main.toc

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\contentsline {chapter}{\numberline {1}{The Deutsch-Josza and Grover's algorithms}}{3}{chapter.1}%
\etoc@startlocaltoc {2}
\contentsline {section}{\numberline {1.1}{Deutsch-Josza algorithm}}{3}{section.1.1}%
\contentsline {subsection}{\numberline {1.1.1}{Matrix representation of the ``oracle''}}{5}{subsection.1.1.1}%
\contentsline {subsection}{\numberline {1.1.2}{Some comments on the ``phase kick-back''}}{6}{subsection.1.1.2}%
\contentsline {subsection}{\numberline {1.1.3}{Full implementation on $n$-qubits input}}{6}{subsection.1.1.3}%
\contentsline {section}{\numberline {1.2}{Grover's algorithm}}{8}{section.1.2}%
\contentsline {subsection}{\numberline {1.2.1}{Classical probabilistic algorithm}}{8}{subsection.1.2.1}%
\contentsline {subsection}{\numberline {1.2.2}{Quantum algorithm for $2$-qubits problem}}{9}{subsection.1.2.2}%
\contentsline {subsection}{\numberline {1.2.3}{Quantum circuit for $2$ qubits}}{11}{subsection.1.2.3}%
\contentsline {subsection}{\numberline {1.2.4}{Graphic interpretation: inversion about the mean}}{13}{subsection.1.2.4}%
\contentsline {subsection}{\numberline {1.2.5}{How to generalize?}}{14}{subsection.1.2.5}%
\contentsline {subsection}{\numberline {1.2.6}{Generalization to $n$ qubits}}{15}{subsection.1.2.6}%
\contentsline {chapter}{\numberline {2}{Shor's algorithm}}{19}{chapter.2}%
\etoc@startlocaltoc {3}
\contentsline {section}{\numberline {2.1}{No-cloning Theorem and Quantum Teleportation Protocol}}{20}{section.2.1}%
\contentsline {subsection}{\numberline {2.1.1}{No-cloning Theorem}}{20}{subsection.2.1.1}%
\contentsline {subsection}{\numberline {2.1.2}{Preliminaries to quantum teleportation}}{21}{subsection.2.1.2}%
\contentsline {subsection}{\numberline {2.1.3}{Shared resources}}{22}{subsection.2.1.3}%
\contentsline {subsection}{\numberline {2.1.4}{Quantum Teleportation Protocol}}{23}{subsection.2.1.4}%