Logic circuits from zero forcing

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Citations (SciVal)
114 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)485-490
Number of pages6
JournalNatural Computing
Volume14
Issue number3
Early online date26 Jul 2014
DOIs
Publication statusPublished - Sept 2015

Keywords

  • Adiabatic quantum computation
  • Logic circuits
  • Zero forcing

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