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Quantum Neural Networks Achieving Quantum Algorithms

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Book cover Artificial Life and Evolutionary Computation (WIVACE 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 830))

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Abstract

This paper explores the possibility to construct quantum algorithms by means of neural networks endowed with quantum gates evolved to achieve prescribed goals. First tentatives are performed on the well known Deutsch and Deutsch-Jozsa problems. Results are promising as solutions are detected for different sizes and initializations of the problems using a standard evolutionary learning process. This approach is then used to design quantum operators by combining simple quantum operators belonging to a predefined set.

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Notes

  1. 1.

    The selection is performed by a roulette wheel selection. The genetic operators are the 1-point crossover and the uniform mutation. Their respective rates are 0.9 and 0.01. The population size is 100 and the maximum number of generations is 10000. The survival of best individuals is ensured by elitism.

  2. 2.

    The temperature is initialized to 1, in such a way that a candidate decreasing the objective function by 0.5 has a probability of \(\frac{2}{3}\) to be accepted. The cooling parameter is fixed to 0.99995 for a slow diminution of this probability.

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Acknowledgements

We thank Andrea Roli for his critical reading of a preliminary version of the paper.

This research used computational resources of the “Plateforme Technologique de Calcul Intensif (PTCI)” located at the University of Namur, Belgium, which is supported by the F.R.S.-FNRS.

This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimisation), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its authors.

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Authors and Affiliations

  1. Department of Mathematics, Namur Institute for Complex Systems (naXys), University of Namur, Namur, Belgium

    Delphine Nicolay & Timoteo Carletti

Authors
  1. Delphine Nicolay
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  2. Timoteo Carletti
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Corresponding author

Correspondence to Delphine Nicolay .

Editor information

Editors and Affiliations

  1. Ca’ Foscari University of Venice, Venice, Italy

    Marcello Pelillo

  2. Ca’ Foscari University of Venice, Venice, Italy

    Irene Poli

  3. University of Bologna, Cesena, Italy

    Andrea Roli

  4. University of Modena and Reggio Emilia, Modena, Italy

    Roberto Serra

  5. Ca’ Foscari University of Venice, Venice, Italy

    Debora Slanzi

  6. University of Modena and Reggio Emilia, Modena, Italy

    Marco Villani

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Nicolay, D., Carletti, T. (2018). Quantum Neural Networks Achieving Quantum Algorithms. In: Pelillo, M., Poli, I., Roli, A., Serra, R., Slanzi, D., Villani, M. (eds) Artificial Life and Evolutionary Computation. WIVACE 2017. Communications in Computer and Information Science, vol 830. Springer, Cham. https://doi.org/10.1007/978-3-319-78658-2_1

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  • DOI: https://doi.org/10.1007/978-3-319-78658-2_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78657-5

  • Online ISBN: 978-3-319-78658-2

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