Quantum realization of quaternary Feynman and Toffoli gates

Multiple-valued logic functions having many input variables can be easily expressed as Galois Field Sum of Products (GFSOP) expression and can be realized using cascade of multiple-valued Feymnan and Toffoli gates [3, 5, 6]. Conventional binary functions can be expressed very easily as quaternary functions by grouping 2-bits together. These quaternary functions can be expressed as quaternary Galois Field Sum of Products expression and can be implemented as cascade of quaternary Feynman and Toffoli gates. These gates are macro-level gates and need to be realized using technology based primitive gates. In this paper, we show the realization of quaternary Feynman and Toffoli gates on the top of theoretically liquid ion-trap realizable 1-qudit and 2-qudit Muthukrishnan-Stroud gates [8].