\relax \citation{pre}\citation{shor}\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}\@writefile{toc}{\contentsline {section}{\numberline {2}Foundations of quantum computation}{1}}\citation{ste}\citation{eke}\citation{ste}\@writefile{toc}{\contentsline {section}{\numberline {3}Simulating quantum computation}{3}}\citation{joz}\citation{shor}\citation{ste}\citation{shor}\citation{eke}\citation{joz}\@writefile{toc}{\contentsline {section}{\numberline {4}Shor's factoring algorithm}{4}}\citation{shor}\citation{shor}\citation{eke}\citation{eke}\citation{shor}\citation{eke}\citation{har}\citation{ibm}\@writefile{toc}{\contentsline {section}{\numberline {5}Simulating Shor's algorithm}{6}}\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces \relax \fontsize  {10}{12}\normalfont  \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip Contents of the first register following measurement of the second register in the factorization of 15.}}{7}}\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces \relax \fontsize  {10}{12}\normalfont  \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip Contents of the first register following application of the QFT in the factorization of 15.}}{7}}\citation{shor}\bibcite{pre}{1}\bibcite{shor}{2}\bibcite{ste}{3}\bibcite{eke}{4}\bibcite{joz}{5}\bibcite{har}{6}\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces \relax \fontsize  {10}{12}\normalfont  \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip (at left) Time required to factor 15, 21, 33, 45, and 55 on a 233 MHz AMD K6 using the IBM compiler.}}{8}}\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces \relax \fontsize  {10}{12}\normalfont  \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip (at right) Quantum operations required to perform the QFT when factoring numbers from 15 to 128, inclusive.}}{8}}\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusion}{8}}\bibcite{ibm}{7}