update week 11

Author: mhjensen

doc/pub/week11/html/week11-bs.html

@@ -62,6 +62,7 @@
                2,
                None,
                'discrete-fourier-transformations'),
+              ('Simple example', 2, None, 'simple-example'),
               ('More details on Discrete Fourier transforms',
                2,
                None,
@@ -248,6 +249,7 @@
      <!-- navigation toc: --> <li><a href="#output-vector" style="font-size: 80%;">Output vector</a></li>
      <!-- navigation toc: --> <li><a href="#simple-example" style="font-size: 80%;">Simple example</a></li>
      <!-- navigation toc: --> <li><a href="#discrete-fourier-transformations" style="font-size: 80%;">Discrete Fourier Transformations</a></li>
+     <!-- navigation toc: --> <li><a href="#simple-example" style="font-size: 80%;">Simple example</a></li>
      <!-- navigation toc: --> <li><a href="#more-details-on-discrete-fourier-transforms" style="font-size: 80%;">More details on Discrete Fourier transforms</a></li>
      <!-- navigation toc: --> <li><a href="#inverse-dft" style="font-size: 80%;">Inverse DFT</a></li>
      <!-- navigation toc: --> <li><a href="#orthonormality" style="font-size: 80%;">Orthonormality</a></li>
@@ -359,7 +361,7 @@ <h2 id="plans-for-the-week-of-march-31-april-4-2025" class="anchor">Plans for th
 <div class="panel-body">
 <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
 <ol>
-<li> Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (additional slides)</li>
+<li> Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (see <a href="https://en.wikipedia.org/wiki/Fast_Fourier_transform" target="_self"><tt>https://en.wikipedia.org/wiki/Fast_Fourier_transform</tt></a>)</li>
 <li> Quantum Fourier transforms (QFTs), reminder from last week</li>
 <li> Setting up circuits for QFTs</li>
 <li> Quantum phase estimation algorithm</li>
@@ -409,7 +411,7 @@ <h2 id="fast-fourier-transform-fft" class="anchor">Fast Fourier transform (FFT)
 To read more about Fast Fourier transforms and similar topics, see for example <a href="https://link.springer.com/book/10.1007/978-1-4020-6629-0" target="_self">Fast Fourier Transform - Algorithms and Applications</a>. See also <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/Textbooks/fastfourier.pdf" target="_self"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/Textbooks/fastfourier.pdf</tt></a>
 </p>
 
-<p>For a discussion of FFT, see additional slides at (address to be added)</p>
+<p>For a discussion of FFT, see for example <a href="https://en.wikipedia.org/wiki/Fast_Fourier_transform" target="_self"><tt>https://en.wikipedia.org/wiki/Fast_Fourier_transform</tt></a></p>
 
 <!-- !split -->
 <h2 id="the-discrete-fourier-transform-dft" class="anchor">The discrete Fourier transform (DFT) </h2>
@@ -485,6 +487,8 @@ <h2 id="discrete-fourier-transformations" class="anchor">Discrete Fourier Transf
 
 <p>As an example, assume \( x_0=1 \) and \( x_1=1 \). We can then use the above expression to find \( y_0 \) and \( y_1 \).</p>
 
+<!-- !split -->
+<h2 id="simple-example" class="anchor">Simple example </h2>
 <p>With the above formula we get then</p>
 $$
 \begin{align*}

doc/pub/week11/html/week11-reveal.html

@@ -198,7 +198,7 @@ <h2 id="plans-for-the-week-of-march-31-april-4-2025">Plans for the week of March
 <b></b>
 <p>
 <ol>
-<p><li> Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (additional slides)</li>
+<p><li> Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (see <a href="https://en.wikipedia.org/wiki/Fast_Fourier_transform" target="_blank"><tt>https://en.wikipedia.org/wiki/Fast_Fourier_transform</tt></a>)</li>
 <p><li> Quantum Fourier transforms (QFTs), reminder from last week</li>
 <p><li> Setting up circuits for QFTs</li>
 <p><li> Quantum phase estimation algorithm</li>
@@ -249,7 +249,7 @@ <h2 id="fast-fourier-transform-fft">Fast Fourier transform (FFT) </h2>
 To read more about Fast Fourier transforms and similar topics, see for example <a href="https://link.springer.com/book/10.1007/978-1-4020-6629-0" target="_blank">Fast Fourier Transform - Algorithms and Applications</a>. See also <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/Textbooks/fastfourier.pdf" target="_blank"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/Textbooks/fastfourier.pdf</tt></a>
 </p>
 
-<p>For a discussion of FFT, see additional slides at (address to be added)</p>
+<p>For a discussion of FFT, see for example <a href="https://en.wikipedia.org/wiki/Fast_Fourier_transform" target="_blank"><tt>https://en.wikipedia.org/wiki/Fast_Fourier_transform</tt></a></p>
 </section>
 
 <section>
@@ -336,7 +336,10 @@ <h2 id="discrete-fourier-transformations">Discrete Fourier Transformations </h2>
 <p>&nbsp;<br>
 
 <p>As an example, assume \( x_0=1 \) and \( x_1=1 \). We can then use the above expression to find \( y_0 \) and \( y_1 \).</p>
+</section>
 
+<section>
+<h2 id="simple-example">Simple example </h2>
 <p>With the above formula we get then</p>
 <p>&nbsp;<br>
 $$

doc/pub/week11/html/week11-solarized.html

@@ -89,6 +89,7 @@
                2,
                None,
                'discrete-fourier-transformations'),
+              ('Simple example', 2, None, 'simple-example'),
               ('More details on Discrete Fourier transforms',
                2,
                None,
@@ -278,7 +279,7 @@ <h2 id="plans-for-the-week-of-march-31-april-4-2025">Plans for the week of March
 <b></b>
 <p>
 <ol>
-<li> Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (additional slides)</li>
+<li> Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (see <a href="https://en.wikipedia.org/wiki/Fast_Fourier_transform" target="_blank"><tt>https://en.wikipedia.org/wiki/Fast_Fourier_transform</tt></a>)</li>
 <li> Quantum Fourier transforms (QFTs), reminder from last week</li>
 <li> Setting up circuits for QFTs</li>
 <li> Quantum phase estimation algorithm</li>
@@ -327,7 +328,7 @@ <h2 id="fast-fourier-transform-fft">Fast Fourier transform (FFT) </h2>
 To read more about Fast Fourier transforms and similar topics, see for example <a href="https://link.springer.com/book/10.1007/978-1-4020-6629-0" target="_blank">Fast Fourier Transform - Algorithms and Applications</a>. See also <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/Textbooks/fastfourier.pdf" target="_blank"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/Textbooks/fastfourier.pdf</tt></a>
 </p>
 
-<p>For a discussion of FFT, see additional slides at (address to be added)</p>
+<p>For a discussion of FFT, see for example <a href="https://en.wikipedia.org/wiki/Fast_Fourier_transform" target="_blank"><tt>https://en.wikipedia.org/wiki/Fast_Fourier_transform</tt></a></p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="the-discrete-fourier-transform-dft">The discrete Fourier transform (DFT) </h2>
@@ -403,6 +404,8 @@ <h2 id="discrete-fourier-transformations">Discrete Fourier Transformations </h2>
 
 <p>As an example, assume \( x_0=1 \) and \( x_1=1 \). We can then use the above expression to find \( y_0 \) and \( y_1 \).</p>
 
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+<h2 id="simple-example">Simple example </h2>
 <p>With the above formula we get then</p>
 $$
 \begin{align*}

doc/pub/week11/html/week11.html

@@ -166,6 +166,7 @@
                2,
                None,
                'discrete-fourier-transformations'),
+              ('Simple example', 2, None, 'simple-example'),
               ('More details on Discrete Fourier transforms',
                2,
                None,
@@ -355,7 +356,7 @@ <h2 id="plans-for-the-week-of-march-31-april-4-2025">Plans for the week of March
 <b></b>
 <p>
 <ol>
-<li> Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (additional slides)</li>
+<li> Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (see <a href="https://en.wikipedia.org/wiki/Fast_Fourier_transform" target="_blank"><tt>https://en.wikipedia.org/wiki/Fast_Fourier_transform</tt></a>)</li>
 <li> Quantum Fourier transforms (QFTs), reminder from last week</li>
 <li> Setting up circuits for QFTs</li>
 <li> Quantum phase estimation algorithm</li>
@@ -404,7 +405,7 @@ <h2 id="fast-fourier-transform-fft">Fast Fourier transform (FFT) </h2>
 To read more about Fast Fourier transforms and similar topics, see for example <a href="https://link.springer.com/book/10.1007/978-1-4020-6629-0" target="_blank">Fast Fourier Transform - Algorithms and Applications</a>. See also <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/Textbooks/fastfourier.pdf" target="_blank"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/Textbooks/fastfourier.pdf</tt></a>
 </p>
 
-<p>For a discussion of FFT, see additional slides at (address to be added)</p>
+<p>For a discussion of FFT, see for example <a href="https://en.wikipedia.org/wiki/Fast_Fourier_transform" target="_blank"><tt>https://en.wikipedia.org/wiki/Fast_Fourier_transform</tt></a></p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="the-discrete-fourier-transform-dft">The discrete Fourier transform (DFT) </h2>
@@ -480,6 +481,8 @@ <h2 id="discrete-fourier-transformations">Discrete Fourier Transformations </h2>
 
 <p>As an example, assume \( x_0=1 \) and \( x_1=1 \). We can then use the above expression to find \( y_0 \) and \( y_1 \).</p>
 
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+<h2 id="simple-example">Simple example </h2>
 <p>With the above formula we get then</p>
 $$
 \begin{align*}