Correlation and coherence in quantum-dot cellular automata

In this thesis we investigate the role of correlation and coherence in two possible realizations of Quantum-dot Cellular Automata (QCA): realizations as a semiconductor multi-quantum-dot structure and as a metal-island single electron tunneling circuit. The two are different from the point of view of the underlying physics. The metal island circuits are very strongly connected to the heat bath and they can be modeled semi-classically, using classical quantities such as charging energy and capacitance. To model the semiconductor realization, a quantum mechanical treatment is necessary. The quantum mechanical state of the cells evolves coherently, at least for time scales smaller than the decoherence time. In the first part of the thesis the theory of metal island circuits is used to design a cell structure permitting adiabatic clocking. It is also used to analyze the conductance suppression of coupled double-dots and reproduce the corresponding experimental results from the theory by modeling coherent electron motion inside the QCA cell. In the second part the semiconductor QCA realization is studied. Using Hartree-Fock approximation the basic phenomena in the one dimensional QCA array (large and small amplitude polarization wave propagation and collision) is investigated. The approach is also used to define Quantum Cellular Neural Networks. In the last part of the thesis intermediate approximations are constructed between the Hartree-Fock and the exact model. An alternative of the density matrix description, the coherence vector formalism is reviewed and used to investigate possibility of quantum computing with QCA. Using the coherence vector formalism as a basis an approximation is presented that includes all two-point correlations while neglects the higher order correlations. Another approach is shown for improving the self-consistent Hartree-Fock model for a majority gate by including correlation effects. The method fixes the qualitatively wrong results obtained if the length of the input legs are very different.