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The duality game: a quantum algorithm for body dynamics modeling

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Abstract

In recent years, quantum algorithms have emerged as a groundbreaking approach toward solving complex computational problems, particularly in physical modeling and artificial intelligence. This study introduces a novel quantum algorithm termed the duality game, tailored for addressing challenges in body dynamics modeling. The practicality and efficacy of the proposed algorithm are elucidated through three distinct data scenarios: (1) approximation of classical von Bertalanffy growth in the presence of random noise (simulated), (2) personalized tumor burden modeling leveraging a small dataset, and (3) modeling of COVID-19 population growth employing big data analytics. The algorithm’s performance in these scenarios underscores its potential for practical applications at a large scale. Moreover, the findings foster optimism regarding the algorithm’s promise in the burgeoning field of physical-based quantum artificial intelligence (quantum AI). Through the duality game, a pathway is delineated for addressing real-world problems in body dynamics, opening avenues for further research and development in quantum AI, aimed at harnessing quantum computational advantages for solving intricate physical modeling problems.

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The data used in this study are available upon request from the corresponding author.

References

  1. Abbas, A., Sutter, D., Zoufal, C., Lucchi, A., Figalli, A., Woerner, S.: The power of quantum neural networks. Nat. Comput. Sci. 1(6), 403–409 (2021)

    Article  Google Scholar 

  2. Bergholm, V., Izaac, J., Schuld, M., Gogolin, C., Alam, M.S., Ahmed, S., Arrazola, J.M., Blank, C., Delgado, A., Jahangiri, S., et al.: Pennylane: automatic differentiation of hybrid quantum-classical computations (2018). arXiv preprint arXiv:1811.04968

  3. Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Rev. Mod. Phys. 91(4), 045002 (2019)

    Article  ADS  Google Scholar 

  4. Cerezo, M., Verdon, G., Huang, H.-Y., Cincio, L., Coles, P.J.: Challenges and opportunities in quantum machine learning. Nat. Comput. Sci. 2(9), 567–576 (2022)

    Article  Google Scholar 

  5. Date, P., Potok, T.: Adiabatic quantum linear regression. Sci. Rep. 11(1), 1905 (2021)

    Article  Google Scholar 

  6. Fudenberg, D., Tirole, J.: Game Theory. MIT Press, Cambridge (1991)

    Google Scholar 

  7. García, D.P., Cruz-Benito, J., García-Peñalvo, F.J.: Systematic literature review: quantum machine learning and its applications (2022). arXiv preprint arXiv:2201.04093

  8. Griffiths, D.J., Schroeter, D.F.: Introduction to Quantum Mechanics. Cambridge University Press, Cambridge (2018)

    Book  Google Scholar 

  9. Hashemi, A., Orzechowski, G., Mikkola, A., McPhee, J.: Multibody dynamics and control using machine learning. In: Multibody System Dynamics, pp. 1–35 (2023)

  10. Huang, H.-Y., Broughton, M., Mohseni, M., Babbush, R., Boixo, S., Neven, H., McClean, J.R.: Power of data in quantum machine learning. Nat. Commun. 12(1), 1–9 (2021)

    Google Scholar 

  11. Karniadakis, G.E., Kevrekidis, I.G., Lu, L., Perdikaris, P., Wang, S., Yang, L.: Physics-informed machine learning. Nat. Rev. Phys. 3(6), 422–440 (2021)

    Article  Google Scholar 

  12. Killoran, N., Bromley, T.R., Arrazola, J.M., Schuld, M., Quesada, N., Lloyd, S.: Continuous-variable quantum neural networks. Phys. Rev. Res. 1(3), 033063 (2019)

    Article  Google Scholar 

  13. Kuang, Y., Nagy, J.D., Eikenberry, S.E.: Introduction to Mathematical Oncology. CRC Press, Boca Raton (2018)

    Book  Google Scholar 

  14. Li, G., Zhao, X., Wang, X.: Quantum self-attention neural networks for text classification (2022). arXiv preprint arXiv:2205.05625

  15. Lloyd, S., Schuld, M., Ijaz, A., Izaac, J., Killoran, N.: Quantum embeddings for machine learning (2020). arXiv preprint arXiv:2001.03622

  16. Loève, M.: Probability Theory. Courier Dover Publications, New York (2017)

    Google Scholar 

  17. Lorenz, R., Pearson, A., Meichanetzidis, K., Kartsaklis, D., Coecke, B.: Qnlp in practice: running compositional models of meaning on a quantum computer (2021). arXiv preprint arXiv:2102.12846

  18. Nguyen, N., Chen, K.-C.: Bayesian quantum neural networks. IEEE Access 10, 54110–54122 (2022)

    Article  Google Scholar 

  19. Nguyen, N., Chen, K.-C.: Quantum embedding search for quantum machine learning. IEEE Access 10, 41444–41456 (2022)

    Article  Google Scholar 

  20. Nielsen, M.A., Chuang, I.: Quantum computation and quantum information (2002)

  21. Osborne, M.J., et al.: An Introduction to Game Theory, vol. 3. Oxford University Press, New York (2004)

    Google Scholar 

  22. Preskill, J.: Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018)

    Article  Google Scholar 

  23. Rockne, R.C., Scott, J.G.: Introduction to mathematical oncology. JCO Clin. Cancer Inf. 3, 21 (2019)

    Google Scholar 

  24. Schuld, M., Killoran, N.: Is quantum advantage the right goal for quantum machine learning? (2022). arXiv preprint arXiv:2203.01340

  25. Ullah, A., Dral, P.O.: Mlqd: a package for machine learning-based quantum dissipative dynamics. Comput. Phys. Commun. 294, 108940 (2024)

    Article  Google Scholar 

  26. Vadyala, S.R., Betgeri, S.N., Matthews, J.C., Matthews, E.: A review of physics-based machine learning in civil engineering. Results Eng. 13, 100316 (2022)

    Article  Google Scholar 

  27. Varna, M., Bertheau, P., Legrès, L.G., et al.: Tumor microenvironment in human tumor xenografted mouse models. J. Anal. Oncol. 3(3), 159–166 (2014)

    Google Scholar 

  28. Von Bertalanffy, L.: Quantitative laws in metabolism and growth. Q. Rev. Biol. 32(3), 217–231 (1957)

    Article  Google Scholar 

  29. Zeguendry, A., Jarir, Z., Quafafou, M.: Quantum machine learning: a review and case studies. Entropy 25(2), 287 (2023)

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Faculty of Computer Science, PHENIKAA University, Yen Nghia, Ha Dong, Hanoi, 12116, Vietnam

    Phuong-Nam Nguyen

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  1. Phuong-Nam Nguyen
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Contributions

Nam Nguyen conceptualized the algorithm and performed numerical analysis. The author would like to thank colleagues for stimulating discussion.

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Correspondence to Phuong-Nam Nguyen.

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The author declares that they have no known competing financial interests reported in this paper.

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Informed consent was obtained from all of the subjects involved in this study.

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The code used in this study is available upon request from the corresponding author.

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Appendix A: Pseudo-code

Appendix A: Pseudo-code

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Nguyen, PN. The duality game: a quantum algorithm for body dynamics modeling. Quantum Inf Process 23, 21 (2024). https://doi.org/10.1007/s11128-023-04223-7

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