Toffoli-type reversible gates are analyzed. Peres-type ternary gates are introduced for the first time. Conjunctive, disjunctive, majority, XOR types and hybrid control strategies are disclosed. Barenco-type of quantum models for these cases are developed.
The paper introduces dual Toffoli and Peres reversible gates, which operate under disjunctive control, and shows their functionality based on the Barenco et al. quantum model. Both uniform and mixed polarity are considered for the controls. Rewriting rules are presented, which provide a possible reduction of the number of gates and quantum cost of reversible (sub)circuits using standard Toffoli or Peres gates. Finally, a Clifford+T realization of a dual Toffoli and a dual Peres gate is shown, which may be used when mapping reversible circuits to the IBM quantum computers.
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.