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update on week 10
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‎doc/pub/week10/html/week10-bs.html‎

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None,
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'possible-paths-for-project-2'),
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('Overarching motivation', 2, None, 'overarching-motivation'),
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('Quantum Fourier Transforms (QFTs)',
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'quantum-fourier-transforms-qfts'),
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('Why Quantum Fourier Transforms and exponential speedup',
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('Quantum Fourier Transforms and implementation',
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('Why Quantum Fourier Transforms? VI',
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('Why Quantum Fourier Transforms? I',
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('A familiar case', 2, None, 'a-familiar-case'),
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('Several driving forces', 2, None, 'several-driving-forces'),
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('Periodicity', 2, None, 'periodicity'),
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<!-- navigation toc: --> <li><a href="#plans-for-the-week-of-march-24-28-2025" style="font-size: 80%;"><b>Plans for the week of March 24-28, 2025</b></a></li>
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<!-- navigation toc: --> <li><a href="#possible-paths-for-project-2" style="font-size: 80%;"><b>Possible paths for project 2</b></a></li>
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<!-- navigation toc: --> <li><a href="#overarching-motivation" style="font-size: 80%;"><b>Overarching motivation</b></a></li>
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<!-- navigation toc: --> <li><a href="#quantum-fourier-transforms-qfts" style="font-size: 80%;"><b>Quantum Fourier Transforms (QFTs)</b></a></li>
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<!-- navigation toc: --> <li><a href="#why-quantum-fourier-transforms-and-exponential-speedup" style="font-size: 80%;"><b>Why Quantum Fourier Transforms and exponential speedup</b></a></li>
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<!-- navigation toc: --> <li><a href="#quantum-fourier-transforms-and-quantum-parallelism" style="font-size: 80%;"><b>Quantum Fourier Transforms and quantum parallelism</b></a></li>
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<!-- navigation toc: --> <li><a href="#quantum-fourier-transforms-and-implementation" style="font-size: 80%;"><b>Quantum Fourier Transforms and implementation</b></a></li>
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<!-- navigation toc: --> <li><a href="#why-quantum-fourier-transforms-vi" style="font-size: 80%;"><b>Why Quantum Fourier Transforms? VI</b></a></li>
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<!-- navigation toc: --> <li><a href="#why-quantum-fourier-transforms-i" style="font-size: 80%;"><b>Why Quantum Fourier Transforms? I</b></a></li>
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<!-- navigation toc: --> <li><a href="#a-familiar-case" style="font-size: 80%;"><b>A familiar case</b></a></li>
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<!-- navigation toc: --> <li><a href="#several-driving-forces" style="font-size: 80%;"><b>Several driving forces</b></a></li>
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<!-- navigation toc: --> <li><a href="#periodicity" style="font-size: 80%;"><b>Periodicity</b></a></li>
@@ -392,6 +422,45 @@ <h2 id="overarching-motivation" class="anchor">Overarching motivation </h2>
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items.
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</p>
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<!-- !split -->
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<h2 id="quantum-fourier-transforms-qfts" class="anchor">Quantum Fourier Transforms (QFTs) </h2>
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<ol>
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<li> QFTs are the quantum analogue of the Discrete Fourier Transforms (DFTs).</li>
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<li> They play a crucial role in quantum algorithms like Shor&#8217;s Algorithm and Quantum Phase Estimation.</li>
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<li> QFTs provide an <em>exponential speedup</em> over classical Fourier Transform methods.</li>
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</ol>
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<!-- !split -->
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<h2 id="why-quantum-fourier-transforms-and-exponential-speedup" class="anchor">Why Quantum Fourier Transforms and exponential speedup </h2>
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<ol>
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<li> Classical Discrete Fourier Transforms (DFTs) require \( O(N^2) \) operations.</li>
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<li> The Fast Fourier Transform (FFT) improves this to \( O(N \log N) \) operations.</li>
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<li> QFTs reduce complexity to \( O((\log N)^2) \) using quantum gates.</li>
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</ol>
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<!-- !split -->
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<h2 id="quantum-fourier-transforms-and-quantum-parallelism" class="anchor">Quantum Fourier Transforms and quantum parallelism </h2>
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<ol>
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<li> QFTs acts on a <em>superposition</em> of states, processing all inputs simultaneously.</li>
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<li> This is crucial in algorithms like:
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<ol type="a"></li>
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<li> Shor&#8217;s Algorithm for factoring large numbers.</li>
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<li> Quantum Phase Estimation (QPE) for eigenvalue extraction.</li>
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</ol>
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</ol>
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<!-- !split -->
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<h2 id="quantum-fourier-transforms-and-implementation" class="anchor">Quantum Fourier Transforms and implementation </h2>
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<ol>
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<li> QFT requires only <em>Hadamard gates and controlled-phase gates</em>.</li>
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<li> A 3-qubit QFT circuit uses only \( O(n^2) \).</li>
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<li> This makes QFT highly efficient for <em>quantum hardware</em>.</li>
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</ol>
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<!-- !split -->
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<h2 id="why-quantum-fourier-transforms-vi" class="anchor">Why Quantum Fourier Transforms? VI </h2>
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<!-- !split -->
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<h2 id="why-quantum-fourier-transforms-i" class="anchor">Why Quantum Fourier Transforms? I </h2>
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<!-- !split -->
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<h2 id="a-familiar-case" class="anchor">A familiar case </h2>
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‎doc/pub/week10/html/week10-reveal.html‎

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</p>
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</section>
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<section>
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<h2 id="quantum-fourier-transforms-qfts">Quantum Fourier Transforms (QFTs) </h2>
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<ol>
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<p><li> QFTs are the quantum analogue of the Discrete Fourier Transforms (DFTs).</li>
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<p><li> They play a crucial role in quantum algorithms like Shor&#8217;s Algorithm and Quantum Phase Estimation.</li>
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<p><li> QFTs provide an <em>exponential speedup</em> over classical Fourier Transform methods.</li>
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</ol>
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</section>
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<section>
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<h2 id="why-quantum-fourier-transforms-and-exponential-speedup">Why Quantum Fourier Transforms and exponential speedup </h2>
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<ol>
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<p><li> Classical Discrete Fourier Transforms (DFTs) require \( O(N^2) \) operations.</li>
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<p><li> The Fast Fourier Transform (FFT) improves this to \( O(N \log N) \) operations.</li>
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<p><li> QFTs reduce complexity to \( O((\log N)^2) \) using quantum gates.</li>
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</ol>
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</section>
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<section>
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<h2 id="quantum-fourier-transforms-and-quantum-parallelism">Quantum Fourier Transforms and quantum parallelism </h2>
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<ol>
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<p><li> QFTs acts on a <em>superposition</em> of states, processing all inputs simultaneously.</li>
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<p><li> This is crucial in algorithms like:
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<ol type="a"></li>
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<p><li> Shor&#8217;s Algorithm for factoring large numbers.</li>
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<p><li> Quantum Phase Estimation (QPE) for eigenvalue extraction.</li>
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</ol>
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<p>
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</ol>
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</section>
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<section>
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<h2 id="quantum-fourier-transforms-and-implementation">Quantum Fourier Transforms and implementation </h2>
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<ol>
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<p><li> QFT requires only <em>Hadamard gates and controlled-phase gates</em>.</li>
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<p><li> A 3-qubit QFT circuit uses only \( O(n^2) \).</li>
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<p><li> This makes QFT highly efficient for <em>quantum hardware</em>.</li>
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</ol>
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</section>
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<section>
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<h2 id="why-quantum-fourier-transforms-vi">Why Quantum Fourier Transforms? VI </h2>
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</section>
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<section>
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<h2 id="why-quantum-fourier-transforms-i">Why Quantum Fourier Transforms? I </h2>
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</section>
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<section>
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<h2 id="a-familiar-case">A familiar case </h2>
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‎doc/pub/week10/html/week10-solarized.html‎

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('Periodicity', 2, None, 'periodicity'),
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items.
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</p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="quantum-fourier-transforms-qfts">Quantum Fourier Transforms (QFTs) </h2>
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<ol>
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<li> QFTs are the quantum analogue of the Discrete Fourier Transforms (DFTs).</li>
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<li> They play a crucial role in quantum algorithms like Shor&#8217;s Algorithm and Quantum Phase Estimation.</li>
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<li> QFTs provide an <em>exponential speedup</em> over classical Fourier Transform methods.</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="why-quantum-fourier-transforms-and-exponential-speedup">Why Quantum Fourier Transforms and exponential speedup </h2>
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<ol>
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<li> Classical Discrete Fourier Transforms (DFTs) require \( O(N^2) \) operations.</li>
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<li> The Fast Fourier Transform (FFT) improves this to \( O(N \log N) \) operations.</li>
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<li> QFTs reduce complexity to \( O((\log N)^2) \) using quantum gates.</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="quantum-fourier-transforms-and-quantum-parallelism">Quantum Fourier Transforms and quantum parallelism </h2>
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<ol>
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<li> QFTs acts on a <em>superposition</em> of states, processing all inputs simultaneously.</li>
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<li> This is crucial in algorithms like:
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<ol type="a"></li>
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<li> Shor&#8217;s Algorithm for factoring large numbers.</li>
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<li> Quantum Phase Estimation (QPE) for eigenvalue extraction.</li>
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</ol>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="quantum-fourier-transforms-and-implementation">Quantum Fourier Transforms and implementation </h2>
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<ol>
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<li> QFT requires only <em>Hadamard gates and controlled-phase gates</em>.</li>
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<li> A 3-qubit QFT circuit uses only \( O(n^2) \).</li>
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<li> This makes QFT highly efficient for <em>quantum hardware</em>.</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="why-quantum-fourier-transforms-vi">Why Quantum Fourier Transforms? VI </h2>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="why-quantum-fourier-transforms-i">Why Quantum Fourier Transforms? I </h2>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="a-familiar-case">A familiar case </h2>
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‎doc/pub/week10/html/week10.html‎

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('A familiar case', 2, None, 'a-familiar-case'),
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('Several driving forces', 2, None, 'several-driving-forces'),
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('Periodicity', 2, None, 'periodicity'),
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</p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="quantum-fourier-transforms-qfts">Quantum Fourier Transforms (QFTs) </h2>
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<ol>
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<li> QFTs are the quantum analogue of the Discrete Fourier Transforms (DFTs).</li>
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<li> They play a crucial role in quantum algorithms like Shor&#8217;s Algorithm and Quantum Phase Estimation.</li>
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<li> QFTs provide an <em>exponential speedup</em> over classical Fourier Transform methods.</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="why-quantum-fourier-transforms-and-exponential-speedup">Why Quantum Fourier Transforms and exponential speedup </h2>
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<ol>
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<li> Classical Discrete Fourier Transforms (DFTs) require \( O(N^2) \) operations.</li>
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<li> The Fast Fourier Transform (FFT) improves this to \( O(N \log N) \) operations.</li>
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<li> QFTs reduce complexity to \( O((\log N)^2) \) using quantum gates.</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="quantum-fourier-transforms-and-quantum-parallelism">Quantum Fourier Transforms and quantum parallelism </h2>
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<ol>
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<li> QFTs acts on a <em>superposition</em> of states, processing all inputs simultaneously.</li>
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<li> This is crucial in algorithms like:
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<ol type="a"></li>
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<li> Shor&#8217;s Algorithm for factoring large numbers.</li>
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<li> Quantum Phase Estimation (QPE) for eigenvalue extraction.</li>
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</ol>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="quantum-fourier-transforms-and-implementation">Quantum Fourier Transforms and implementation </h2>
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<ol>
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<li> QFT requires only <em>Hadamard gates and controlled-phase gates</em>.</li>
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<li> A 3-qubit QFT circuit uses only \( O(n^2) \).</li>
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<li> This makes QFT highly efficient for <em>quantum hardware</em>.</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="why-quantum-fourier-transforms-vi">Why Quantum Fourier Transforms? VI </h2>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="why-quantum-fourier-transforms-i">Why Quantum Fourier Transforms? I </h2>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="a-familiar-case">A familiar case </h2>
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‎doc/pub/week10/ipynb/ipynb-week10-src.tar.gz‎

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