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Random Networks with Quantum Boolean Functions

Author

Listed:
  • Mario Franco

    (Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Ciudad de Mexico 04510, Mexico
    Posgrado en Ciencia e Ingeniería de la Computación, Universidad Nacional Autónoma de México, Ciudad de Mexico 04510, Mexico)

  • Octavio Zapata

    (Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Ciudad de Mexico 04510, Mexico)

  • David A. Rosenblueth

    (Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Ciudad de Mexico 04510, Mexico
    Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Ciudad de Mexico 04510, Mexico)

  • Carlos Gershenson

    (Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Ciudad de Mexico 04510, Mexico
    Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Ciudad de Mexico 04510, Mexico
    Lakeside Labs GmbH, Lakeside Park B04, 9020 Klagenfurt am Wörthersee, Austria)

Abstract

We propose quantum Boolean networks, which can be classified as deterministic reversible asynchronous Boolean networks. This model is based on the previously developed concept of quantum Boolean functions. A quantum Boolean network is a Boolean network where the functions associated with the nodes are quantum Boolean functions. We study some properties of this novel model and, using a quantum simulator, we study how the dynamics change in function of connectivity of the network and the set of operators we allow. For some configurations, this model resembles the behavior of reversible Boolean networks, while for other configurations a more complex dynamic can emerge. For example, cycles larger than 2 N were observed. Additionally, using a scheme akin to one used previously with random Boolean networks, we computed the average entropy and complexity of the networks. As opposed to classic random Boolean networks, where “complex” dynamics are restricted mainly to a connectivity close to a phase transition, quantum Boolean networks can exhibit stable, complex, and unstable dynamics independently of their connectivity.

Suggested Citation

  • Mario Franco & Octavio Zapata & David A. Rosenblueth & Carlos Gershenson, 2021. "Random Networks with Quantum Boolean Functions," Mathematics, MDPI, vol. 9(8), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:792-:d:531204
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