  In this paper, in order to investigate natural transformations from discrete
CA to QCA, we introduce a new formulation of finite cyclic QCA and generalized
notion of partitioned QCA. According to the formulations, we demonstrate the
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
quantumization of its cells is well-formed QCA. Finally we report some results
of computer simulations of quantumization of classical CA.
