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A method of majority logic reduction for quantum cellular automata

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4 Author(s)
Rumi Zhang ; Dept. of Electr. & Comput. Eng., Univ. of Western Ontario, London, Ont., Canada ; K. Walus ; Wei Wang ; G. A. Jullien

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.

Published in:

IEEE Transactions on Nanotechnology  (Volume:3 ,  Issue: 4 )