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doc/pub/week7/html/week7-bs.html

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@@ -970,9 +970,9 @@ <h2 id="rewriting-the-string-of-matrices" class="anchor">Rewriting the string of
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<p>Use the commutation relations of the Pauli matrices to reorder the string. The commutation relations are:</p>
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$$
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[\sigma_i, \sigma_j] = 2i \epsilon_{ijk} \sigma_k,
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\]
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where $\epsilon_{ijk}$ is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.
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$$
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<p>where \( \epsilon_{ijk} \) is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.</p>
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</div>
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</div>
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doc/pub/week7/html/week7-reveal.html

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@@ -800,22 +800,24 @@ <h2 id="rewriting-the-string-of-matrices">Rewriting the string of matrices </h2>
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<b>Commute and reorder:</b>
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<p>
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<p>Use the commutation relations of the Pauli matrices to reorder the string. The commutation relations are:</p>
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<p>&nbsp;<br>
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$$
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[\sigma_i, \sigma_j] = 2i \epsilon_{ijk} \sigma_k,
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\]
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where $\epsilon_{ijk}$ is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.
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<p>&nbsp;<br>
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$$
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<p>&nbsp;<br>
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<p>where \( \epsilon_{ijk} \) is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.</p>
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</div>
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<div class="alert alert-block alert-block alert-text-normal">
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<b>Simplify using identities:</b>
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<p>
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<p>Use the fact that \( \sigma_i^2 = I \) and \( \sigma_i \sigma_j = -\sigma_j \sigma_i \) for \( i \neq j \) to simplify the expression. For example:</p>
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$$
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<p>&nbsp;<br>
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$$
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\boldsymbol{X} \boldsymbol{Y} = -\boldsymbol{Y} \boldsymbol{X} = i \boldsymbol{X}.
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$$
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<p>&nbsp;<br>
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</div>
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</section>
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doc/pub/week7/html/week7-solarized.html

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@@ -892,9 +892,9 @@ <h2 id="rewriting-the-string-of-matrices">Rewriting the string of matrices </h2>
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<p>Use the commutation relations of the Pauli matrices to reorder the string. The commutation relations are:</p>
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$$
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[\sigma_i, \sigma_j] = 2i \epsilon_{ijk} \sigma_k,
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\]
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where $\epsilon_{ijk}$ is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.
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$$
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<p>where \( \epsilon_{ijk} \) is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.</p>
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</div>
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<div class="alert alert-block alert-block alert-text-normal">

doc/pub/week7/html/week7.html

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@@ -969,9 +969,9 @@ <h2 id="rewriting-the-string-of-matrices">Rewriting the string of matrices </h2>
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<p>Use the commutation relations of the Pauli matrices to reorder the string. The commutation relations are:</p>
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$$
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[\sigma_i, \sigma_j] = 2i \epsilon_{ijk} \sigma_k,
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\]
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where $\epsilon_{ijk}$ is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.
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$$
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<p>where \( \epsilon_{ijk} \) is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.</p>
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</div>
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<div class="alert alert-block alert-block alert-text-normal">
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