Logic circuits from zero forcing View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-09

AUTHORS

Daniel Burgarth, Vittorio Giovannetti, Leslie Hogben, Simone Severini, Michael Young

ABSTRACT

We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices to encode each logical bit, we obtain universal computation. We also highlight a phenomenon of "back forcing" as a property of each function. Such a phenomenon occurs in a circuit when the input of gates which have been already used at a given time step is further modified by a computation actually performed at a later stage. Finally, we show that zero forcing can be also used to implement reversible computation. The model introduced here provides a potentially new tool in the analysis of Boolean functions, with particular attention to monotonicity. Moreover, in the light of applications of zero forcing in quantum mechanics, the link with Boolean functions may suggest a new directions in quantum control theory and in the study of engineered quantum spin systems. It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits. More... »

PAGES

485-490

References to SciGraph publications

  • 1987-03. The monotone circuit complexity of boolean functions in COMBINATORICA
  • 1980. Reversible computing in AUTOMATA, LANGUAGES AND PROGRAMMING
  • 1982-04. Conservative logic in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11047-014-9438-5

    DOI

    http://dx.doi.org/10.1007/s11047-014-9438-5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1033708937

    PUBMED

    https://www.ncbi.nlm.nih.gov/pubmed/26300713


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