On Some Basic Aspects of Ternary Reversible and Quantum Computing

This paper addresses basic aspects of reversible and quantum computing in the context of ternary systems. Ternary extensions of the Pauli matrices are presented and interactions with the Vilenkin-Chrestenson matrix are disclosed. The realization of extended ternary Toffoli gates under the Barenco et al. type of structure is shown not to be possible without ancillary lines, meanwhile a Sasanian-Wang-Perkowski type of structure leads to a five elementary gates realization. The presence of entanglement in ternary quantum computing is addressed and illustrated with an example.