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 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 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.
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15 June 2001
Research Article|
June 15 2001
Role of correlation in the operation of quantum-dot cellular automata
Géza Tóth;
Géza Tóth
Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
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Craig S. Lent
Craig S. Lent
Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
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J. Appl. Phys. 89, 7943–7953 (2001)
Article history
Received:
December 27 2000
Accepted:
March 07 2001
Citation
Géza Tóth, Craig S. Lent; Role of correlation in the operation of quantum-dot cellular automata. J. Appl. Phys. 15 June 2001; 89 (12): 7943–7953. https://doi.org/10.1063/1.1368389
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