\contentsline {section}{\numberline {\uppercase {i}}Introduction}{3}
\contentsline {section}{\numberline {\uppercase {ii}}Computation in Classical and Quantum Physics}{4}
\contentsline {subsection}{\numberline {A}Classical Gates}{4}
\contentsline {subsection}{\numberline {B}Quantum Gates}{5}
\contentsline {subsection}{\numberline {C}Quantum Entanglement}{6}
\contentsline {section}{\numberline {\uppercase {iii}}Simple Quantum Networks}{6}
\contentsline {subsection}{\numberline {A}Simple Arithmetic}{7}
\contentsline {subsection}{\numberline {B}Plain adder}{7}
\contentsline {subsection}{\numberline {C}Garbage Disposal}{8}
\contentsline {subsection}{\numberline {D}Deutsch's Problem}{9}
\contentsline {section}{\numberline {\uppercase {iv}}Outline of Quantum Factorization}{10}
\contentsline {section}{\numberline {\uppercase {v}}How to realize a Quantum Computer}{12}
\contentsline {subsection}{\numberline {A}The ion trap quantum computer}{12}
\contentsline {subsection}{\numberline {B}The implementation of the CNOT gate}{13}
\contentsline {section}{\numberline {\uppercase {vi}}Decoherence and Quantum Computation}{15}
\contentsline {subsection}{\numberline {A}Decoherence of entangled states}{15}
\contentsline {subsection}{\numberline {B}A general error model}{16}
\contentsline {subsection}{\numberline {C}Quantum error correction}{17}
\contentsline {section}{\numberline {\uppercase {vii}}Summary and Future Prospects}{19}
\contentsline {section}{\numberline {\uppercase {viii}} Acknowledgements}{19}