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Ternary reversible logic functions are generally represented as ternary Galois field sum of products (TGFSOP) expressions and the TGFSOP expressions are mapped to reversible circuits using cascades of Feynman and Toffoli gates. Although a ternary logic function with a large number of variables can be minimized as a TGFSOP expression, the process is computationally expensive and the resulting reversible circuit tends to have a high quantum cost and ancilla in puts. To overcome these limitations, in this work we propose a new method of representing ternary reversible logic functions as Max of Min-terms (Max-Min) expressions, which can be mapped to a reversible circuit using multiple-controlled unary gates requiring lower quantum cost and fewer ancilla inputs. We propose a map-based minimization method for Max-Min expressions of up to four variables focusing on restrictions of the reversible circuit mapping technique.

Synthesis of reversible sequential circuits is a very new research area. It has been shown that such circuits can be implemented using emerging technologies such as quantum dot cellular automata. Earlier work uses traditional designs for sequential circuits and replaces the flip-flops and the gates with their reversible counterparts. Our earlier work used a direct feedback method without any flip-flops, which proved to be better than the replacement technique in terms of both quantum cost and ancilla inputs. This work is an improved version of our direct feedback method, which uses a different approach to the reversible mapping of sequential circuits. Design examples show that the proposed method produces better results than our earlier method in terms of both quantum cost and ancilla inputs.

Ternary reversible circuits are normally realized as Toffoli cascades using ternary Galois field sum of products (TGFSOP) expressions. In this work we propose a new method for realization of ternary reversible circuits using ternary Max-Min expressions. The proposed method uses ternary multiple-controlled unary gates to map Max-Min expression into reversible circuit. We also present techniques for realizations of multiple-controlled unary gates using M-S gates at the quantum level. Preliminary results show that the proposed method produces better results than TGFSOP-based method in terms of both quantum cost and ancilla inputs.