Role of correlation in the operation of quantum-dot cellular automata

Quantum-dot cellular automata (QCA) may offer a viable alternative of tradi tional transistor-based technology at the nanoscale. When modeling a QCA ci rcuit, the number of degrees of freedom necessary to describe the quantum m echanical state increases exponentially making modeling even modest size ce ll arrays difficult. The intercellular Hartree approximation largely reduce s the number of state variables and still gives good results especially whe n the system remains near ground state. This suggests that a 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 majo rity gate with unequal input legs, the Hartree approximation gives qualitat ively wrong results. An intermediate model is constructed between the Hartr ee approximation and the exact model, based on the coherence vector formali sm. By including correlation effects to a desired degree, it improves the r esults of the Hartree method and gives the approximate dynamics of the corr elation 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 syst ems with a more complicated Hamiltonian. (C) 2001 American Institute of Phy sics.