diff --git a/Advanced/Introduction to Quantum/src/parts/03 two qubits.tex b/Advanced/Introduction to Quantum/src/parts/03 two qubits.tex index 2739e6b..e1972eb 100644 --- a/Advanced/Introduction to Quantum/src/parts/03 two qubits.tex +++ b/Advanced/Introduction to Quantum/src/parts/03 two qubits.tex @@ -2,7 +2,7 @@ \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 \begin{equation} \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 $\mathcal{P}(\ket{11}) = d^2$ \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{} diff --git a/Advanced/Introduction to Quantum/src/parts/04 logic gates.tex b/Advanced/Introduction to Quantum/src/parts/04 logic gates.tex index 1b619c4..152a4f8 100644 --- a/Advanced/Introduction to Quantum/src/parts/04 logic gates.tex +++ b/Advanced/Introduction to Quantum/src/parts/04 logic gates.tex @@ -26,11 +26,11 @@ map, we can write it as follows: \definition{} 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{} -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} \item $X\ket{0} = \ket{1}$ diff --git a/Advanced/Introduction to Quantum/src/parts/05 quantum gates.tex b/Advanced/Introduction to Quantum/src/parts/05 quantum gates.tex index 0cb05bc..8ccb374 100644 --- a/Advanced/Introduction to Quantum/src/parts/05 quantum gates.tex +++ b/Advanced/Introduction to Quantum/src/parts/05 quantum gates.tex @@ -10,7 +10,7 @@ satisfies $GG^\text{T} = I$. \par This implies the following: \par \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{ 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. @@ -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 $\mathbb{U}^n$. -\definition{} +\generic{Remark:} Let $G$ be a quantum gate. \par Since quantum gates are, by definition, \textit{linear} maps, the following holds: \par diff --git a/Advanced/Introduction to Quantum/src/parts/07 superdense.tex b/Advanced/Introduction to Quantum/src/parts/07 superdense.tex index 0361fcd..cf60ded 100644 --- a/Advanced/Introduction to Quantum/src/parts/07 superdense.tex +++ b/Advanced/Introduction to Quantum/src/parts/07 superdense.tex @@ -53,6 +53,7 @@ The $Z$ gate is defined as follows: \par \problem{} 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 +\note[Note]{We could say that they each have \say{half} of $\ket{\Phi^+}$.} 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 to Bob by only sending one qubit? diff --git a/Advanced/Introduction to Quantum/src/week 1.tex b/Advanced/Introduction to Quantum/src/week 1.tex index 30cdafd..d7be7ff 100755 --- a/Advanced/Introduction to Quantum/src/week 1.tex +++ b/Advanced/Introduction to Quantum/src/week 1.tex @@ -24,7 +24,7 @@ \input{tikzset} \uptitlel{Advanced 2} -\uptitler{Winter 2022} +\uptitler{Winter 2024} \title{Intro to Quantum Computing I} \subtitle{Prepared by \githref{Mark} on \today{}} diff --git a/Advanced/Introduction to Quantum/src/week 2.tex b/Advanced/Introduction to Quantum/src/week 2.tex index c259b10..6e64395 100755 --- a/Advanced/Introduction to Quantum/src/week 2.tex +++ b/Advanced/Introduction to Quantum/src/week 2.tex @@ -16,7 +16,7 @@ % use the [nosolutions] flag to hide solutions, % use the [solutions] flag to show solutions. \documentclass[ - solutions, + nosolutions, singlenumbering, shortwarning ]{../../../resources/ormc_handout} @@ -28,7 +28,7 @@ \def\bra#1{\left\langle#1\right|} \uptitlel{Advanced 2} -\uptitler{Winter 2022} +\uptitler{Winter 2024} \title{Intro to Quantum Computing II} \subtitle{Prepared by \githref{Mark} on \today{}}