m-Valued Quantum Representations and Operations of Elementary Cellular Automata

This paper introduces the m-valued Swap-based quantum computations (QC) of ECA. The fundamental m-valued quantum representations of: (1) m-valued orthonormal computational basis states quantum decision trees (QDTs) and (2) m-valued orthonormal composite basis states QDTs are also introduced as quantum modeling for the representations and operations of the QECA dynamics. The new m-valued quantum representations and their associated operations can play an important role in the automated design of future QECA circuits that consume minimal power in the quantum domain.