On Addition-Rule Based Cellular Automata
We argue that for a general-purpose quantum computing, the addition rules must be imposed and implemented first. The consequence of this condition brings the addition operation into the architecture of one-dimensional cellular automaton with a dual-bit in each cell. They are then transformed into a 16 specific right-nearest neighbor interaction rules for each cell. Thus addition-rule based general-purpose quantum computing can only be found in one set out of roughly 4.3 billion available sets in the cellular automata. Some addition-rule incompatible examples are also presented and compared.
Keywords: Cellular Automata, Quantum Computing, Aharonov-Bohm Effect, Symbolic Substitution, Turing Machine