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We present a three-dimensional simulation of the quantum cellular automaton introduced by Lent etal [P. D. Tougaw and C. S. Lent, J. Appl. Phys. 75, 1818 (1994)]. The Hamiltonian for their Hubbard model is derived as a zero-dimensional approximation to the Hamiltonian in our simulation. This provides a link between device properties and the phenomenological parameters such as tunneling coefficients. © 1998 American Institute of Physics.