Generalized Partitioned Quantum Cellular Automata and Quantization of Classical CA

In this paper, in order to investigate natural transformations from discrete CA to QCA, we introduce a formulation of finite cyclic QCA and generalized notion of partitioned QCA. According to the formulations, we demonstratethe condition of local transition functions, which induce a global transition of well-formed QCA. Following the results, extending a natural correspondence of classical cells and quantum cells to the correspondence of classical CA and QCA, we have the condition of classical CA such that CA generated by quantization of its cells is well-formed QCA. Finally we report some results of computer simulations of quantization of classical CA.