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‎doc/pub/week5/ipynb/ipynb-week5-src.tar.gz‎

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‎doc/pub/week5/ipynb/week5.ipynb‎

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‎doc/src/week5/README.txt‎

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This IPython notebook week5.ipynb does not require any additional
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programs.

‎doc/src/week5/_minted-week5/FB713208D3D4DE4B3D52DFD0C74CB636BEBC502BB4EBC6615CDA31C1DB62B216.pygtex‎

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\begin{Verbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{o}{\PYGZpc{}}\PYG{n}{matplotlib} \PYG{n}{inline}
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\PYG{k+kn}{from} \PYG{n+nn}{matplotlib} \PYG{k+kn}{import} \PYG{n}{pyplot} \PYG{k}{as} \PYG{n}{plt}
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\PYG{k+kn}{import} \PYG{n+nn}{numpy} \PYG{k}{as} \PYG{n+nn}{np}
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\PYG{k+kn}{from} \PYG{n+nn}{scipy.linalg} \PYG{k+kn}{import} \PYG{n}{logm}\PYG{p}{,} \PYG{n}{expm}
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\PYG{k}{def} \PYG{n+nf}{log2M}\PYG{p}{(}\PYG{n}{a}\PYG{p}{):} \PYG{c+c1}{\PYGZsh{} base 2 matrix logarithm}
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\PYG{k}{return} \PYG{n}{logm}\PYG{p}{(}\PYG{n}{a}\PYG{p}{)}\PYG{o}{/}\PYG{n}{np}\PYG{o}{.}\PYG{n}{log}\PYG{p}{(}\PYG{l+m+mf}{2.0}\PYG{p}{)}
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\PYG{n}{dim} \PYG{o}{=} \PYG{l+m+mi}{4}
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\PYG{n}{Hamiltonian} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{zeros}\PYG{p}{((}\PYG{n}{dim}\PYG{p}{,}\PYG{n}{dim}\PYG{p}{))}
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\PYG{c+c1}{\PYGZsh{}number of lambda values}
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\PYG{n}{n} \PYG{o}{=} \PYG{l+m+mi}{40}
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\PYG{n}{lmbd} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{linspace}\PYG{p}{(}\PYG{l+m+mf}{0.0}\PYG{p}{,}\PYG{l+m+mf}{1.0}\PYG{p}{,}\PYG{n}{n}\PYG{p}{)}
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\PYG{n}{Hx} \PYG{o}{=} \PYG{l+m+mf}{2.0}
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\PYG{n}{Hz} \PYG{o}{=} \PYG{l+m+mf}{3.0}
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\PYG{c+c1}{\PYGZsh{} Non\PYGZhy{}diagonal part as sigma\PYGZus{}x tensor product with sigma\PYGZus{}x}
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\PYG{n}{sx} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{matrix}\PYG{p}{([[}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{],[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{0}\PYG{p}{]])}
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\PYG{n}{sx2} \PYG{o}{=} \PYG{n}{Hx}\PYG{o}{*}\PYG{n}{np}\PYG{o}{.}\PYG{n}{kron}\PYG{p}{(}\PYG{n}{sx}\PYG{p}{,} \PYG{n}{sx}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} Diagonal part as sigma\PYGZus{}z tensor product with sigma\PYGZus{}z}
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\PYG{n}{sz} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{matrix}\PYG{p}{([[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{0}\PYG{p}{],[}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{o}{\PYGZhy{}}\PYG{l+m+mi}{1}\PYG{p}{]])}
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\PYG{n}{sz2} \PYG{o}{=} \PYG{n}{Hz}\PYG{o}{*}\PYG{n}{np}\PYG{o}{.}\PYG{n}{kron}\PYG{p}{(}\PYG{n}{sz}\PYG{p}{,} \PYG{n}{sz}\PYG{p}{)}
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\PYG{n}{noninteracting} \PYG{o}{=} \PYG{p}{[}\PYG{l+m+mf}{0.0}\PYG{p}{,} \PYG{l+m+mf}{2.5}\PYG{p}{,} \PYG{l+m+mf}{6.5}\PYG{p}{,} \PYG{l+m+mf}{7.0}\PYG{p}{]}
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\PYG{n}{D} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{diag}\PYG{p}{(}\PYG{n}{noninteracting}\PYG{p}{)}
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\PYG{n}{Eigenvalue} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{zeros}\PYG{p}{((}\PYG{n}{dim}\PYG{p}{,}\PYG{n}{n}\PYG{p}{))}
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\PYG{n}{Entropy} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{zeros}\PYG{p}{(}\PYG{n}{n}\PYG{p}{)}
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\PYG{k}{for} \PYG{n}{i} \PYG{o+ow}{in} \PYG{n+nb}{range}\PYG{p}{(}\PYG{n}{n}\PYG{p}{):}
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\PYG{n}{Hamiltonian} \PYG{o}{=} \PYG{n}{lmbd}\PYG{p}{[}\PYG{n}{i}\PYG{p}{]}\PYG{o}{*}\PYG{p}{(}\PYG{n}{sx2}\PYG{o}{+}\PYG{n}{sz2}\PYG{p}{)}\PYG{o}{+}\PYG{n}{D}
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\PYG{c+c1}{\PYGZsh{} diagonalize and obtain eigenvalues, not necessarily sorted}
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\PYG{n}{EigValues}\PYG{p}{,} \PYG{n}{EigVectors} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{linalg}\PYG{o}{.}\PYG{n}{eig}\PYG{p}{(}\PYG{n}{Hamiltonian}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} sort eigenvectors and eigenvalues}
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\PYG{n}{permute} \PYG{o}{=} \PYG{n}{EigValues}\PYG{o}{.}\PYG{n}{argsort}\PYG{p}{()}
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\PYG{n}{EigValues} \PYG{o}{=} \PYG{n}{EigValues}\PYG{p}{[}\PYG{n}{permute}\PYG{p}{]}
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\PYG{n}{EigVectors} \PYG{o}{=} \PYG{n}{EigVectors}\PYG{p}{[:,}\PYG{n}{permute}\PYG{p}{]}
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\PYG{c+c1}{\PYGZsh{} Compute density matrix for selected system state, here ground state}
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\PYG{n}{DensityMatrix} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{zeros}\PYG{p}{((}\PYG{n}{dim}\PYG{p}{,}\PYG{n}{dim}\PYG{p}{))}
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\PYG{n}{DensityMatrix} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{outer}\PYG{p}{(}\PYG{n}{EigVectors}\PYG{p}{[:,}\PYG{l+m+mi}{0}\PYG{p}{],}\PYG{n}{EigVectors}\PYG{p}{[:,}\PYG{l+m+mi}{0}\PYG{p}{])}
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\PYG{c+c1}{\PYGZsh{} Project down on substates and find density matrix for subsystem}
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\PYG{n}{d} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{matrix}\PYG{p}{([[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{0}\PYG{p}{],[}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{]])}
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\PYG{n}{v1} \PYG{o}{=} \PYG{p}{[}\PYG{l+m+mf}{1.0}\PYG{p}{,}\PYG{l+m+mf}{0.0}\PYG{p}{]}
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\PYG{n}{proj1} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{kron}\PYG{p}{(}\PYG{n}{v1}\PYG{p}{,}\PYG{n}{d}\PYG{p}{)}
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\PYG{n}{x1} \PYG{o}{=} \PYG{n}{proj1} \PYG{o}{@} \PYG{n}{DensityMatrix} \PYG{o}{@} \PYG{n}{proj1}\PYG{o}{.}\PYG{n}{T}
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\PYG{n}{v2} \PYG{o}{=} \PYG{p}{[}\PYG{l+m+mf}{0.0}\PYG{p}{,}\PYG{l+m+mf}{1.0}\PYG{p}{]}
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\PYG{n}{proj2} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{kron}\PYG{p}{(}\PYG{n}{v2}\PYG{p}{,}\PYG{n}{d}\PYG{p}{)}
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\PYG{n}{x2} \PYG{o}{=} \PYG{n}{proj2} \PYG{o}{@} \PYG{n}{DensityMatrix} \PYG{o}{@} \PYG{n}{proj2}\PYG{o}{.}\PYG{n}{T}
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\PYG{c+c1}{\PYGZsh{} Total density matrix for subsystem}
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\PYG{n}{total} \PYG{o}{=} \PYG{n}{x1}\PYG{o}{+}\PYG{n}{x2}
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\PYG{c+c1}{\PYGZsh{} von Neumann Entropy for subsystem}
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\PYG{n}{Entropy}\PYG{p}{[}\PYG{n}{i}\PYG{p}{]} \PYG{o}{=} \PYG{o}{\PYGZhy{}}\PYG{n}{np}\PYG{o}{.}\PYG{n}{matrix}\PYG{o}{.}\PYG{n}{trace}\PYG{p}{(}\PYG{n}{total} \PYG{o}{@} \PYG{n}{log2M}\PYG{p}{(}\PYG{n}{total}\PYG{p}{))}
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\PYG{c+c1}{\PYGZsh{} Plotting eigenvalues and entropy as functions of interaction strengths}
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\PYG{n}{Eigenvalue}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{n}{i}\PYG{p}{]} \PYG{o}{=} \PYG{n}{EigValues}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}
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\PYG{n}{Eigenvalue}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{i}\PYG{p}{]} \PYG{o}{=} \PYG{n}{EigValues}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{]}
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\PYG{n}{Eigenvalue}\PYG{p}{[}\PYG{l+m+mi}{2}\PYG{p}{,}\PYG{n}{i}\PYG{p}{]} \PYG{o}{=} \PYG{n}{EigValues}\PYG{p}{[}\PYG{l+m+mi}{2}\PYG{p}{]}
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\PYG{n}{Eigenvalue}\PYG{p}{[}\PYG{l+m+mi}{3}\PYG{p}{,}\PYG{n}{i}\PYG{p}{]} \PYG{o}{=} \PYG{n}{EigValues}\PYG{p}{[}\PYG{l+m+mi}{3}\PYG{p}{]}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{plot}\PYG{p}{(}\PYG{n}{lmbd}\PYG{p}{,} \PYG{n}{Eigenvalue}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{,:]} \PYG{p}{,}\PYG{l+s+s1}{\PYGZsq{}b\PYGZhy{}\PYGZsq{}}\PYG{p}{,}\PYG{n}{lmbd}\PYG{p}{,} \PYG{n}{Eigenvalue}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,:],}\PYG{l+s+s1}{\PYGZsq{}g\PYGZhy{}\PYGZsq{}}\PYG{p}{,)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{plot}\PYG{p}{(}\PYG{n}{lmbd}\PYG{p}{,} \PYG{n}{Eigenvalue}\PYG{p}{[}\PYG{l+m+mi}{2}\PYG{p}{,:]} \PYG{p}{,}\PYG{l+s+s1}{\PYGZsq{}r\PYGZhy{}\PYGZsq{}}\PYG{p}{,}\PYG{n}{lmbd}\PYG{p}{,} \PYG{n}{Eigenvalue}\PYG{p}{[}\PYG{l+m+mi}{3}\PYG{p}{,:],}\PYG{l+s+s1}{\PYGZsq{}y\PYGZhy{}\PYGZsq{}}\PYG{p}{,)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{xlabel}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}\PYGZdl{}\PYGZbs{}lambda\PYGZdl{}\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{ylabel}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}Eigenvalues\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{show}\PYG{p}{()}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{plot}\PYG{p}{(}\PYG{n}{lmbd}\PYG{p}{,} \PYG{n}{Entropy}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{xlabel}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}\PYGZdl{}\PYGZbs{}lambda\PYGZdl{}\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{ylabel}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}Entropy\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{show}
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\end{Verbatim}

‎doc/src/week5/_minted-week5/default.pygstyle‎

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\@namedef{PYG@tok@mi}{\def\PYG@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
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\@namedef{PYG@tok@il}{\def\PYG@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
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\@namedef{PYG@tok@mo}{\def\PYG@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
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\@namedef{PYG@tok@ch}{\let\PYG@it=\textit\def\PYG@tc##1{\textcolor[rgb]{0.24,0.48,0.48}{##1}}}
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\@namedef{PYG@tok@cm}{\let\PYG@it=\textit\def\PYG@tc##1{\textcolor[rgb]{0.24,0.48,0.48}{##1}}}
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\@namedef{PYG@tok@cpf}{\let\PYG@it=\textit\def\PYG@tc##1{\textcolor[rgb]{0.24,0.48,0.48}{##1}}}
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\@namedef{PYG@tok@c1}{\let\PYG@it=\textit\def\PYG@tc##1{\textcolor[rgb]{0.24,0.48,0.48}{##1}}}
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\@namedef{PYG@tok@cs}{\let\PYG@it=\textit\def\PYG@tc##1{\textcolor[rgb]{0.24,0.48,0.48}{##1}}}
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\def\PYGZbs{\char`\\}
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\def\PYGZus{\char`\_}
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\def\PYGZob{\char`\{}
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\def\PYGZcb{\char`\}}
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\def\PYGZca{\char`\^}
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\def\PYGZam{\char`\&}
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\def\PYGZlt{\char`\<}
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\def\PYGZgt{\char`\>}
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\def\PYGZsh{\char`\#}
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\def\PYGZpc{\char`\%}
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\def\PYGZdl{\char`\$}
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\def\PYGZhy{\char`\-}
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\def\PYGZsq{\char`\'}
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\def\PYGZdq{\char`\"}
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\def\PYGZti{\char`\~}
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% for compatibility with earlier versions
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\def\PYGZat{@}
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\def\PYGZlb{[}
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\def\PYGZrb{]}
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\makeatother
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‎doc/src/week5/ipynb-week5-src.tar.gz‎

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‎doc/src/week5/make.sh‎

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system doconce format ipynb $name $opt
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# LaTeX Beamer slides
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beamertheme=red_plain
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system doconce format pdflatex $name --latex_title_layout=beamer --latex_table_format=footnotesize $opt

‎doc/src/week5/reveal.js/.gitignore‎

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.DS_Store
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.svn
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log/*.log
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tmp/**
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node_modules/
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.sass-cache
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css/reveal.min.css
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js/reveal.min.js

‎doc/src/week5/reveal.js/.travis.yml‎

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language: node_js
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node_js:
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- 0.10
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before_script:
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- npm install -g grunt-cli

‎doc/src/week5/reveal.js/CONTRIBUTING.md‎

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## Contributing
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Please keep the [issue tracker](http://github.com/hakimel/reveal.js/issues) limited to **bug reports**, **feature requests** and **pull requests**.
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### Personal Support
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If you have personal support or setup questions the best place to ask those are [StackOverflow](http://stackoverflow.com/questions/tagged/reveal.js).
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### Bug Reports
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When reporting a bug make sure to include information about which browser and operating system you are on as well as the necessary steps to reproduce the issue. If possible please include a link to a sample presentation where the bug can be tested.
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### Pull Requests
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- Should follow the coding style of the file you work in, most importantly:
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- Tabs to indent
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- Single-quoted strings
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- Should be made towards the **dev branch**
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- Should be submitted from a feature/topic branch (not your master)
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### Plugins
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Please do not submit plugins as pull requests. They should be maintained in their own separate repository. More information here: https://github.com/hakimel/reveal.js/wiki/Plugin-Guidelines

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