67 lines
1.7 KiB
TeX
Executable File
67 lines
1.7 KiB
TeX
Executable File
% Copyright (C) 2023 <Mark (mark@betalupi.com)>
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%
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% This program is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% You may have received a copy of the GNU General Public License
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% along with this program. If not, see <https://www.gnu.org/licenses/>.
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%
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%
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%
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% If you edit this, please give credit!
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% Quality handouts take time to make.
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% use the [nosolutions] flag to hide solutions,
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% use the [solutions] flag to show solutions.
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\documentclass[
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solutions,
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singlenumbering
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]{../../resources/ormc_handout}
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\usepackage{../../resources/macros}
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\def\ket#1{\left|#1\right\rangle}
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\def\bra#1{\left\langle#1\right|}
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\usepackage{units}
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\input{tikzset}
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\uptitlel{Advanced 2}
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\uptitler{Winter 2022}
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\title{Intro to Quantum Computing I}
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\subtitle{Prepared by \githref{Mark} on \today{}}
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\begin{document}
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\maketitle
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\input{parts/01 bits}
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\input{parts/02 qubit}
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\input{parts/03 two qubits}
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\input{parts/04 logic gates}
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\input{parts/05 quantum gates}
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\section{Bonus Problems (Putnam)}
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\problem{}
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Suppose $A$ is a real, square matrix that satisfies $A^3 = A + I$. \par
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Show that $\text{det}(A)$ is positive.
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\vfill
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\problem{}
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Suppose $A, B$ are $2 \times 2$ complex matrices satisfying $AB = BA$, \par
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and assume $A$ is not of the form $aI$ for some complex $a$. \par
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Show that $B = xA + yI$ for complex $x$ and $y$.
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\vfill
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\problem{}
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Is there an infinite sequence of real numbers $a_1, a_2, ...$ so that \par
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$a_1^m + a_2^m + ... = m$ for every positive integer $m$?
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\vfill
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\end{document} |