solutions deteriorates.
“If λ is too low, then infeasible states are more likely to occur; if it is too high, then the quality of the obtained solutions deteriorates, because H constraint dominates H cost .”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [135]
Cites
Markowitz, H. M. (1952) · The Journal of Finance · doi:10.1111/j.1540-6261.1952.tb01525.x · Cited by 18,429 · see citing works
Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.
Geman, S., & Geman, D. (1984) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1984.4767596 · Cited by 17,949 · see citing works
Ising formulations of many NP problems
Lucas, A. (2014) · Frontiers in Physics · doi:10.3389/fphy.2014.00005 · Cited by 2,512 · see citing works
Quantum annealing in the transverse Ising model
Kadowaki, T., & Nishimori, H. (1998) · Physical Review E · doi:10.1103/physreve.58.5355 · Cited by 2,339 · see citing works
On the product of semi-groups of operators
Trotter, H. F. (1959) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1959-0108732-6 · Cited by 2,282 · see citing works
Quantum annealing with manufactured spins
Johnson, M. W., Amin, M. H. S., Gildert, S., Lanting, T., Hamze, F., Dickson, N., Harris, R., Berkley, A. J., Johansson, J., Bunyk, P., et al. (2011) · Nature · doi:10.1038/nature10012 · Cited by 1,891 · see citing works
Suzuki, M. (1976) · Progress of Theoretical Physics · doi:10.1143/ptp.56.1454 · Cited by 1,129 · see citing works
Evidence for quantum annealing with more than one hundred qubits
Boixo, S., Rønnow, T. F., Isakov, S. V., Wang, Z., Wecker, D., Lidar, D. A., Martinis, J. M., & Troyer, M. (2014) · Nature Physics · doi:10.1038/nphys2900 · Cited by 810 · see citing works
A coherent Ising machine for 2000-node optimization problems
Inagaki, T., Haribara, Y., Igarashi, K., Sonobe, T., Tamate, S., Honjo, T., Marandi, A., McMahon, P. L., Umeki, T., Enbutsu, K., et al. (2016) · Science · doi:10.1126/science.aah4243 · Cited by 795 · see citing works
A fully programmable 100-spin coherent Ising machine with all-to-all connections
McMahon, P. L., Marandi, A., Haribara, Y., Hamerly, R., Langrock, C., Tamate, S., Inagaki, T., Takesue, H., Utsunomiya, S., Aihara, K., et al. (2016) · Science · doi:10.1126/science.aah5178 · Cited by 700 · see citing works
Traffic Flow Optimization Using a Quantum Annealer
Neukart, F., Compostella, G., Seidel, C., Dollen, D. V., Yarkoni, S., & Parney, B. (2017) · Frontiers in ICT · doi:10.3389/fict.2017.00029 · Cited by 470 · see citing works
What is the Computational Value of Finite-Range Tunneling?
Denchev, V. S., Boixo, S., Isakov, S. V., Ding, N., Babbush, R., Smelyanskiy, V., Martinis, J., & Neven, H. (2016) · Physical Review X · doi:10.1103/physrevx.6.031015 · Cited by 399 · see citing works
A 20k-Spin Ising Chip to Solve Combinatorial Optimization Problems With CMOS Annealing
Yamaoka, M., Yoshimura, C., Hayashi, M., Okuyama, T., Aoki, H., & Mizuno, H. (2015) · IEEE Journal of Solid-State Circuits · doi:10.1109/jssc.2015.2498601 · Cited by 365 · see citing works
Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
Choi, V. (2011) · Quantum Information Processing · doi:10.1007/s11128-010-0200-3 · Cited by 278 · see citing works
Quantum annealing of the traveling-salesman problem
Martoňák, R., Santoro, G. E., & Tosatti, E. (2004) · Physical Review E · doi:10.1103/physreve.70.057701 · Cited by 200 · see citing works
Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer
Rosenberg, G., Haghnegahdar, P., Goddard, P., Carr, P., Wu, K. J., & de Prado, M. L. (2015) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2016.2574703 · Cited by 191 · see citing works
Optimization by quantum annealing: Lessons from hard satisfiability problems
Battaglia, D. A., Santoro, G. E., & Tosatti, E. (2005) · Physical Review E · doi:10.1103/physreve.71.066707 · Cited by 108 · see citing works
Quantum Spin Glasses, Annealing and Computation
Tanaka, S., Tamura, R., & Chakrabarti, B. K. (2017) · International Linear Collider · Cited by 77 · see citing works
Self-citationIsing-Model Optimizer with Parallel-Trial Bit-Sieve Engine
Matsubara, S., Tamura, H., Takatsu, M., Yoo, D., Vatankhahghadim, B., Yamasaki, H., Miyazawa, T., Tsukamoto, S., Watanabe, Y., Takemoto, K., et al. (2017) · Advances in intelligent systems and computing · doi:10.1007/978-3-319-61566-0_39 · Cited by 64 · see citing works
Optimizing adiabatic quantum program compilation using a graph-theoretic framework
Goodrich, T. D., Sullivan, B. D., & Humble, T. S. (2018) · Quantum Information Processing · doi:10.1007/s11128-018-1863-4 · Cited by 50 · see citing works
Toward Practical-Scale Quantum Annealing Machine for Prime Factoring
Maezawa, M., Fujii, G., Hidaka, M., Imafuku, K., Kikuchi, K., Koike, H., Makise, K., Nagasawa, S., Nakagawa, H., Ukibe, M., et al. (2019) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.88.061012 · Cited by 46 · see citing works
ToQ.jl: A high-level programming language for D-Wave machines based on Julia
O’Malley, D., & Vesselinov, V. V. (2016) · IEEE High Performance Extreme Computing Conference · doi:10.1109/hpec.2016.7761616 · Cited by 40 · see citing works
Optimization of neural networks via finite-value quantum fluctuations
Ohzeki, M., Okada, S., Terabe, M., & Taguchi, S. (2018) · Scientific Reports · doi:10.1038/s41598-018-28212-4 · Cited by 32 · see citing works
An Ising model mapping to solve rectangle packing problem
Terada, K., Oku, D., Kanamaru, S., Tanaka, S., Hayashi, M., Yamaoka, M., Yanagisawa, M., & Togawa, N. (2018) · International Symposium on VLSI Design, Automation and Test · doi:10.1109/vlsi-dat.2018.8373233 · Cited by 27 · see citing works
Self-citationQuantum annealing for Dirichlet process mixture models with applications to network clustering
Sato, I., Tanaka, S., Kurihara, K., Miyashita, S., & Nakagawa, H. (2013) · Neurocomputing · doi:10.1016/j.neucom.2013.05.019 · Cited by 13 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
PyQUBO: Python Library for Mapping Combinatorial Optimization Problems to QUBO Form
Zaman, M., Tanahashi, K., & Tanaka, S. (2022) · IEEE Transactions on Computers · doi:10.1109/tc.2021.3063618 · Cited by 114 · see citing works
Self-citationHybrid Annealing Method Based on subQUBO Model Extraction With Multiple Solution Instances
Atobe, Y., Tawada, M., & Togawa, N. (2022) · IEEE Transactions on Computers · doi:10.1109/tc.2021.3138629 · Cited by 38 · see citing works
Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study
Gemeinhardt, F., Garmendia, A., Wimmer, M., Weder, B., & Leymann, F. (2024) · ACM Computing Surveys · doi:10.1145/3620668 · Cited by 22 · see citing works
“Inequality constraints can be mapped to equality constraints, where additional variables have to be introduced [53, 135].”
BackgroundMethodInfluential
- Authors
- Tanahashi, K., Takayanagi, S., Motohashi, T., & Tanaka, S.
- Affiliations
- Nihon University (JP)
- Waseda University (JP)
- Venue
- Journal of the Physical Society of Japan
- Publisher
- Physical Society of Japan
- Published
- 2019-06-15
- Volume
- 88
- Issue
- 6
- Pages
- 061010
- ISSN
- 0031-9015 (ISSN-L)
- 1347-4073
- OpenAlex
- W2946526084
- Cited by
- 142
- References
- 25
- Citations by year
- 2026: 17 · 2025: 26 · 2024: 25 · 2023: 24 · 2022: 13 · 2021: 19 · 2020: 14 · 2019: 4
- FWCI
- 5.77
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by
- Locations
- Journal of the Physical Society of Japan (publishedVersion, cc-by)
- Funders
- Precursory Research for Embryonic Science and Technology (JPMJPR1665)
- Japan Society for the Promotion of Science (15K17720, 15H03699)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Keywords
- Ising machines, quantum annealing, D-Wave 2000Q, combinatorial optimization, Markowitz mean-variance model, portfolio optimization, QUBO, Ising model
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
