The Key Elements of Logic Design in Ternary Quantum-Dot Cellular Automata

The ternary Quantum-dot Cellular Automata (tQCA) were demonstrated to be a possible candidate for the implementation of a future multi-valued processing platform. Recent papers show that the application of the adiabatic pipelining can be used to solve the issues of the tQCA logic primitives. The architectures of the resulting tQCAs become similar to their binary counterparts and the physical design rules remain similar to those for the binary QCA domain. The design of complex processing structures is, however, usually based on logic design. The foundation of logic design is functionally complete set of elementary logic primitives (functions). The currently available tQCA logic primitives, i.e. tQCA majority gate and tQCA inverter gate, do not constitute a functionally complete set. We here present a tQCA implementation of the ternary characteristic functions, which together with the tQCA majority gate and the ternary constants constitute a functionally complete set according to multi-valued Post logic.