  Quantum-dot Cellular Automata (QCA) may offer a viable alternative of
traditional transistor-based technology at the nanoscale. When modeling a QCA
circuit, the number of degrees of freedom necessary to describe the quantum
mechanical state increases exponentially making modeling even modest size cell
arrays difficult. The intercellular Hartree approximation largely reduces the
number of state variables and still gives good results especially when the
system remains near ground state. This suggests that large part of the
correlation degrees of freedom are not essential from the point of view of the
dynamics. In certain cases, however, such as for example the majority gate with
unequal input legs, the Hartree approximation gives qualitatively wrong
results. An intermediate model is constructed between the Hartree approximation
and the exact model, based on the coherence vector formalism. By including
correlation effects to a desired degree, it improves the results of the Hartree
method and gives the approximate dynamics of the correlation terms. It also
models the majority gate correctly. Beside QCA cell arrays, our findings are
valid for Ising spin chains in transverse magnetic field, and can be
straightforwardly generalized for coupled two-level systems with a more
complicated Hamiltonian.
