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IEEE International Conference on Microelectronics (MIEL)

Design of a Ternary Fredkin Reversible Gate

C. Moraga

Published Oct 16, 2023• 0 citations
Publisher

Abstract

Several realizations of a reversible ternary Fredkin gate are developed based on Muthukrishnan-Stroud controlled-controlled Sum modulo 3 gates and controlled scaling gates. It is shown that under positive polarity, the proposed Fredkin gates have the expected controlled swap behaviour and that under mixed polarity, other behaviours are possible. Most introduced realizations have a lower realization complexity than realizations found in the literature.

DOI
10.1109/miel58498.2023.10315866

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Several realizations of a reversible ternary Fredkin gate are developed based on Muthukrishnan-Stroud controlled-controlled Sum modulo 3 gates and controlled scaling gates. It is shown that under positive polarity, the proposed Fredkin gates have the expected controlled swap behaviour and that under mixed polarity, other behaviours are possible. Most introduced realizations have a lower realization complexity than realizations found in the literature.
We present realization of ternary Toffoli gate and modified Fredkin gate for quantum computing on top of ion trap realizable Muthukrishnan-Stroud primitive gates. Our design methodology is based on first realizing the quantum circuits using generalized ternary gates and Feynman gates and then replacing them with their equivalent realization using Muthukrishnan-Stroud gates. Our realization of ternary Toffoli gate is more efficient than the previously published result and modified Fredkin gate is realized for the first time in literature using Muthukrishnan-Stroud gates.
Reversible Computing circuits are characterized by low power consumption and their proximity to circuits for quantum computing. The Fredkin gate was one of the earliest proposed controlled reversible circuits, which however, was soon superseded by the Toffoli gate, the NOT, and CNOT gates, which constituting a flexible functionally complete set could also realize the Fredkin gate as a building block. In quantum computing circuits, the Fredkin gate (under the name controlled SWAP) plays an important role regarding the superposition of states. The present paper studies extensions of the Fredkin gate in terms of mixed polarity in the reversible domain and an application in quantum computing.
While the role of ternary reversible and quantum computation has been growing, synthesis methodologies for such logic, have been addressed in only a few works. A reversible ternary logic function can be expressed as minterms by using projection operators. In this paper, a novel realization of the projection operators using a minimum number of permutative ternary Muthukrishnan-Stroud (M-S) gates is presented. Next, an efficient method for logic simplification for ternary reversible logic is proposed. This method along with the new construction of projection operators yields significantly lower gate cost of approximately 31% less than that obtained by earlier methodologies, for the synthesis of ternary benchmark circuits.
Multiple-valued logic is a promising choice for future computer technologies, which provides a set of advantages comparing to binary circuits. In this paper, we have developed a genetic algorithm-based synthesis of ternary reversible circuits using Muthukrishnan-Stroud gates. The method for chromosomes coding, as well as a reasonable choice of algorithm parameters, allowed obtaining circuits for ternary Toffoli and modified Fredkin gates, which are better than other published methods in terms of quantum cost, delay times and amount of input ancillary and output garbage qutrits.