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2024-02-07 11:26:40 -08:00
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commit 56b72a0531
3 changed files with 46 additions and 66 deletions

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@ -17,8 +17,7 @@
% use the [solutions] flag to show solutions.
\documentclass[
solutions,
singlenumbering,
unfinished
singlenumbering
]{../../resources/ormc_handout}
\usepackage{../../resources/macros}
@ -46,53 +45,25 @@
\input{parts/03.00 logic gates}
\input{parts/03.01 quantum gates}
\end{document}
%\section{Superdense Coding}
%TODO
%\vfill
%\pagebreak
\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
%\section{Quantum Error Correction}
%TODO: no cloning theorem, bit flip code
%\vfill
%\pagebreak
%\section{Quantum Teleportation}
%TODO
%\vfill
%\pagebreak
%\section{One Real Qubit}
% No problems, appendix.
% bloch sphere, etc.
% \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}
\end{document}