Fix typos

Advanced/Introduction to Quantum/src/main.tex

@@ -32,7 +32,7 @@
 \def\bra#1{\left\langle#1\right|}
 
 
-% TODO: spend more time on probabalistic bits.
+% TODO: spend more time on probabalastic bits.
 % This could even be its own handout, especially
 % for younger classes!
 

Advanced/Introduction to Quantum/src/parts/01 bits.tex

@@ -498,7 +498,7 @@ Compute the following product:
 
 \generic{Remark:}
 Also, recall that every matrix is linear map, and that every linear map may be written as a matrix. \par
-We often use the terms \textit{matrix}, \textit{transformation}, and \textit{linear map} interchangably.
+We often use the terms \textit{matrix}, \textit{transformation}, and \textit{linear map} interchangeably.
 
 \pagebreak
 

Advanced/Introduction to Quantum/src/parts/02 qubit.tex

@@ -18,7 +18,7 @@ $\ket{0}$ is pronounced \say{ket zero,} and $\ket{1}$ is pronounced \say{ket one
 \note[Note]{$\bra{0}$ is called a \say{bra,} but we won't worry about that for now.}
 
 \vspace{2mm}
-This is very similiar to the \say{box} $[~]$ notation we used for probabilistic bits. \par
+This is very similar to the \say{box} $[~]$ notation we used for probabilistic bits. \par
 As before, we will write $\ket{0} = \left[\begin{smallmatrix} 1 \\ 0 \end{smallmatrix}\right]$
 and $\ket{1} = \left[\begin{smallmatrix} 0 \\ 1 \end{smallmatrix}\right]$.
 

Advanced/Introduction to Quantum/src/parts/06 hxh.tex

@@ -64,7 +64,7 @@ and like $X$ otherwise. The two circuits above illustrate this fact---take a loo
 
 \vspace{2mm}
 Of course, we can give a gate multiple controls. \par
-An $X$ gate with multiplie controls behaves like an $X$ gate if...
+An $X$ gate with multiple controls behaves like an $X$ gate if...
 \begin{itemize}
 	\item all non-inverted controls are $\ket{1}$, and
 	\item all inverted controls are $\ket{0}$

Advanced/Introduction to Quantum/src/parts/08 teleport.tex

@@ -1,7 +1,8 @@
 \section{Quantum Teleportation}
 
 Superdense coding lets us convert quantum bandwidth into classical bandwidth. \par
-Quantum teleporation does the opposite, using two classical bits and an entangled pair to transmit a quantum state.
+Quantum teleportation does the opposite, using two classical bits and an entangled pair
+to transmit a quantum state.
 
 \generic{Setup:}
 Again, suppose Alice and Bob each have half of a $\ket{\Phi^+}$ state. \par
@@ -131,7 +132,7 @@ With an informal proof, show that it is not possible to use superdense coding to
 more than two classical bits through an entangled two-qubit quantum state.
 
 \begin{solution}
-	If superdense coding was any more efficient, we could repeatedly apply superdense coding and quantum teleporation,
+	If superdense coding was any more efficient, we could repeatedly apply superdense coding and quantum teleportation,
 	to compress an arbitrary number of bits into two \say{seed} bits.
 
 	\linehack{}