We investigate quantum cellular automata which has been proposed as a
new type of quantum device. Using the perturbation expansion for the t
ransfer of the extended Hubbard model, we found that the effective Ham
iltonian of the quantum cellular automata is generally described by th
e Ising model with a longitudinal and a transverse field. The spin rep
resentation method is very useful to design the single cell. We demons
trate the thermodynamics and dynamics of the quantum cellular automata
to understand their properties. (C) 1998 Elsevier Science Ltd. All ri
ghts reserved.