\contentsline {section}{\numberline {1}Introduction}{5}
\contentsline {section}{\numberline {2}Classical information theory}{12}
\contentsline {subsection}{\numberline {2.1}Measures of information}{12}
\contentsline {subsection}{\numberline {2.2}Data compression}{13}
\contentsline {subsection}{\numberline {2.3}The binary symmetric channel}{14}
\contentsline {subsection}{\numberline {2.4}Error-correcting codes}{15}
\contentsline {section}{\numberline {3}Classical theory of computation}{16}
\contentsline {subsection}{\numberline {3.1}Universal computer; Turing machine}{17}
\contentsline {subsection}{\numberline {3.2}Computational complexity}{18}
\contentsline {subsection}{\numberline {3.3}Uncomputable functions}{18}
\contentsline {section}{\numberline {4}Quantum verses classical physics}{20}
\contentsline {subsection}{\numberline {4.1}EPR paradox, Bell's inequality}{21}
\contentsline {section}{\numberline {5}Quantum Information}{22}
\contentsline {subsection}{\numberline {5.1}Qubits}{22}
\contentsline {subsection}{\numberline {5.2}Quantum gates}{22}
\contentsline {subsection}{\numberline {5.3}No cloning}{23}
\contentsline {subsection}{\numberline {5.4}Dense coding}{24}
\contentsline {subsection}{\numberline {5.5}Quantum teleportation}{25}
\contentsline {subsection}{\numberline {5.6}Quantum data compression}{25}
\contentsline {subsection}{\numberline {5.7}Quantum cryptography}{26}
\contentsline {section}{\numberline {6}The universal quantum computer}{27}
\contentsline {subsection}{\numberline {6.1}Universal gate}{28}
\contentsline {subsection}{\numberline {6.2}Church-Turing principle}{28}
\contentsline {section}{\numberline {7}Quantum algorithms}{29}
\contentsline {subsection}{\numberline {7.1}Simulation of physical systems}{29}
\contentsline {subsection}{\numberline {7.2}Period finding and Shor's factorisation algorithm}{29}
\contentsline {subsection}{\numberline {7.3}Grover's search algorithm}{32}
\contentsline {section}{\numberline {8}Experimental quantum information processors}{34}
\contentsline {subsection}{\numberline {8.1}Ion trap}{34}
\contentsline {subsection}{\numberline {8.2}Nuclear magnetic resonance}{35}
\contentsline {subsection}{\numberline {8.3}High-$Q$ optical cavities}{36}
\contentsline {section}{\numberline {9}Quantum error correction}{36}
\contentsline {section}{\numberline {10}Discussion}{40}