\usepackage{amsmath,textcomp} %\usepackage{epsf,shortlst,graphicx,color,amsmath,amssymb} \usepackage{epsf,graphicx,color,amsmath,amssymb} \usepackage[dvips]{hyperref}%\url{http://www.google.com} %\def\coursenumber{CS 294-2} \def\coursenumber{C191} \def\class{Quantum Computation} %\def\semester{Spring 2007} %\def\semester{Fall 2010} \def\semester{Spring 2017} \def\instructor{Vazirani} %% The lecture number is set using e.g. \lecture{6} in the file header %% \lecturenumber should be used in all sections, theorems, equations, etc. \newcount\lecturenumber \def\lecture#1{\global\lecturenumber=#1} \def\endproofmark{$\Box$} \newenvironment{proof}{\par{\bf Proof}:}{\endproofmark} \newcount\axiomnumber \axiomnumber=0 \newenvironment{axiom}[1]{\par\global\advance\axiomnumber by 1 {\bf Axiom \the\lecturenumber.\the\axiomnumber\ (#1)}: \begingroup}% {\endgroup} \newcount\defnnumber \defnnumber=0 \newenvironment{defn}[1]{\par\global\advance\defnnumber by 1 {\bf Definition \the\lecturenumber.\the\defnnumber\ (#1)}: \begingroup}% {\endgroup} \newcount\theoremnumber \theoremnumber=0 \newenvironment{theorem}{\par\global\advance\theoremnumber by 1 {\bf Theorem \the\lecturenumber.\the\theoremnumber}: \begingroup\em}% {\endgroup} \newcount\lemmanumber \lemmanumber=0 \newenvironment{lemma}{\par\global\advance\lemmanumber by 1 {\bf Lemma \the\lecturenumber.\the\lemmanumber}: \begingroup\em}% {\endgroup} \newskip\saveskip \newskip\saveindent \saveskip=\baselineskip %macros for use in assignments and exams \def\q#1#2{{\bf\item (#1 pts.)\quad #2}} \def\qns#1{{\bf\item #1}} \def\tf{{\it True/false}: } \def\mp{{\it Multiple choice}: } \def\tab{\hbox{\kern10pt}} \textheight=9in \textwidth=6.5in \topmargin=-.75in \oddsidemargin=0.25in \evensidemargin=0.25in \parindent=0pt \parskip=5pt \itemsep=-1pt \floatsep 9pt plus 2pt minus 3pt \intextsep 9pt plus 2pt minus 3pt \textfloatsep=9pt plus 2pt minus 3pt \renewcommand{\baselinestretch}{1.0} \font\dunhd=cmdunh10 scaled \magstep4 \font\dunhc=cmdunh10 scaled \magstep3 \font\dunhb=cmdunh10 scaled \magstep2 \font\dunha=cmdunh10 scaled \magstep1 \date{} %%% % Header setup: The \header command sets up all the variables for the new style header. % For example, \header{1}{8/26/03}{Qubits, Measurements} %% \newcommand{\header}[3]{\lecture{#1} \def\lecturenum{#1} \def\title{Lecture #1} \def\lecturedate{#2} \def\lecturetitle{#3}} \def\maketitle{% \begingroup \newpage \global\@topnum\z@ \@maketitle \thispagestyle{myheadings} \endgroup \setcounter{footnote}{0} \let\maketitle\relax \let\@maketitle\relax} % new header style (modified 9/4) \def\@maketitle{\newpage \hrule height6pt \vskip .7em \makebox[1.1in][l]{\dunha \coursenumber} %% for long titles, comment out this line.. { \qquad %% and this one.. \dunhb \lecturetitle \hfill \dunha \lecturedate} \vskip-0.1in %\makebox[1.1in][l]{\dunha \coursenumber}\quad %% and uncomment this line \makebox[1.5in][l]{\dunha \semester} {\hfill \dunhb Lecture \lecturenum \par} \vskip 0.6em \hrule height6pt \par \vskip .5em} % original header style \def\@oldmaketitle{\newpage \hrule height6pt \vskip .7em \makebox[1.5in][l]{\dunha \coursenumber} {\dunhb \class \hfill \ } \vskip-0.1in \makebox[1.5in][l]{\dunha \semester} {\dunhb \instructor \hfill \dunhc \title \par} \vskip 0.6em \hrule height6pt \par \vskip .5em} \def\section{\@startsection {section}{1}{\z@}{-3.0ex plus -.6ex minus -.2ex}{1.3ex plus .1ex}{\dunhb}} \def\subsection{\@startsection{subsection}{2}{\z@}{-1.6ex plus -.5ex minus -.1ex}{0.9ex plus .1ex}{\dunha}} %%%%%% page headings \def\foottext{\begin{footnotesize}\coursenumber, \semester, \title \hfill\qquad\thepage\end{footnotesize}} \def\ps@myheadings{\let\@mkboth\@gobbletwo \def\@oddfoot{\foottext}% \def\@evenfoot{\foottext}% \def\@evenhead{}\def\@oddhead{}} \pagestyle{myheadings} %%%%%% Figures \def\fig#1{\centerline{\epsffile{#1}}} \def\twofig#1#2{% \noindent\epsfxsize=0.48\textwidth \noindent \epsffile{#1}\hfill \epsfxsize=0.48\textwidth \epsffile{#2}\\ \makebox[0.48\textwidth]{(a)}\hfill\makebox[0.48\textwidth]{(b)}% } %%%%%% cross references \newcommand{\chapref}[1]{Chapter~\ref{#1}} \newcommand{\secref}[1]{Section~\ref{#1}} \newcommand{\figref}[1]{Figure~\ref{#1}} \newcommand{\tabref}[1]{Table~\ref{#1}} \newcommand{\exref}[1]{Exercise~\ref{#1}} %\newcommand{\eqref}[1]{Equation~(\ref{#1})} \newcommand{\partref}[1]{Part~\ref{#1}} \newcommand{\appref}[1]{Appendix~\ref{#1}} \newcommand{\sideref}[1]{the sidebar titled #1} \newcommand{\pgref}[1]{page~\pageref{#1}} %%%%%% additional symbols or names for them %\newcommand{\implies}{\:\;{\Rightarrow}\:\;} \newcommand{\impliessymbol}{\Rightarrow} \newcommand{\entails}{\models} \newcommand{\lequiv}{\;\;{\Leftrightarrow}\;\;} \newcommand{\lequivsymbol}{\Leftrightarrow} \newcommand{\xor}{\not\lequiv} \newcommand{\All}[1]{\forall\,#1\;\;} \newcommand{\Exi}[1]{\exists\,#1\;\;} \newcommand{\Exii}[1]{\exists!\,#1\;\;}% -pnorvig \newcommand{\Iot}[2]{\iota\,#1\,#2} \newcommand{\Lam}[2]{\lambda #1\;#2} \newcommand{\Qua}[3]{[#1\,#2\;#3]} \def\<{\langle} \def\>{\rangle} \newcommand{\union}{{\,{\cup}\,}} \newcommand{\elt}{{\,{\in}\,}} %%%cuts down on spacing \newcommand{\eq}{{\,{=}\,}} %%%cuts down on spacing \def\stimes{{\,\times\,}} %%%cuts down on spacing \def\ceil#1{\lceil #1 \rceil} \def\floor#1{\lfloor #1 \rfloor} %\def\cents{\mbox{c}} %\AtBeginDocument{\def\cents{\hbox{\rm\rlap{\hspace{.07ex}$/$}c}}} \newcommand{\cents}{\text{\textcent{}}} \def\cons{{}\bullet{}} %%%%%% bold font in math mode; this sucks but is simplest for now \newcommand{\mbf}[1]{\mbox{{\bfseries #1}}} \newcommand{\smbf}[1]{\mbox{{\scriptsize\bfseries #1}}} \def\N{\mbf{N}} \def\X{\mbf{X}} \def\x{\mbf{x}} \def\sx{\smbf{x}} \def\Y{\mbf{Y}} \def\y{\mbf{y}} \def\sy{\smbf{y}} \def\E{\mbf{E}} \def\e{\mbf{e}} \def\T{\mbf{T}} \def\O{\mbf{O}} \def\se{\smbf{e}} \def\Z{\mbf{Z}} \def\z{\mbf{z}} \def\sz{\smbf{z}} \def\F{\mbf{F}} \def\f{\mbf{f}} \def\A{\mbf{A}} \def\P{\mbf{P}} \def\B{\mbf{B}} \def\b{\mbf{b}} \def\m{\mbf{m}} \def\I{\mbf{I}} \def\ones{\mbf{1}} \def\ev{\mbf{ev}} \def\fv{\mbf{ev}} \def\sv{\mbf{sv}} \def\C{{\cal C}} %%%math definitions \newcommand{\ket}[1]{\textsf{\big{|}} #1 \textsf{\big{>}}\,} \newcommand{\bra}[1]{\textsf{\big{<}} #1 \textsf{\big{|}}\,} \newcommand{\braket}[2]{\textsf{\big{<}} #1 \textsf{\big{|\,}} #2\textsf{\big{>}}} \newcommand{\ketbra}[2]{\textsf{\big{|}} #1 \textsf{\big{>}}\textsf{\big{<}} #2\textsf{\big{|}}} \def\tbra #1{\langle #1\vert} \def\tket #1{\vert #1\rangle} \def\tbraket #1#2{\langle #1 \vert #2\rangle} \def\tketbra #1#2{\vert #1\rangle \! \langle #2\vert} \def\sub #1{\!_#1\!} \newcommand{\condexpect}[3]{E_{#1}\!\left[\,#2\ \vrule\ #3\,\right]} \renewcommand{\d}{\textrm{ d}} %\newcommand{\elt}{\in} \newcommand{\inter}{\cup} \renewcommand{\mod}[1]{\hbox{ mod $#1$}} \newcommand{\grad}[2]{{\nabla{#1}}_{#2}} \newcommand{\trace}[1]{\rm{Tr({#1})}} \renewcommand{\det}[1]{\rm{Det({#1})}} \newcommand{\elec}{\textit{$e^-~$}} \newcommand{\prob}[1]{\Pr\left\{#1\right\}} \newcommand{\condprob}[2]{\Pr\left\{#1 \; \vrule \; #2\right\}} \newcommand{\deriv}[2]{\frac{\d #1}{\d #2}} \newcommand{\derivp}[2]{\left( \frac{\d #1}{\d #2} \right)} \newcommand{\pderiv}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\pderivp}[2]{\left( \frac{\partial #1}{\partial #2} \right)} \newcommand{\st}{\hbox{ s.t. }} \newcommand{\abs}[1]{\lvert#1\rvert} \newcommand{\norm}[1]{\lVert#1\rVert} \newcommand{\set}[1]{\left\{#1\right\}} \def\tensor{\otimes} \newcommand{\bea}{\begin{eqnarray*}} \newcommand{\eea}{\end{eqnarray*}} \newcommand{\beq}{\begin{equation*}} \newcommand{\eeq}{\end{equation*}} %%%%%% for notes (either in margin or not to appear at all) %\newcommand{\comment}[1]{\marginpar{\scriptsize #1}} \newcommand{\comment}[1]{} \newcommand{\secondedition}[1]{} \reversemarginpar %% puts into left margin %%%%%% special keywords are marked in the margin %% Can be turned off if desired \newlength{\marginlineskip} \newlength{\marginwidth} \setlength{\marginlineskip}{3.5pt} \setlength{\marginwidth}{\marginparwidth} \addtolength{\marginwidth}{\marginparsep} \newlength{\savelineskip} \newcommand{\term}[1]{{\bfseries #1}}% maybe put into index,glossary too? \newcommand{\newterm}[1]{% {\bfseries #1}% \marginalnote{#1}}% maybe put into index,glossary too? \newcommand{\marginalnote}[1]{\yesmarginalnote{#1}} \newcommand{\yesmarginalnote}[1]{% \setlength{\savelineskip}{\baselineskip}% \marginpar{% \raisebox{0pt}[0pt][0pt]{\parbox[c]{\marginparwidth}{\begin{flushleft} {\nt \uppercase{#1}}% \setlength{\baselineskip}{\marginlineskip}% \end{flushleft}}}}% % end marginpar \setlength{\baselineskip}{\savelineskip}% } \newcommand{\nomarginalnote}[1]{} %%% [[check this - seems wrong]] \font\nt=phvrrn scaled 625 %% margin notes \usepackage{times,latexsym,mathptmx,comment} \def\mdw@dots#1{\ensuremath{\mathpalette\mdw@dots@i{#1}}} \def\mdw@dots@i#1#2{% \setbox\z@\hbox{$#1\mskip1.8mu$}% \dimen@\wd\z@% \setbox\z@\hbox{$#1.$}% #2% } \def\Ddots{% \mdw@dots{\mathinner{% \mkern1mu% \raise\dimen@\vbox{\kern7\dimen@\copy\z@}% \mkern2mu% \raise4\dimen@\copy\z@% \mkern2mu% \raise7\dimen@\box\z@% \mkern1mu% }}% }