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Mark 2024-02-22 12:53:20 -08:00
parent 579e05e2c3
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4
Advanced/Introduction to Quantum/src/parts/03 two qubits.tex
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@ -2,7 +2,7 @@
\definition{} \definition{}
Just as before, we'll represent multi-quibit states as linear combinations of multi-qubit basis states. \par Just as before, we'll represent multi-qubit states as linear combinations of multi-qubit basis states. \par
For example, a two-qubit state $\ket{ab}$ is the four-dimensional unit vector For example, a two-qubit state $\ket{ab}$ is the four-dimensional unit vector
\begin{equation} \begin{equation}
\begin{bmatrix} \begin{bmatrix}
@ -33,7 +33,7 @@ we get one of the four basis states with the following probabilities:
\item $\mathcal{P}(\ket{10}) = c^2$ \item $\mathcal{P}(\ket{10}) = c^2$
\item $\mathcal{P}(\ket{11}) = d^2$ \item $\mathcal{P}(\ket{11}) = d^2$
\end{itemize} \end{itemize}
Of course, the sum of all the above probabilities is $1$. As before, the sum of all the above probabilities is $1$.
\problem{} \problem{}

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Advanced/Introduction to Quantum/src/parts/04 logic gates.tex
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@ -26,11 +26,11 @@ map, we can write it as follows:
\definition{} \definition{}
Before we discussing multi-qubit quantum gates, we need to review to classical logic. \par Before we discussing multi-qubit quantum gates, we need to review to classical logic. \par
Of course, a classical logic gate is a linear map from $\mathbb{B}^m$ to $\mathbb{B}^n$ Of course, a classical logic gate is a linear map from $\{0,1\}^m$ to $\{0,1\}^n$
\problem{}<notgatex> \problem{}<notgatex>
The \texttt{not} gate is a map from $\mathbb{B}$ to $\mathbb{B}$ defined by the following table: \par The \texttt{not} gate is a map defined by the following table: \par
\begin{itemize} \begin{itemize}
\item $X\ket{0} = \ket{1}$ \item $X\ket{0} = \ket{1}$

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Advanced/Introduction to Quantum/src/parts/05 quantum gates.tex
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@ -10,7 +10,7 @@ satisfies $GG^\text{T} = I$. \par
This implies the following: \par This implies the following: \par
\begin{itemize} \begin{itemize}
\item $G$ is square \par \item $G$ is square. In other words, it has as many rows as it has columns. \par
\note{ \note{
If we think of $G$ as a map, this means that $G$ has as many inputs as it has outputs. \\ If we think of $G$ as a map, this means that $G$ has as many inputs as it has outputs. \\
This is to be expected: we stated earlier that quantum gates do not destroy or create qubits. This is to be expected: we stated earlier that quantum gates do not destroy or create qubits.
@ -29,7 +29,7 @@ We can restate the above definition as follows: \par
A quantum gate is an invertible map from $\mathbb{U}^n$ to $\mathbb{U}^n$. A quantum gate is an invertible map from $\mathbb{U}^n$ to $\mathbb{U}^n$.
\definition{}<qgateislinear> \generic{Remark:}
Let $G$ be a quantum gate. \par Let $G$ be a quantum gate. \par
Since quantum gates are, by definition, \textit{linear} maps, Since quantum gates are, by definition, \textit{linear} maps,
the following holds: \par the following holds: \par

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Advanced/Introduction to Quantum/src/parts/07 superdense.tex
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@ -53,6 +53,7 @@ The $Z$ gate is defined as follows: \par
\problem{} \problem{}
Suppose that Alice and Bob are each in possession of one qubit. \par Suppose that Alice and Bob are each in possession of one qubit. \par
These two qubits are entangled, and have the compound state $\ket{\Phi^+}$. \par These two qubits are entangled, and have the compound state $\ket{\Phi^+}$. \par
\note[Note]{We could say that they each have \say{half} of $\ket{\Phi^+}$.}
How can Alice send a two-bit classical state How can Alice send a two-bit classical state
(i.e, one of the four values \texttt{00}, \texttt{01}, \texttt{10}, \texttt{11}) \par (i.e, one of the four values \texttt{00}, \texttt{01}, \texttt{10}, \texttt{11}) \par
to Bob by only sending one qubit? to Bob by only sending one qubit?

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Advanced/Introduction to Quantum/src/week 1.tex
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@ -24,7 +24,7 @@
\input{tikzset} \input{tikzset}
\uptitlel{Advanced 2} \uptitlel{Advanced 2}
\uptitler{Winter 2022} \uptitler{Winter 2024}
\title{Intro to Quantum Computing I} \title{Intro to Quantum Computing I}
\subtitle{Prepared by \githref{Mark} on \today{}} \subtitle{Prepared by \githref{Mark} on \today{}}

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Advanced/Introduction to Quantum/src/week 2.tex
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@ -16,7 +16,7 @@
% use the [nosolutions] flag to hide solutions, % use the [nosolutions] flag to hide solutions,
% use the [solutions] flag to show solutions. % use the [solutions] flag to show solutions.
\documentclass[ \documentclass[
solutions, nosolutions,
singlenumbering, singlenumbering,
shortwarning shortwarning
]{../../../resources/ormc_handout} ]{../../../resources/ormc_handout}
@ -28,7 +28,7 @@
\def\bra#1{\left\langle#1\right|} \def\bra#1{\left\langle#1\right|}
\uptitlel{Advanced 2} \uptitlel{Advanced 2}
\uptitler{Winter 2022} \uptitler{Winter 2024}
\title{Intro to Quantum Computing II} \title{Intro to Quantum Computing II}
\subtitle{Prepared by \githref{Mark} on \today{}} \subtitle{Prepared by \githref{Mark} on \today{}}