Published January 8, 2022 | Version v1
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Quantum Computing for Dealing with Inaccurate Knowledge Related to the Certainty Factors Model

  • 1. University of A Coruña

Description

In this paper, we illustrate that inaccurate knowledge can be efficiently implemented in a quantum environment. For this purpose, we analyse the correlation between certainty factors and quantum probability. We first explore the certainty factors approach for inexact reasoning from a classical point of view. Next, we introduce some basic aspects of quantum computing, and we pay special attention to quantum rule-based systems. In this context, a specific use case was built: an inferential network for testing the behaviour of the certainty factors approach in a quantum environment. After the design and execution of the experiments, the corresponding analysis of the obtained results was performed in three different scenarios: (1) inaccuracy in declarative knowledge, or imprecision, (2) inaccuracy in procedural knowledge, or uncertainty, and (3) inaccuracy in both declarative and procedural knowledge. This paper, as stated in the conclusions, is intended to pave the way for future quantum implementations of well-established methods for handling inaccurate knowledge.

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Funding

NEASQC – NExt ApplicationS of Quantum Computing 951821
European Commission

References

  • Smolensky, P. Connectionist AI, symbolic AI, and the brain. Artif. Intell. Rev. 1987, 1, 95–109, doi:10.1007/BF00130011.
  • Jordan, M.I.; Mitchell, T.M. Machine learning: Trends, perspectives, and prospects. doi:10.1126/science.aaa8415
  • Shor, P.W. Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM Rev. 1999, 41, 303–332, doi:10.1137/S0036144598347011.
  • Grover, L.K. A fast quantum mechanical algorithm for database search. In Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, Philadelphia, PA, USA, 22–24 May 1996; pp. 212–219.
  • Havlíˇcek, V.; Córcoles, A.D.; Temme, K.; Harrow, A.W.; Kandala, A.; Chow, J.M.; Gambetta, J.M. Supervised learning with quantum-enhanced feature spaces. Nature 2019, 567, 209–212, doi:10.1038/s41586-019-0980-2.
  • Biamonte, J.; Wittek, P.; Pancotti, N.; Rebentrost, P.; Wiebe, N.; Lloyd, S. Quantum machine learning. Nature 2017, 549, 195–202, doi:10.1038/nature23474.
  • Ciliberto, C.; Herbster, M.; Ialongo, A.D.; Pontil, M.; Rocchetto, A.; Severini, S.; Wossnig, L. Quantum machine learning: A classical perspective. Proc. R. Soc. A Math. Phys. Eng. Sci. 2018, 474, 20170551, doi:10.1098/rspa.2017.0551.
  • Dunjko, V.; Briegel, H.J. Machine learning & artificial intelligence in the quantum domain: a review of recent progress. Rep. Prog. Phys. 2018, 81, 074001, doi:10.1088/1361-6633/aab406.
  • Gabor, T.; Sünkel, L.; Ritz, F.; Phan, T.; Belzner, L.; Roch, C.; Feld, S.; Linnhoff-Popien, C. The Holy Grail of Quantum Artificial Intelligence: Major Challenges in Accelerating the Machine Learning Pipeline. In Proceedings of the IEEE/ACM 42nd International Conference on Software Engineering Workshops, Seoul, Korea, 27 June–19 July 2020; Association for Computing Machinery: New York, NY, USA, 2020; pp. 456–461, doi:10.1145/3387940.3391469.
  • Soni, K.K.; Rasool, A. Pattern matching: A quantum oriented approach. Procedia Comput. Sci. 2020, 167, 1991–2002.
  • Montanaro, A. Quantum pattern matching fast on average. Algorithmica 2017, 77, 16–39.
  • Moret-Bonillo, V. Emerging technologies in artificial intelligence: Quantum rule-based systems. Prog. Artif. Intell. 2018, 7, 155–166.
  • Moret-Bonillo, V.; Fernández-Varela, I.; Álvarez-Estévez, D. Uncertainty in Quantum Rule-Based Systems. Arch. Clin. Biomed. Res. 2018, 5, 42–60.
  • Lindley, D.V. Understanding Uncertainty; John Wiley & Sons: Hoboken, NJ, USA, 2013; doi:10.1002/0470055480.
  • Shortliffe, E.H.; Buchanan, B.G. A model of inexact reasoning in medicine. Math. Biosci. 1975, 23, 351–379, doi:10.1016/0025-5564(75)90047-4.
  • Heckerman, D. Probabilistic Interpretations for Mycin's Certainty Factors. In Uncertainty in Artificial Intelligence; Machine Intelligence and Pattern Recognition; Kanal, L.N., Lemmer, J.F., Eds.; North-Holland: Amsterdam, The Netherlands, 1986; Volume 4, pp. 167–196, doi:10.1016/B978-0-444-70058-2.50017-6.
  • Zadeh, L. Fuzzy sets. Inf. Control 1965, 8, 338–353, doi:10.1016/S0019-9958(65)90241-X.
  • Shafer, G. A Mathematical Theory of Evidence; Princeton University Press: Princeton, NJ, USA, 1976.
  • Pearl, J. Fusion, propagation, and structuring in belief networks. Artif. Intell. 1986, 29, 241–288, doi:10.1016/0004-3702(86)90072-X.
  • Preskill, J. Quantum Computing in the NISQ era and beyond. Quantum 2018, 2, 79, doi:10.22331/q-2018-08-06-79.
  • Moret-Bonillo, V. Can artificial intelligence benefit from quantum computing? Prog. Artif. Intell. 2015, 3, 89–105.
  • Zhao, X.; Chen, W. GIS-Based Evaluation of Landslide Susceptibility Models Using Certainty Factors and Functional Trees-Based Ensemble Techniques. Appl. Sci. 2020, 10, 16, doi:10.3390/app10010016.
  • Hou, E.; Wang, J.; Chen, W. A comparative study on groundwater spring potential analysis based on statistical index, index of entropy and certainty factors models. Geocarto Int. 2018, 33, 754–769, doi:10.1080/10106049.2017.1299801.
  • Cui, K.; Lu, D.; Li, W. Comparison of landslide susceptibility mapping based on statistical index, certainty factors, weights of evidence and evidential belief function models. Geocarto Int. 2017, 32, 935–955, doi:10.1080/10106049.2016.1195886.
  • Pourghasemi, H.R.; Pradhan, B.; Gokceoglu, C.; Mohammadi, M.; Moradi, H.R. Application of weights-of-evidence and certainty factor models and their comparison in landslide susceptibility mapping at Haraz watershed, Iran. Arab. J. Geosci. 2013, 6, 2351–2365, doi:10.1007/s12517-012-0532-7.
  • Lucas, P.J. Certainty-factor-like structures in Bayesian belief networks. Knowl. Based Syst. 2001, 14, 327–335.
  • Yanofsky, N.S.; Mannucci, M.A. Quantum Computing for Computer Scientists; Cambridge University Press: Cambridge, UK, 2008.
  • Mermin, N.D. Extreme quantum entanglement in a superposition of macroscopically distinct states. Phys. Rev. Lett. 1990, 65, 1838.
  • Mishra, N. Understanding the Basics of Measurements in Quantum Computation. Available online: https://towardsdatascience. com/understanding-basics-of-measurements-in-quantum-computation-4c885879eba0 (accessed on 15 November 2021).
  • Feynman, R.P.; Hey, T.; Allen, R.W. Feynman Lectures on Computation; CRC Press: Boca Raton, FL, USA, 2018.
  • Sutor, R.S. Dancing with Qubits: How Quantum Computing Works and How It Can Change the World; Packt Publishing Ltd.: Birmingham, UK, 2019.
  • IBM. IBM Quantum. Available online: https://quantum-computing.ibm.com/ (accessed on 7 December 2021).
  • Bloch, F. Nuclear induction. Phys. Rev. 1946, 70, 460.
  • Atos. Quantum Application Toolset—myQLM Documentation Documentation. Available online: https://myqlm.github.io/(accessed on 9 December 2021).
  • NEASQC. NExt ApplicationS of Quantum Computing. Available online: https://www.neasqc.eu/ (accessed on 9 December 2021).
  • Vapnik, V.; Izmailov, R. Knowledge transfer in SVM and neural networks. Ann. Math. Artif. Intell. 2017, 81, 3–19.
  • Bremner, M.J.; Montanaro, A.; Shepherd, D.J. Average-Case Complexity Versus Approximate Simulation of Commuting Quantum Computations. Phys. Rev. Lett. 2016, 117, 080501, doi:10.1103/PhysRevLett.117.080501.
  • Nadaban, S. From Classical Logic to Fuzzy Logic and Quantum Logic: A General View. Int. J. Comput. Commun. Control 2021, 16, doi:10.15837/ijccc.2021.1.4125.
  • Vourdas, A. Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces. J. Math. Phys. 2014, 55, 082107.
  • Borujeni, S.E.; Nannapaneni, S.; Nguyen, N.H.; Behrman, E.C.; Steck, J.E. Quantum circuit representation of Bayesian networks. Expert Syst. Appl. 2021, 176, 114768, doi:10.1016/j.eswa.2021.114768.