{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {2.1}Deutsch-Jozsa Algorithm}{\reset@font\mtcSfont 28}{section.2.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.1.1}Premise}{\reset@font\mtcSSfont 28}{subsection.2.1.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.1.2}Description of Algorithm \ref {algo:dj}}{\reset@font\mtcSSfont 28}{subsection.2.1.2}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Remarks.}{\reset@font\mtcPfont 28}{section*.26}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {2.2}Grover's Search}{\reset@font\mtcSfont 29}{section.2.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.2.1}Premise}{\reset@font\mtcSSfont 29}{subsection.2.2.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.2.2}Classical Search}{\reset@font\mtcSSfont 29}{subsection.2.2.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.2.3}Description of Grover's algorithm}{\reset@font\mtcSSfont 29}{subsection.2.2.3}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Optimization.}{\reset@font\mtcPfont 30}{section*.28}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {2.3}Amplitude Amplification}{\reset@font\mtcSfont 30}{section.2.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {2.4}BHT Algorithm}{\reset@font\mtcSfont 31}{section.2.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.4.1}Premise}{\reset@font\mtcSSfont 31}{subsection.2.4.1}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Remark.}{\reset@font\mtcPfont 31}{section*.29}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Classical algorithm.}{\reset@font\mtcPfont 31}{section*.30}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.4.2}Description}{\reset@font\mtcSSfont 31}{subsection.2.4.2}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Full quantum circuit.}{\reset@font\mtcPfont 31}{section*.31}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {2.5}Shor's Algorithm}{\reset@font\mtcSfont 32}{section.2.5}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.5.1}Reducing Factorization to Period Finding}{\reset@font\mtcSSfont 32}{subsection.2.5.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.5.2}Shor's Period Finding Algorithm}{\reset@font\mtcSSfont 32}{subsection.2.5.2}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {2.5.2.1}Premise for Shor's algorithm}{\reset@font\mtcSSSfont 32}{subsubsection.2.5.2.1}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {2.5.2.2}Description of the Algorithm}{\reset@font\mtcSSSfont 32}{subsubsection.2.5.2.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.5.3}Reducing Discrete Logarithm to Period Finding}{\reset@font\mtcSSfont 33}{subsection.2.5.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {2.6}Simon's Algorithm}{\reset@font\mtcSfont 33}{section.2.6}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.6.1}Simon's Problem}{\reset@font\mtcSSfont 34}{subsection.2.6.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.6.2}Description of the Algorithm}{\reset@font\mtcSSfont 34}{subsection.2.6.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.6.3}Weakening Simon's Premise}{\reset@font\mtcSSfont 35}{subsection.2.6.3}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Remark.}{\reset@font\mtcPfont 36}{section*.34}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.6.4}Simon's algorithm as a quantum circuit}{\reset@font\mtcSSfont 36}{subsection.2.6.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {2.7}Kuperberg's Algorithm}{\reset@font\mtcSfont 36}{section.2.7}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.7.1}Kuperberg's Premise}{\reset@font\mtcSSfont 36}{subsection.2.7.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {2.7.2}Description of the Algorithm}{\reset@font\mtcSSfont 37}{subsection.2.7.2}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {2.7.2.1}Kuperberg's routine}{\reset@font\mtcSSSfont 37}{subsubsection.2.7.2.1}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Exploiting the Result.}{\reset@font\mtcPfont 38}{section*.37}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {2.7.2.2}Combining Outputs}{\reset@font\mtcSSSfont 38}{subsubsection.2.7.2.2}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {2.7.2.3}Recovering $\mathinner {|{\psi _{2^{n-1}}}\rangle }$}{\reset@font\mtcSSSfont 39}{subsubsection.2.7.2.3}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Recovering $s$.}{\reset@font\mtcPfont 39}{section*.39}}
