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A Quantum Annealing Approach to Biclustering

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Theory and Practice of Natural Computing (TPNC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10071))

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Abstract

Several problem in Artificial Intelligence and Pattern Recognition are computationally intractable due to their inherent complexity and the exponential size of the solution space. One example of such problems is biclustering, a specific clustering problem where rows and columns of a data-matrix must be clustered simultaneously. Quantum information processing could provide a viable alternative to combat such a complexity. A notable work in this direction is the recent development of the D-Wave™  computer, whose processor is able to exploit quantum mechanical effects in order to perform quantum annealing. The question motivating this work is whether the use of this special hardware is a viable approach to efficiently solve the biclustering problem. As a first step towards the solution of this problem, we show a feasible encoding of biclustering into the D-Wave™  quantum annealing hardware, and provide a theoretical analysis of its correctness.

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Notes

  1. 1.

    According to the quantum adiabatic theorem, a quantum system that begins in the non-degenerate ground state of a time-dependent Hamiltonian will remain in the instantaneous ground state provided the Hamiltonian changes sufficiently slowly.

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Authors and Affiliations

  1. University of Verona, Strada le Grazie 15, 37134, Verona, Italy

    Lorenzo Bottarelli, Manuele Bicego, Matteo Denitto, Alessandra Di Pierro & Alessandro Farinelli

Authors
  1. Lorenzo Bottarelli
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  2. Manuele Bicego
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  3. Matteo Denitto
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  4. Alessandra Di Pierro
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  5. Alessandro Farinelli
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Corresponding author

Correspondence to Alessandra Di Pierro .

Editor information

Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  2. Tohoku University, Sendai, Japan

    Takaaki Mizuki

  3. University of Extremadura, Cáceres, Spain

    Miguel A. Vega-Rodríguez

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Bottarelli, L., Bicego, M., Denitto, M., Di Pierro, A., Farinelli, A. (2016). A Quantum Annealing Approach to Biclustering. In: Martín-Vide, C., Mizuki, T., Vega-Rodríguez, M. (eds) Theory and Practice of Natural Computing. TPNC 2016. Lecture Notes in Computer Science(), vol 10071. Springer, Cham. https://doi.org/10.1007/978-3-319-49001-4_14

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  • DOI: https://doi.org/10.1007/978-3-319-49001-4_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-49000-7

  • Online ISBN: 978-3-319-49001-4

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