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Merge branch 'master' of ssh://git.betalupi.com:33/Mark/ormc-handouts

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Mark 2024-02-10 21:05:40 -08:00
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2
Advanced/Introduction to Quantum/parts/01 bits.tex
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@ -55,7 +55,7 @@ What is the size of $\mathbb{B}^n$?
% NOTE: this is time-travelled later in the handout. % NOTE: this is time-travelled later in the handout.
% if you edit this, edit that too. % 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 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 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 We'll therefore say that \texttt{0} and \texttt{1} \textit{orthogonal} (or equivalently, \textit{perpendicular}). \par

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Advanced/Introduction to Quantum/parts/02 two bits.tex
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@ -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: When we have two bits, we have four orthogonal states:
$\overrightarrow{00}$, $\overrightarrow{01}$, $\overrightarrow{10}$, and $\overrightarrow{11}$. \par $\overrightarrow{00}$, $\overrightarrow{01}$, $\overrightarrow{10}$, and $\overrightarrow{11}$. \par
We need four dimensions to draw all of these vectors, so I can't provide a picture... \par 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 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. A set of $n$ bits gives us $2^n$ possible states, which forms a basis in $2^n$ dimensions.

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Advanced/Introduction to Quantum/parts/03 half a qubit.tex
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@ -38,7 +38,7 @@ A \textit{normalized vector} (also called a \textit{unit vector}) is a vector wi
\end{tcolorbox} \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 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. However, \texttt{0} and \texttt{1} aren't the only states a qubit may have.

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Advanced/Introduction to Quantum/parts/05 logic gates.tex
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@ -105,7 +105,7 @@ Find a matrix $A$ so that $A\ket{\texttt{ab}}$ works as expected. \par
\vfill \vfill
\pagebreak \pagebreak
\generic{Remark:} \cgeneric{Remark}
The way a quantum circuit handles information is a bit different than the way a classical circuit does. 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: 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 \vfill
\generic{Remark:} \cgeneric{Remark}
We could draw the above transformation as a combination $X$ and $I$ (identity) gate: We could draw the above transformation as a combination $X$ and $I$ (identity) gate:
\begin{center} \begin{center}
\begin{tikzpicture}[scale=0.8] \begin{tikzpicture}[scale=0.8]

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Advanced/Introduction to Quantum/parts/06 quantum gates.tex
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@ -127,7 +127,7 @@ If we measure the result of \ref{applycnot}, what are the probabilities of getti
\vfill \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 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}. (or, $\ket{00...0}$ through $\ket{11...1}$ for multi-qubit gates). This directly follows from \ref{qgateislinear}.

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resources/ormc_handout.cls
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@ -576,6 +576,16 @@
\IfNoValueF{#2}{\@customlabel{#2}{#1}} \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. % Make a new section type.
% Args: command, counter, title. % Args: command, counter, title.
\newcommand\@newobj[3]{ \newcommand\@newobj[3]{