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lines changed Original file line number Diff line number Diff line change @@ -2132,7 +2132,7 @@ <h2 id="the-hamiltonian-in-terms-of-pauli-boldsymbol-x-and-pauli-boldsymbol-z-ma
21322132
21332133< p > with</ p >
21342134$$
2135- \mathcal{H}_0=\epsilon_{II}\boldsymbol{I}\otimes\boldsymbol{I}+\epsilon_{ZI}\boldsymbol{Z}\otimes\boldsymbol{I}+\epsilon_{IZ}\boldsymbol{I}\otimes\boldsymbol{Z}+\epsilon_{II}+\epsilon_{ ZZ}\boldsymbol{Z}\otimes\boldsymbol{Z},
2135+ \mathcal{H}_0=\epsilon_{II}\boldsymbol{I}\otimes\boldsymbol{I}+\epsilon_{ZI}\boldsymbol{Z}\otimes\boldsymbol{I}+\epsilon_{IZ}\boldsymbol{I}\otimes\boldsymbol{Z}+\epsilon_{ZZ}\boldsymbol{Z}\otimes\boldsymbol{Z},
21362136$$
21372137
21382138< p > and</ p >
@@ -2166,10 +2166,10 @@ <h2 id="explicit-expressions" class="anchor">Explicit expressions </h2>
21662166< p > In order to perform our measurements, will then need the following operators \( \boldsymbol{U} \)</ p >
21672167$$
21682168\begin{align*}
2169- \boldsymbol{Z}\otimes\boldsymbol{I} & \boldsymbol{U}=\boldsymbol{I}\otimes\boldsymbol{I}\\
2170- \boldsymbol{I}\otimes\boldsymbol{Z} & \boldsymbol{U}=\text{SWAP}\\
2171- \boldsymbol{Z}\otimes\boldsymbol{Z} & \boldsymbol{U}=CX_{10}\\
2172- \boldsymbol{X}\otimes\boldsymbol{X} & \boldsymbol{U}=CX_{10}(\boldsymbol{H}\otimes\boldsymbol{H}\\
2169+ \boldsymbol{Z}\otimes\boldsymbol{I}\hspace{1cm} & \boldsymbol{U}=\boldsymbol{I}\otimes\boldsymbol{I}\\
2170+ \boldsymbol{I}\otimes\boldsymbol{Z}\hspace{1cm} & \boldsymbol{U}=\text{SWAP}\\
2171+ \boldsymbol{Z}\otimes\boldsymbol{Z}\hspace{1cm} & \boldsymbol{U}=CX_{10}\\
2172+ \boldsymbol{X}\otimes\boldsymbol{X}\hspace{1cm} & \boldsymbol{U}=CX_{10}(\boldsymbol{H}\otimes\boldsymbol{H}) \\
21732173\end{align*}
21742174$$
21752175
Original file line number Diff line number Diff line change @@ -2172,7 +2172,7 @@ <h2 id="the-hamiltonian-in-terms-of-pauli-boldsymbol-x-and-pauli-boldsymbol-z-ma
21722172< p > with</ p >
21732173< p > < br >
21742174$$
2175- \mathcal{H}_0=\epsilon_{II}\boldsymbol{I}\otimes\boldsymbol{I}+\epsilon_{ZI}\boldsymbol{Z}\otimes\boldsymbol{I}+\epsilon_{IZ}\boldsymbol{I}\otimes\boldsymbol{Z}+\epsilon_{II}+\epsilon_{ ZZ}\boldsymbol{Z}\otimes\boldsymbol{Z},
2175+ \mathcal{H}_0=\epsilon_{II}\boldsymbol{I}\otimes\boldsymbol{I}+\epsilon_{ZI}\boldsymbol{Z}\otimes\boldsymbol{I}+\epsilon_{IZ}\boldsymbol{I}\otimes\boldsymbol{Z}+\epsilon_{ZZ}\boldsymbol{Z}\otimes\boldsymbol{Z},
21762176$$
21772177< p > < br >
21782178
@@ -2213,10 +2213,10 @@ <h2 id="explicit-expressions">Explicit expressions </h2>
22132213< p > < br >
22142214$$
22152215\begin{align*}
2216- \boldsymbol{Z}\otimes\boldsymbol{I} & \boldsymbol{U}=\boldsymbol{I}\otimes\boldsymbol{I}\\
2217- \boldsymbol{I}\otimes\boldsymbol{Z} & \boldsymbol{U}=\text{SWAP}\\
2218- \boldsymbol{Z}\otimes\boldsymbol{Z} & \boldsymbol{U}=CX_{10}\\
2219- \boldsymbol{X}\otimes\boldsymbol{X} & \boldsymbol{U}=CX_{10}(\boldsymbol{H}\otimes\boldsymbol{H}\\
2216+ \boldsymbol{Z}\otimes\boldsymbol{I}\hspace{1cm} & \boldsymbol{U}=\boldsymbol{I}\otimes\boldsymbol{I}\\
2217+ \boldsymbol{I}\otimes\boldsymbol{Z}\hspace{1cm} & \boldsymbol{U}=\text{SWAP}\\
2218+ \boldsymbol{Z}\otimes\boldsymbol{Z}\hspace{1cm} & \boldsymbol{U}=CX_{10}\\
2219+ \boldsymbol{X}\otimes\boldsymbol{X}\hspace{1cm} & \boldsymbol{U}=CX_{10}(\boldsymbol{H}\otimes\boldsymbol{H}) \\
22202220\end{align*}
22212221$$
22222222< p > < br >
Original file line number Diff line number Diff line change @@ -2051,7 +2051,7 @@ <h2 id="the-hamiltonian-in-terms-of-pauli-boldsymbol-x-and-pauli-boldsymbol-z-ma
20512051
20522052< p > with</ p >
20532053$$
2054- \mathcal{H}_0=\epsilon_{II}\boldsymbol{I}\otimes\boldsymbol{I}+\epsilon_{ZI}\boldsymbol{Z}\otimes\boldsymbol{I}+\epsilon_{IZ}\boldsymbol{I}\otimes\boldsymbol{Z}+\epsilon_{II}+\epsilon_{ ZZ}\boldsymbol{Z}\otimes\boldsymbol{Z},
2054+ \mathcal{H}_0=\epsilon_{II}\boldsymbol{I}\otimes\boldsymbol{I}+\epsilon_{ZI}\boldsymbol{Z}\otimes\boldsymbol{I}+\epsilon_{IZ}\boldsymbol{I}\otimes\boldsymbol{Z}+\epsilon_{ZZ}\boldsymbol{Z}\otimes\boldsymbol{Z},
20552055$$
20562056
20572057< p > and</ p >
@@ -2085,10 +2085,10 @@ <h2 id="explicit-expressions">Explicit expressions </h2>
20852085< p > In order to perform our measurements, will then need the following operators \( \boldsymbol{U} \)</ p >
20862086$$
20872087\begin{align*}
2088- \boldsymbol{Z}\otimes\boldsymbol{I} & \boldsymbol{U}=\boldsymbol{I}\otimes\boldsymbol{I}\\
2089- \boldsymbol{I}\otimes\boldsymbol{Z} & \boldsymbol{U}=\text{SWAP}\\
2090- \boldsymbol{Z}\otimes\boldsymbol{Z} & \boldsymbol{U}=CX_{10}\\
2091- \boldsymbol{X}\otimes\boldsymbol{X} & \boldsymbol{U}=CX_{10}(\boldsymbol{H}\otimes\boldsymbol{H}\\
2088+ \boldsymbol{Z}\otimes\boldsymbol{I}\hspace{1cm} & \boldsymbol{U}=\boldsymbol{I}\otimes\boldsymbol{I}\\
2089+ \boldsymbol{I}\otimes\boldsymbol{Z}\hspace{1cm} & \boldsymbol{U}=\text{SWAP}\\
2090+ \boldsymbol{Z}\otimes\boldsymbol{Z}\hspace{1cm} & \boldsymbol{U}=CX_{10}\\
2091+ \boldsymbol{X}\otimes\boldsymbol{X}\hspace{1cm} & \boldsymbol{U}=CX_{10}(\boldsymbol{H}\otimes\boldsymbol{H}) \\
20922092\end{align*}
20932093$$
20942094
Original file line number Diff line number Diff line change @@ -2128,7 +2128,7 @@ <h2 id="the-hamiltonian-in-terms-of-pauli-boldsymbol-x-and-pauli-boldsymbol-z-ma
21282128
21292129< p > with</ p >
21302130$$
2131- \mathcal{H}_0=\epsilon_{II}\boldsymbol{I}\otimes\boldsymbol{I}+\epsilon_{ZI}\boldsymbol{Z}\otimes\boldsymbol{I}+\epsilon_{IZ}\boldsymbol{I}\otimes\boldsymbol{Z}+\epsilon_{II}+\epsilon_{ ZZ}\boldsymbol{Z}\otimes\boldsymbol{Z},
2131+ \mathcal{H}_0=\epsilon_{II}\boldsymbol{I}\otimes\boldsymbol{I}+\epsilon_{ZI}\boldsymbol{Z}\otimes\boldsymbol{I}+\epsilon_{IZ}\boldsymbol{I}\otimes\boldsymbol{Z}+\epsilon_{ZZ}\boldsymbol{Z}\otimes\boldsymbol{Z},
21322132$$
21332133
21342134< p > and</ p >
@@ -2162,10 +2162,10 @@ <h2 id="explicit-expressions">Explicit expressions </h2>
21622162< p > In order to perform our measurements, will then need the following operators \( \boldsymbol{U} \)</ p >
21632163$$
21642164\begin{align*}
2165- \boldsymbol{Z}\otimes\boldsymbol{I} & \boldsymbol{U}=\boldsymbol{I}\otimes\boldsymbol{I}\\
2166- \boldsymbol{I}\otimes\boldsymbol{Z} & \boldsymbol{U}=\text{SWAP}\\
2167- \boldsymbol{Z}\otimes\boldsymbol{Z} & \boldsymbol{U}=CX_{10}\\
2168- \boldsymbol{X}\otimes\boldsymbol{X} & \boldsymbol{U}=CX_{10}(\boldsymbol{H}\otimes\boldsymbol{H}\\
2165+ \boldsymbol{Z}\otimes\boldsymbol{I}\hspace{1cm} & \boldsymbol{U}=\boldsymbol{I}\otimes\boldsymbol{I}\\
2166+ \boldsymbol{I}\otimes\boldsymbol{Z}\hspace{1cm} & \boldsymbol{U}=\text{SWAP}\\
2167+ \boldsymbol{Z}\otimes\boldsymbol{Z}\hspace{1cm} & \boldsymbol{U}=CX_{10}\\
2168+ \boldsymbol{X}\otimes\boldsymbol{X}\hspace{1cm} & \boldsymbol{U}=CX_{10}(\boldsymbol{H}\otimes\boldsymbol{H}) \\
21692169\end{align*}
21702170$$
21712171
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