update

Author: mhjensen

doc/pub/week13/html/week13-bs.html

@@ -1861,19 +1861,19 @@ <h2 id="what-will-we-need-in-the-case-of-a-quantum-computer" class="anchor">What
 <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
 <p>We will have to translate the classical data point \(\vec{x}\)
 into a quantum datapoint \(\vert \Phi{(\vec{x})} \rangle\). This can
-be achieved by a circuit \( \mathcal{U}\_\{\Phi(\vec{x})\} \vert 0\rangle \).
+be achieved by a circuit \( \mathcal{U}_{\Phi(\vec{x})} \vert 0\rangle \).
 </p>
 
-<p>Here \(\Phi()\) could be any classical function applied
-on the classical data \(\vec{x}\).
+<p>Here \( \Phi() \) could be any classical function applied
+on the classical data \( \vec{x} \).
 </p>
 </div>
 </div>
 
 <div class="panel panel-default">
 <div class="panel-body">
 <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-<p>We need a parameterized quantum circuit \(W( \theta )\) that
+<p>We need a parameterized quantum circuit \( W(\theta) \) that
 processes the data in a way that in the end we
 can apply a measurement that returns a classical value \(-1\) or
 \(1\) for each classical input \(\vec{x}\) that indentifies the label
@@ -1887,16 +1887,23 @@ <h2 id="what-will-we-need-in-the-case-of-a-quantum-computer" class="anchor">What
 <h2 id="the-most-general-ansatz" class="anchor">The most general ansatz </h2>
 
 <p>Following these steps we can define an ansatz for this kind of problem
-which is \(W(\theta) \mathcal{U}_{\Phi}(\vec{x}) \vert 0 \rangle\).
+which is
 </p>
+$$
+W(\theta) \mathcal{U}_{\Phi}(\vec{x}) \vert 0 \rangle.
+$$
 
-<p>These kind of ansatz are called quantum variational circuits.</p>
+<p>These kind of ansatzes are called quantum variational circuits.</p>
 
 <!-- !split -->
 <h2 id="quantum-svm" class="anchor">Quantum SVM </h2>
 
-<p>In the case of a quantum SVM we will only used the quantum feature maps
-\(\mathcal{U}_{\Phi(\vec{x})}\) to translate the classical data into
+<p>In the case of a quantum SVM we will only use the quantum feature maps</p>
+$$
+\mathcal{U}_{\Phi(\vec{x})},
+$$
+
+<p>to translate the classical data into
 quantum states and build the Kernel of the SVM out of these quantum
 states. After calculating the Kernel matrix on the quantum computer we
 can train the Quantum SVM the same way as the classical SVM.
@@ -1907,10 +1914,19 @@ <h2 id="defining-the-quantum-kernel" class="anchor">Defining the Quantum Kernel
 
 <p>The idea of the quantum kernel is exactly the same as in the classical
 case. We take the inner product
-\(K(\vec{x}, \vec{z}) = \vert \langle \Phi (\vec{x}) \vert \Phi(\vec{z}) \rangle \vert^2 = \langle 0^n \vert \mathcal{U}_{\Phi(\vec{x})}^{t} \mathcal{U}_{\Phi(\vec{z})} \vert 0^n \rangle\),
-but now with the quantum feature maps \(\mathcal{U}_{\Phi(\vec{x})}\).
-The idea is that if we choose a quantum feature maps that is not easy to
-simulate with a classical computer we might obtain a quantum advantage.
+</p>
+$$
+K(\vec{x}, \vec{z}) = \vert \langle \Phi (\vec{x}) \vert \Phi(\vec{z}) \rangle \vert^2 = \langle 0^n \vert \mathcal{U}_{\Phi(\vec{x})}^{t} \mathcal{U}_{\Phi(\vec{z})} \vert 0^n \rangle,
+$$
+
+<p>but now with the quantum feature maps</p>
+$$
+\mathcal{U}_{\Phi(\vec{x})}.
+$$
+
+<p>The idea is that if we choose a quantum feature maps that is not easy
+to simulate with a classical computer we might obtain a quantum
+advantage.
 </p>
 
 <!-- !split -->

doc/pub/week13/html/week13-reveal.html

@@ -1918,18 +1918,18 @@ <h2 id="what-will-we-need-in-the-case-of-a-quantum-computer">What will we need i
 <p>
 <p>We will have to translate the classical data point \(\vec{x}\)
 into a quantum datapoint \(\vert \Phi{(\vec{x})} \rangle\). This can
-be achieved by a circuit \( \mathcal{U}\_\{\Phi(\vec{x})\} \vert 0\rangle \).
+be achieved by a circuit \( \mathcal{U}_{\Phi(\vec{x})} \vert 0\rangle \).
 </p>
 
-<p>Here \(\Phi()\) could be any classical function applied
-on the classical data \(\vec{x}\).
+<p>Here \( \Phi() \) could be any classical function applied
+on the classical data \( \vec{x} \).
 </p>
 </div>
 
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
-<p>We need a parameterized quantum circuit \(W( \theta )\) that
+<p>We need a parameterized quantum circuit \( W(\theta) \) that
 processes the data in a way that in the end we
 can apply a measurement that returns a classical value \(-1\) or
 \(1\) for each classical input \(\vec{x}\) that indentifies the label
@@ -1942,17 +1942,28 @@ <h2 id="what-will-we-need-in-the-case-of-a-quantum-computer">What will we need i
 <h2 id="the-most-general-ansatz">The most general ansatz </h2>
 
 <p>Following these steps we can define an ansatz for this kind of problem
-which is \(W(\theta) \mathcal{U}_{\Phi}(\vec{x}) \vert 0 \rangle\).
+which is
 </p>
+<p>&nbsp;<br>
+$$
+W(\theta) \mathcal{U}_{\Phi}(\vec{x}) \vert 0 \rangle.
+$$
+<p>&nbsp;<br>
 
-<p>These kind of ansatz are called quantum variational circuits.</p>
+<p>These kind of ansatzes are called quantum variational circuits.</p>
 </section>
 
 <section>
 <h2 id="quantum-svm">Quantum SVM </h2>
 
-<p>In the case of a quantum SVM we will only used the quantum feature maps
-\(\mathcal{U}_{\Phi(\vec{x})}\) to translate the classical data into
+<p>In the case of a quantum SVM we will only use the quantum feature maps</p>
+<p>&nbsp;<br>
+$$
+\mathcal{U}_{\Phi(\vec{x})},
+$$
+<p>&nbsp;<br>
+
+<p>to translate the classical data into
 quantum states and build the Kernel of the SVM out of these quantum
 states. After calculating the Kernel matrix on the quantum computer we
 can train the Quantum SVM the same way as the classical SVM.
@@ -1964,10 +1975,23 @@ <h2 id="defining-the-quantum-kernel">Defining the Quantum Kernel </h2>
 
 <p>The idea of the quantum kernel is exactly the same as in the classical
 case. We take the inner product
-\(K(\vec{x}, \vec{z}) = \vert \langle \Phi (\vec{x}) \vert \Phi(\vec{z}) \rangle \vert^2 = \langle 0^n \vert \mathcal{U}_{\Phi(\vec{x})}^{t} \mathcal{U}_{\Phi(\vec{z})} \vert 0^n \rangle\),
-but now with the quantum feature maps \(\mathcal{U}_{\Phi(\vec{x})}\).
-The idea is that if we choose a quantum feature maps that is not easy to
-simulate with a classical computer we might obtain a quantum advantage.
+</p>
+<p>&nbsp;<br>
+$$
+K(\vec{x}, \vec{z}) = \vert \langle \Phi (\vec{x}) \vert \Phi(\vec{z}) \rangle \vert^2 = \langle 0^n \vert \mathcal{U}_{\Phi(\vec{x})}^{t} \mathcal{U}_{\Phi(\vec{z})} \vert 0^n \rangle,
+$$
+<p>&nbsp;<br>
+
+<p>but now with the quantum feature maps</p>
+<p>&nbsp;<br>
+$$
+\mathcal{U}_{\Phi(\vec{x})}.
+$$
+<p>&nbsp;<br>
+
+<p>The idea is that if we choose a quantum feature maps that is not easy
+to simulate with a classical computer we might obtain a quantum
+advantage.
 </p>
 </section>
 

doc/pub/week13/html/week13-solarized.html

@@ -1778,18 +1778,18 @@ <h2 id="what-will-we-need-in-the-case-of-a-quantum-computer">What will we need i
 <p>
 <p>We will have to translate the classical data point \(\vec{x}\)
 into a quantum datapoint \(\vert \Phi{(\vec{x})} \rangle\). This can
-be achieved by a circuit \( \mathcal{U}\_\{\Phi(\vec{x})\} \vert 0\rangle \).
+be achieved by a circuit \( \mathcal{U}_{\Phi(\vec{x})} \vert 0\rangle \).
 </p>
 
-<p>Here \(\Phi()\) could be any classical function applied
-on the classical data \(\vec{x}\).
+<p>Here \( \Phi() \) could be any classical function applied
+on the classical data \( \vec{x} \).
 </p>
 </div>
 
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
-<p>We need a parameterized quantum circuit \(W( \theta )\) that
+<p>We need a parameterized quantum circuit \( W(\theta) \) that
 processes the data in a way that in the end we
 can apply a measurement that returns a classical value \(-1\) or
 \(1\) for each classical input \(\vec{x}\) that indentifies the label
@@ -1802,16 +1802,23 @@ <h2 id="what-will-we-need-in-the-case-of-a-quantum-computer">What will we need i
 <h2 id="the-most-general-ansatz">The most general ansatz </h2>
 
 <p>Following these steps we can define an ansatz for this kind of problem
-which is \(W(\theta) \mathcal{U}_{\Phi}(\vec{x}) \vert 0 \rangle\).
+which is
 </p>
+$$
+W(\theta) \mathcal{U}_{\Phi}(\vec{x}) \vert 0 \rangle.
+$$
 
-<p>These kind of ansatz are called quantum variational circuits.</p>
+<p>These kind of ansatzes are called quantum variational circuits.</p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="quantum-svm">Quantum SVM </h2>
 
-<p>In the case of a quantum SVM we will only used the quantum feature maps
-\(\mathcal{U}_{\Phi(\vec{x})}\) to translate the classical data into
+<p>In the case of a quantum SVM we will only use the quantum feature maps</p>
+$$
+\mathcal{U}_{\Phi(\vec{x})},
+$$
+
+<p>to translate the classical data into
 quantum states and build the Kernel of the SVM out of these quantum
 states. After calculating the Kernel matrix on the quantum computer we
 can train the Quantum SVM the same way as the classical SVM.
@@ -1822,10 +1829,19 @@ <h2 id="defining-the-quantum-kernel">Defining the Quantum Kernel </h2>
 
 <p>The idea of the quantum kernel is exactly the same as in the classical
 case. We take the inner product
-\(K(\vec{x}, \vec{z}) = \vert \langle \Phi (\vec{x}) \vert \Phi(\vec{z}) \rangle \vert^2 = \langle 0^n \vert \mathcal{U}_{\Phi(\vec{x})}^{t} \mathcal{U}_{\Phi(\vec{z})} \vert 0^n \rangle\),
-but now with the quantum feature maps \(\mathcal{U}_{\Phi(\vec{x})}\).
-The idea is that if we choose a quantum feature maps that is not easy to
-simulate with a classical computer we might obtain a quantum advantage.
+</p>
+$$
+K(\vec{x}, \vec{z}) = \vert \langle \Phi (\vec{x}) \vert \Phi(\vec{z}) \rangle \vert^2 = \langle 0^n \vert \mathcal{U}_{\Phi(\vec{x})}^{t} \mathcal{U}_{\Phi(\vec{z})} \vert 0^n \rangle,
+$$
+
+<p>but now with the quantum feature maps</p>
+$$
+\mathcal{U}_{\Phi(\vec{x})}.
+$$
+
+<p>The idea is that if we choose a quantum feature maps that is not easy
+to simulate with a classical computer we might obtain a quantum
+advantage.
 </p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>

doc/pub/week13/html/week13.html

@@ -1855,18 +1855,18 @@ <h2 id="what-will-we-need-in-the-case-of-a-quantum-computer">What will we need i
 <p>
 <p>We will have to translate the classical data point \(\vec{x}\)
 into a quantum datapoint \(\vert \Phi{(\vec{x})} \rangle\). This can
-be achieved by a circuit \( \mathcal{U}\_\{\Phi(\vec{x})\} \vert 0\rangle \).
+be achieved by a circuit \( \mathcal{U}_{\Phi(\vec{x})} \vert 0\rangle \).
 </p>
 
-<p>Here \(\Phi()\) could be any classical function applied
-on the classical data \(\vec{x}\).
+<p>Here \( \Phi() \) could be any classical function applied
+on the classical data \( \vec{x} \).
 </p>
 </div>
 
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
-<p>We need a parameterized quantum circuit \(W( \theta )\) that
+<p>We need a parameterized quantum circuit \( W(\theta) \) that
 processes the data in a way that in the end we
 can apply a measurement that returns a classical value \(-1\) or
 \(1\) for each classical input \(\vec{x}\) that indentifies the label
@@ -1879,16 +1879,23 @@ <h2 id="what-will-we-need-in-the-case-of-a-quantum-computer">What will we need i
 <h2 id="the-most-general-ansatz">The most general ansatz </h2>
 
 <p>Following these steps we can define an ansatz for this kind of problem
-which is \(W(\theta) \mathcal{U}_{\Phi}(\vec{x}) \vert 0 \rangle\).
+which is
 </p>
+$$
+W(\theta) \mathcal{U}_{\Phi}(\vec{x}) \vert 0 \rangle.
+$$
 
-<p>These kind of ansatz are called quantum variational circuits.</p>
+<p>These kind of ansatzes are called quantum variational circuits.</p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="quantum-svm">Quantum SVM </h2>
 
-<p>In the case of a quantum SVM we will only used the quantum feature maps
-\(\mathcal{U}_{\Phi(\vec{x})}\) to translate the classical data into
+<p>In the case of a quantum SVM we will only use the quantum feature maps</p>
+$$
+\mathcal{U}_{\Phi(\vec{x})},
+$$
+
+<p>to translate the classical data into
 quantum states and build the Kernel of the SVM out of these quantum
 states. After calculating the Kernel matrix on the quantum computer we
 can train the Quantum SVM the same way as the classical SVM.
@@ -1899,10 +1906,19 @@ <h2 id="defining-the-quantum-kernel">Defining the Quantum Kernel </h2>
 
 <p>The idea of the quantum kernel is exactly the same as in the classical
 case. We take the inner product
-\(K(\vec{x}, \vec{z}) = \vert \langle \Phi (\vec{x}) \vert \Phi(\vec{z}) \rangle \vert^2 = \langle 0^n \vert \mathcal{U}_{\Phi(\vec{x})}^{t} \mathcal{U}_{\Phi(\vec{z})} \vert 0^n \rangle\),
-but now with the quantum feature maps \(\mathcal{U}_{\Phi(\vec{x})}\).
-The idea is that if we choose a quantum feature maps that is not easy to
-simulate with a classical computer we might obtain a quantum advantage.
+</p>
+$$
+K(\vec{x}, \vec{z}) = \vert \langle \Phi (\vec{x}) \vert \Phi(\vec{z}) \rangle \vert^2 = \langle 0^n \vert \mathcal{U}_{\Phi(\vec{x})}^{t} \mathcal{U}_{\Phi(\vec{z})} \vert 0^n \rangle,
+$$
+
+<p>but now with the quantum feature maps</p>
+$$
+\mathcal{U}_{\Phi(\vec{x})}.
+$$
+
+<p>The idea is that if we choose a quantum feature maps that is not easy
+to simulate with a classical computer we might obtain a quantum
+advantage.
 </p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>