Numbering tweak
This commit is contained in:
		| @ -30,7 +30,7 @@ | ||||
|  | ||||
| \uptitlel{Advanced 2} | ||||
| \uptitler{Winter 2022} | ||||
| \title{Intro to Quantum Computing} | ||||
| \title{Intro to Quantum Computing I} | ||||
| \subtitle{Prepared by \githref{Mark} on \today{}} | ||||
|  | ||||
|  | ||||
| @ -38,12 +38,15 @@ | ||||
|  | ||||
| 	\maketitle | ||||
|  | ||||
| 	\input{parts/00.00 bits} | ||||
| 	\input{parts/00.01 two bits} | ||||
| 	\input{parts/02.00 half a qubit} | ||||
| 	\input{parts/02.01 two halves} | ||||
| 	\input{parts/03.00 logic gates} | ||||
| 	\input{parts/03.01 quantum gates} | ||||
| 	\input{parts/00 vectors} | ||||
| 	\input{parts/01 bits} | ||||
| 	\input{parts/02 two bits} | ||||
| 	\input{parts/03 half a qubit} | ||||
| 	\input{parts/04 two halves} | ||||
| 	\input{parts/05 logic gates} | ||||
| 	\input{parts/06 quantum gates} | ||||
| 	%\input{parts/03.00 logic gates} | ||||
| 	%\input{parts/03.01 quantum gates} | ||||
|  | ||||
| 	%\section{Superdense Coding} | ||||
| 	%TODO | ||||
|  | ||||
| @ -55,7 +55,7 @@ What is the size of $\mathbb{B}^n$? | ||||
|  | ||||
| % NOTE: this is time-travelled later in the handout. | ||||
| % if you edit this, edit that too. | ||||
| \generic{Remark:} | ||||
| \cgeneric{Remark} | ||||
| Consider a single classical bit. It takes states in $\{\texttt{0}, \texttt{1}\}$, picking one at a time. \par | ||||
| The states \texttt{0} and \texttt{1} are fully independent. They are completely disjoint; they share no parts. \par | ||||
| We'll therefore say that \texttt{0} and \texttt{1} \textit{orthogonal} (or equivalently, \textit{perpendicular}). \par | ||||
|  | ||||
| @ -16,7 +16,7 @@ What is the set of possible states of two bits (i.e, $\mathbb{B}^2$)? | ||||
|  | ||||
|  | ||||
|  | ||||
| \generic{Remark:} | ||||
| \cgeneric{Remark} | ||||
| When we have two bits, we have four orthogonal states: | ||||
| $\overrightarrow{00}$, $\overrightarrow{01}$, $\overrightarrow{10}$, and $\overrightarrow{11}$. \par | ||||
| We need four dimensions to draw all of these vectors, so I can't provide a picture... \par | ||||
| @ -42,7 +42,7 @@ with respect to the orthonormal basis $\{\overrightarrow{00}, \overrightarrow{01 | ||||
|  | ||||
|  | ||||
|  | ||||
| \generic{Remark:} | ||||
| \cgeneric{Remark} | ||||
| So, we represent each possible state as an axis in an $n$-dimensional space. \par | ||||
| A set of $n$ bits gives us $2^n$ possible states, which forms a basis in $2^n$ dimensions. | ||||
|  | ||||
|  | ||||
| @ -38,7 +38,7 @@ A \textit{normalized vector} (also called a \textit{unit vector}) is a vector wi | ||||
| \end{tcolorbox} | ||||
|  | ||||
|  | ||||
| \generic{Remark:} | ||||
| \cgeneric{Remark} | ||||
| Just like a classical bit, a \textit{quantum bit} (or \textit{qubit}) can take the values $\ket{0}$ and $\ket{1}$. \par | ||||
| However, \texttt{0} and \texttt{1} aren't the only states a qubit may have. | ||||
|  | ||||
|  | ||||
| @ -105,7 +105,7 @@ Find a matrix $A$ so that $A\ket{\texttt{ab}}$ works as expected. \par | ||||
| \vfill | ||||
| \pagebreak | ||||
|  | ||||
| \generic{Remark:} | ||||
| \cgeneric{Remark} | ||||
| The way a quantum circuit handles information is a bit different than the way a classical circuit does. | ||||
| We usually think of logic gates as \textit{functions}: they consume one set of bits, and return another: | ||||
|  | ||||
| @ -275,7 +275,7 @@ Find the matrix that corresponds to the above transformation. \par | ||||
|  | ||||
| \vfill | ||||
|  | ||||
| \generic{Remark:} | ||||
| \cgeneric{Remark} | ||||
| We could draw the above transformation as a combination $X$ and $I$ (identity) gate: | ||||
| \begin{center} | ||||
| \begin{tikzpicture}[scale=0.8] | ||||
|  | ||||
| @ -127,7 +127,7 @@ If we measure the result of \ref{applycnot}, what are the probabilities of getti | ||||
|  | ||||
| \vfill | ||||
|  | ||||
| \generic{Remark:} | ||||
| \cgeneric{Remark} | ||||
| As we just saw, a quantum gate is fully defined by the place it maps our basis states $\ket{0}$ and $\ket{1}$ \par | ||||
| (or, $\ket{00...0}$ through $\ket{11...1}$ for multi-qubit gates). This directly follows from \ref{qgateislinear}. | ||||
|  | ||||
|  | ||||
| @ -576,6 +576,16 @@ | ||||
| 	\IfNoValueF{#2}{\@customlabel{#2}{#1}} | ||||
| } | ||||
|  | ||||
| % Problem-counter generic object. | ||||
| % Same format as \problem, \theorem, etc, but has a counter. | ||||
| \NewDocumentCommand{\cgeneric}{ m d<> }{ | ||||
| 	\stepcounter{\@problemcounter} | ||||
| 	\par | ||||
| 	\vspace{3mm} | ||||
| 	{\bf\normalsize #1 \arabic{\@problemcounter}:} \\* | ||||
| 	\IfNoValueF{#2}{\@customlabel{#2}{#1}} | ||||
| } | ||||
|  | ||||
| % Make a new section type. | ||||
| % Args: command, counter, title. | ||||
| \newcommand\@newobj[3]{ | ||||
|  | ||||
		Reference in New Issue
	
	Block a user