chore(typos): fix typos, add URLs references to footnotes

lectures/phase-i/lecture4.tex

@@ -46,7 +46,7 @@ \subsection*{Measurement and Superposition Collapse}
 
 In the computational basis, the probability of measuring $|b\rangle$ is:
 
-\index{univesal basis!computational!measurement}
+\index{universal bases!computational!measurement}
 
 \[
   \boxed{
@@ -194,7 +194,8 @@ \subsection*{Circuit Notation} \index{Circuit notation}
 Quantum circuits visually represent quantum operations. Each qubit is
 represented as a horizontal line, and gates are applied sequentially from
 left to right. Important circuit elements include: \footnote{For rendering
-quantum circuits, consider using the \texttt{quantikz} package in \LaTeX.}
+quantum circuits, consider using the \texttt{quantikz} package in \LaTeX:
+\url{https://ctan.org/pkg/quantikz}}
 
 \begin{itemize}
 
@@ -204,7 +205,7 @@ \subsection*{Circuit Notation} \index{Circuit notation}
 
   \item \textbf{Time flow:} Left to right in circuits (\textit{\textbf{opposite
     of matrix multiplication order}}) \footnote {
-      Dor example, the circuit $U_1U_2$ corresponds to the
+      For example, the circuit $U_1U_2$ corresponds to the
       matrix product $U_2U_1$.
   }
 

lectures/phase-i/lecture7.tex

@@ -372,11 +372,11 @@ \subsection*{Toffoli Gate}
       % Input nodes and AND gate
       (0,1) node[left] {$A$} -- ++(1,0)
       (0,0) node[left] {$B$} -- ++(1,0)
-      (2,0.5) node[and port] (myand) {}
+      (2,0.5) node[and port] (and) {}
       % Connect everything
-      (1,1) -- (myand.in 1)
-      (1,0) -- (myand.in 2)
-      (myand.out) -- ++(1,0) node[right] {$A \land B$};
+      (1,1) -- (and.in 1)
+      (1,0) -- (and.in 2)
+      (and.out) -- ++(1,0) node[right] {$A \land B$};
     \end{circuitikz}
     &
     % Truth table
@@ -438,9 +438,10 @@ \subsection*{Toffoli Gate}
     that no information is lost.
   \item The composition of unitary gates remains unitary, preserving
     reversibility.
-  \item Classical \textbf{Toffoli and Fredkin gates} are reversible and can
-    be used to construct reversible classical circuits, which is why they
-    are also fundamental in quantum computing.
+  \item Classical Toffoli and Fredkin
+    \footnote{More on Fredkin gates: \url{https://en.wikipedia.org/wiki/Fredkin_gate}}
+    are reversible and can be used to construct reversible classical circuits,
+    which is why they are also fundamental in quantum computing.
   \item Measurement is \textbf{not} reversible, as it collapses the quantum
     state and introduces information loss.
 \end{enumerate}