A method of majority logic reduction for quantum cellular automata

  • Authors:

  • Rumi Zhang;K. Walus;Wei Wang;G. A. Jullien

  • Affiliations:

  • Dept. of Electr. & Comput. Eng., Univ. of Western Ontario, London, Ont., Canada;-;-;-

  • Venue:
  • IEEE Transactions on Nanotechnology
  • Year:
  • 2004

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Abstract

The basic Boolean primitive in quantum cellular automata (QCA) is the majority gate. In this paper, a method for reducing the number of majority gates required for computing three-variable Boolean functions is developed to facilitate the conversion of sum-of-products expression into QCA majority logic. Thirteen standard functions are introduced to represent all three-variable Boolean functions and the simplified majority expressions corresponding to these standard functions are presented. We describe a novel method for using these standard functions to convert the sum-of-products expression to majority logic. By applying this method, the hardware requirements for a QCA design can be reduced. As an example, a 1-bit QCA adder is constructed with only three majority gates and two inverters. The adder is designed and simulated using QCADesigner, a design and simulation tool for QCA. We will show that the proposed method is very efficient and fast in deriving the simplified majority expressions in QCA design.