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Logic circuits from zero forcing.

Daniel Burgarth1, Vittorio Giovannetti2, Leslie Hogben3

  • 1Department of Mathematics and Physics, Aberystwyth University, Aberystwyth, SY23 3BZ UK.

Natural Computing
|August 25, 2015
PubMed
Summary
This summary is machine-generated.

We introduce logic circuits using zero forcing on graphs to evaluate monotone Boolean functions, achieving universal computation and reversible computation. This new model may link Boolean functions to quantum control theory.

Keywords:
Adiabatic quantum computationLogic circuitsZero forcing

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Area of Science:

  • * Theoretical Computer Science
  • * Graph Theory
  • * Quantum Information Science

Background:

  • * Boolean functions are fundamental in computation.
  • * Zero forcing is a graph theory concept with emerging applications.
  • * Existing models for Boolean functions may not fully capture certain properties.

Purpose of the Study:

  • * To design novel logic circuits based on zero forcing.
  • * To demonstrate the capability of these circuits for evaluating monotone Boolean functions.
  • * To explore the potential for universal and reversible computation using this framework.

Main Methods:

  • * Designing logic circuits where each gate performs zero forcing.
  • * Utilizing two vertices to encode each logical bit for universal computation.
  • * Analyzing the phenomenon of "back forcing" in circuit computation.

Main Results:

  • * Circuits based on zero forcing can evaluate all monotone Boolean functions.
  • * Universal computation is achieved by encoding bits with two vertices.
  • * The phenomenon of "back forcing" is identified as a key property.
  • * Zero forcing is shown to be applicable to reversible computation.

Conclusions:

  • * The zero forcing model offers a new approach to analyzing Boolean functions, especially monotonicity.
  • * The connection to quantum mechanics suggests potential in quantum control and engineered quantum systems.
  • * Further research is needed to explore links with contact circuits.