Quantum edits

Advanced/Introduction to Quantum/main.tex

@@ -44,6 +44,55 @@
 	\input{parts/02.00 half a qubit}
 	\input{parts/02.01 two halves}
 	\input{parts/03.00 logic gates}
-	%\input{parts/03.01 quantum gates}
+	\input{parts/03.01 quantum gates}
 
-\end{document}
+\end{document}
+
+\problem{}
+The SWAP gate swaps two bits: $\text{SWAP}\ket{ab} = \ket{ba}$. \par
+Find its matrix.
+
+\begin{solution}
+	\begin{equation*}
+		\text{SWAP} = \begin{bmatrix}
+			1 & 0 & 0 & 0 \\
+			0 & 0 & 1 & 0 \\
+			0 & 1 & 0 & 0 \\
+			0 & 0 & 0 & 1 \\
+		\end{bmatrix}
+	\end{equation*}
+\end{solution}
+
+\vfill
+
+
+
+
+
+
+
+
+
+% \problem{}
+% The $T$ gate is a three-bit gate that inverts its right bit iff its left and middle inputs are both $\ket{1}$. \par
+% In other words, $T\ket{11x} = \ket{11}\ket{\text{not } x}$, and $T\ket{abx} = \ket{abx}$ for all other inputs. \par
+% Find the $T$ gate's matrix. \par
+% \note{
+% 	This gate is particularly interesting because it's a \textit{universal quantum gate}: \\
+% 	like NOR and NAND in classical logic, any quantum gate may emulated by only applying $T$ gates.
+% }
+%
+% \begin{solution}
+% 	\begin{equation*}
+% 		\text{T} = \begin{bmatrix}
+% 			1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+% 			0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
+% 			0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
+% 			0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
+% 			0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
+% 			0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
+% 			0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
+% 			0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
+% 		\end{bmatrix}
+% 	\end{equation*}
+% \end{solution}