Correlation and coherence in quantum-dot cellular automata

by Géza Tóth In this thesis we investigate the role of correlation and coherence in two pos realizations of Quantum-dot Cellular Automata (QCA): realizations as a semicondu multi-quantum-dot structure and as a metal-island single electron tunneling circuit. two are different from the point of view of the underlying physics. The metal isla circuits are very strongly connected to the heat bath and they can be modeled classically, using classical quantities such as charging energy and capacitance. To the semiconductor realization, a quantum mechanical treatment is necessary. The qu mechanical state of the cells evolves coherently, at least for time scales smaller tha decoherence time. In the first part of the thesis the theory of metal island circuits is us design a cell structure permitting adiabatic clocking. It is also used to analyze conductance suppression of coupled double-dots and reproduce the correspo experimental results from the theory by modeling coherent electron motion inside QCA cell. In the second part the semiconductor QCA realization is studied. U Hartree-Fock approximation the basic phenomena in the one dimensional QCA (large and small amplitude polarization wave propagation and collision) is investiga art of nd the ctor with d that ther ority ults The approach is also used to define Quantum Cellular Neural Networks. In the last p the thesis intermediate approximations are constructed between the Hartree-Fock a exact model. An alternative of the density matrix description, the coherence ve formalism is reviewed and used to investigate possibility of quantum computing QCA. Using the coherence vector formalism as a basis an approximation is presente includes all two-point correlations while neglects the higher order correlations. Ano approach is shown for improving the self-consistent Hartree-Fock model for a maj gate by including correlation effects. The method fixes the qualitatively wrong res obtained if the length of the input legs are very different. .......v ..... vi .. xiii ......1 ......6 .....8 ....13 .16 ....17 ...29 ....32 .....35 ....40 .....42 ......44 ....46 .....51 .....55 ....58 ....58 ....61 .....64 ..64 ....67 ....70 .....74 ....76 ....77 ...79 .....82 ...84 ....85 ...86 ..88 .....88 TABLE OF CONTENTS LIST OF TABLES ....................................................................................................... LIST OF FIGURES ..................................................................................................... ACKNOLEDGEMENTS ..............................................................................................