Quantum Realization of Multiple-Valued Feynman and Toffoli Gates without Ancilla Input

Abstract

Multiple-valued Feynman and Toffoli gates are used in GFSOP based synthesis of quantum logic circuits. These gates are macro-level gates and need to be realized using technology dependent primitive gates. In this paper, we present ancilla input free architectures for realization of d-valued (d≫=3 ) Feynman and n-qudit (n≫=3 ) Toffoli gates on the top of liquid ion-trap realizable Muthukrishnan-Stroud gates. The proposed architectures can be used for any d if GF(d) can be constructed. We show realization examples of ternary, quaternary, and quinary Feynman gates, and 3 and 4-qudit Toffoli gates. The present realizations require either less or equal primitive gates than the previously reported realizations. Moreover, in contrast to the earlier realizations, the present Toffoli gate realizations do not require any ancilla input, which reduce the register width of a synthesized quantum logic circuit.