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Cited by 39Advanced Control Systems OptimizationQuantum Computing Algorithms and ArchitectureAdvanced Optimization Algorithms Research

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Model Predictive Control for Finite Input Systems using the D-Wave Quantum Annealer

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Inoue, Daisuke, Yoshida, Hiroaki·2020·Scientific Reports
DOI 10.1038/s41598-020-58081-9PMC PMC6994678
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Abstract

The D-Wave quantum annealer has emerged as a novel computational architecture that is attracting significant interest, but there have been only a few practical algorithms exploiting the power of quantum annealers. Here we present a model predictive control (MPC) algorithm using a quantum annealer for a system allowing a finite number of input values. Such an MPC problem is classified as a non-deterministic polynomial-time-hard combinatorial problem, and thus real-time sequential optimization is difficult to obtain with conventional computational systems. We circumvent this difficulty by converting the original MPC problem into a quadratic unconstrained binary optimization problem, which is then solved by the D-Wave quantum annealer. Two practical applications, namely stabilization of a spring-mass-damper system and dynamic audio quantization, are demonstrated. For both, the D-Wave method exhibits better performance than the classical simulated annealing method. Our results suggest new applications of quantum annealers in the direction of dynamic control problems.

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Figures

Figure 1 Result of the stabilization of a spring-mass-damper system. (a) Input u(t) generated with each method. (b) Time response of the first component of the state x(t). (c) Time response of the second component of the state x(t). In (a)–(c), the input generated with the quantum annealing is compared to the input from the simulated annealing and the brute-force search. (d) Value of evaluation function given in Eq. 15. The box-and-whisker plots are created by performing 10 numerical simulations.
Figure 1 Result of the stabilization of a spring-mass-damper system. (a) Input u(t) generated with each method. (b) Time response of the first component of the state x(t). (c) Time response of the second component of the state x(t). In (a)–(c), the input generated with the quantum annealing is compared to the input from the simulated annealing and the brute-force search. (d) Value of evaluation function given in Eq. 15. The box-and-whisker plots are created by performing 10 numerical simulations.CC BY · PubMed Central
Figure 2 Result of dynamic audio quantization. (a) Bode plot of perception filter given in Eq. 22. (b) Value of evaluation function given in Eq. 27. The solution from the quantum annealing (green) is compared to that from the simulated annealing (orange) and exact solution (blue). The box-and-whisker plot is created by performing 10 numerical simulations.
Figure 2 Result of dynamic audio quantization. (a) Bode plot of perception filter given in Eq. 22. (b) Value of evaluation function given in Eq. 27. The solution from the quantum annealing (green) is compared to that from the simulated annealing (orange) and exact solution (blue). The box-and-whisker plot is created by performing 10 numerical simulations.CC BY · PubMed Central
Figure 3 Iteration number for the simulated annealing versus the value of the evaluation function given in Eq. 15. At each value of iteration number, 10 computations are performed (blue dot) and the average value is plotted (blue solid line). The corresponding value of the evaluation function obtained with the quantum annealing method is also shown by the green dashed line.
Figure 3 Iteration number for the simulated annealing versus the value of the evaluation function given in Eq. 15. At each value of iteration number, 10 computations are performed (blue dot) and the average value is plotted (blue solid line). The corresponding value of the evaluation function obtained with the quantum annealing method is also shown by the green dashed line.CC BY · PubMed Central
Figure 4 Histogram of the absolute value of the QUBO matrix. (a) Stabilization of spring-mass-damper system. (b) Dynamic audio quantization.
Figure 4 Histogram of the absolute value of the QUBO matrix. (a) Stabilization of spring-mass-damper system. (b) Dynamic audio quantization.CC BY · PubMed Central

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Research works printed but not linked: 1

  1. W. Johnson, M. Future Hardware Directions of Quantum Annealing. In Qubits Europe 2018 D-Wave Users Conference (Munich, 2018).

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Metadata

Authors
Inoue, D., & Yoshida, H.
Affiliations
Toyota Central Research and Development Laboratories (Japan) (JP)
Corresponding author
Inoue, Daisuke
ORCID
Venue
Scientific Reports
Publisher
Springer Science and Business Media LLC
Published
2020-01-31
Volume
10
Issue
1
Pages
1591-1591
ISSN
2045-2322 (ISSN-L)
DOI
10.1038/s41598-020-58081-9
PMC
PMC6994678
OpenAlex
W3004136046
Cited by
39
References
44
Citations by year
2026: 3 · 2025: 5 · 2024: 18 · 2023: 8 · 2022: 3 · 2021: 2
FWCI
1.60
Type
journal article
Language
en
Open access
Licence
Locations
  • Scientific Reports (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
Keywords
model predictive control, D-Wave quantum annealer, quantum annealing, QUBO, combinatorial optimization, mass-spring-damper system, simulated annealing comparison, dynamic control

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CoChat. (2026). Citation check: Model Predictive Control for Finite Input Systems using the D-Wave Quantum Annealer. https://app.cochat.ai/papers/10.1038/s41598-020-58081-9
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Inoue, D., & Yoshida, H. (2020). Model Predictive Control for Finite Input Systems using the D-Wave Quantum Annealer. Scientific Reports. https://doi.org/10.1038/s41598-020-58081-9