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update week 11
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‎doc/pub/week11/html/week11-bs.html‎

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'plans-for-the-week-of-march-31-april-4-2025'),
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('Possible paths for project 2',
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2,
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None,
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'possible-paths-for-project-2'),
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('Brief reminder on Fourier transforms',
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2,
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None,
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('Inverse DFT', 2, None, 'inverse-dft'),
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('Orthonormality', 2, None, 'orthonormality'),
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('Inverse transform', 2, None, 'inverse-transform'),
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('Fast Fourier transform and polynomial multiplication',
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2,
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None,
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'fast-fourier-transform-and-polynomial-multiplication'),
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('From DFT to QFT', 2, None, 'from-dft-to-qft'),
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('In terms of arbitrary states',
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2,
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="#plans-for-the-week-of-march-31-april-4-2025" style="font-size: 80%;">Plans for the week of March 31-April 4, 2025</a></li>
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<!-- navigation toc: --> <li><a href="#possible-paths-for-project-2" style="font-size: 80%;">Possible paths for project 2</a></li>
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<!-- navigation toc: --> <li><a href="#brief-reminder-on-fourier-transforms" style="font-size: 80%;">Brief reminder on Fourier transforms</a></li>
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<!-- navigation toc: --> <li><a href="#discrete-fourier-transforms" style="font-size: 80%;">Discrete Fourier transforms</a></li>
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<!-- navigation toc: --> <li><a href="#fast-fourier-transform-fft" style="font-size: 80%;">Fast Fourier transform (FFT)</a></li>
@@ -194,7 +185,6 @@
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<!-- navigation toc: --> <li><a href="#inverse-dft" style="font-size: 80%;">Inverse DFT</a></li>
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<!-- navigation toc: --> <li><a href="#orthonormality" style="font-size: 80%;">Orthonormality</a></li>
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<!-- navigation toc: --> <li><a href="#inverse-transform" style="font-size: 80%;">Inverse transform</a></li>
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<!-- navigation toc: --> <li><a href="#fast-fourier-transform-and-polynomial-multiplication" style="font-size: 80%;">Fast Fourier transform and polynomial multiplication</a></li>
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<!-- navigation toc: --> <li><a href="#from-dft-to-qft" style="font-size: 80%;">From DFT to QFT</a></li>
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<!-- navigation toc: --> <li><a href="#in-terms-of-arbitrary-states" style="font-size: 80%;">In terms of arbitrary states</a></li>
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<!-- navigation toc: --> <li><a href="#unitarity" style="font-size: 80%;">Unitarity</a></li>
@@ -261,14 +251,11 @@ <h1>Quantum Computing, Quantum Machine Learning and Quantum Information Theories
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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b> [1, 2]
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</center>
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<!-- institution(s) -->
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<center>
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[1] <b>Department of Physics, University of Oslo</b>
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<b>Morten Hjorth-Jensen</b>
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</center>
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<!-- institution -->
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<center>
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[2] <b>Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University</b>
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<b>Department of Physics, University of Oslo, Norway</b>
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</center>
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<br>
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<center>
@@ -286,37 +273,23 @@ <h2 id="plans-for-the-week-of-march-31-april-4-2025" class="anchor">Plans for th
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<div class="panel-body">
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<!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
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<ol>
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<li> Discrete Fourier transforms (DFTs) and the fast Fourier Transform (FFT)</li>
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<li> Quantum Fourier transforms (QFTs), basic mathematical expressions</li>
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<li> Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (additional slides)</li>
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<li> Quantum Fourier transforms (QFTs), reminder from last week</li>
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<li> Setting up circuits for QFT</li>
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<li> Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT.</li>
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<li> <a href="https://youtu.be/" target="_self">Video of lecture TBA</a>
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<li> Quantum phase estimation algorithm</li>
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<li> Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT.
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<!-- o <a href="https://youtu.be/" target="_self">Video of lecture TBA</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2024/NotesApril3.pdf" target="_self">Whiteboard notes</a> --></li>
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</ol>
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</div>
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</div>
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<!-- !split -->
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<h2 id="possible-paths-for-project-2" class="anchor">Possible paths for project 2 </h2>
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<ul>
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<li> Implement QFTs</li>
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<li> Study other algorithms
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<ol type="a"></li>
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<li> Deutsch-Jozsa algorithm: Determine if a function is constant or balance using the fewest number of queries.</li>
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<li> SImon's algorithm: Determine if a function (Oracle) is one-to-one or two-to-one</li>
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<li> Grover's algorithm: Search unstructured list of data fast</li>
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<li> Possibly: Shor's algorithm and how to Factorize integers efficiently</li>
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</ol>
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<li> Study the solution of quantum mechanical eigenvalue problems with systems from atomic/molecular physics and quantum chemistry</li>
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<li> Quantum machine learning projects, quantum boltzmann machines or related topics
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<!-- For project 2, in order to be time efficient, you can use software like Qiskit, Pennylane, qBraid and/or other --></li>
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</ul>
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<!-- !split -->
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<h2 id="brief-reminder-on-fourier-transforms" class="anchor">Brief reminder on Fourier transforms </h2>
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<p>Last week we reviewed some basic properties of Fourier transforms. We restate some of these results here.
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<p>Last week we reviewed some basic properties of Fourier transforms and derived the expressions for the quantum Fourier variant.
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We restate some of these results here.
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<a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/pub/week10/ipynb/week10.ipynb" target="_self">For more information, see slides from previous week</a>
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</p>
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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>
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</p>
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<p>Our emphasis is on the link between discrete Fourier transforms and quantum Fourier transforms. We will not discuss FFT in this course.</p>
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<p>For a discussion of FFT, see additional slides at (address to be added)</p>
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<!-- !split -->
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<h2 id="the-discrete-fourier-transform-dft" class="anchor">The discrete Fourier transform (DFT) </h2>
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$$
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<!-- !split -->
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<h2 id="fast-fourier-transform-and-polynomial-multiplication" class="anchor">Fast Fourier transform and polynomial multiplication </h2>
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<p>The FFT algorithm is an \( O(n\log{n}) \) divide and conquer algorithm for DFT, used by
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Gauss circa 1805, and popularized by Cooley and Turkey and 1965. Gauss used the
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algorithm to determine periodic asteroid orbits, while Cooley and Turkey used it to
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detect Soviet nuclear tests from o&#64256;shore readings.
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A practical implementation of FFT is FFTW, which was described by Frigo and
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Johnson at MIT. The algorithm is often implemented directly in hardware, for fixed \( n \).
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</p>
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<!-- !split -->
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<h2 id="from-dft-to-qft" class="anchor">From DFT to QFT </h2>
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</footer>
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-->
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<center style="font-size:80%">
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<!-- copyright --> &copy; 1999-2024, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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<!-- copyright --> &copy; 1999-2025, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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‎doc/pub/week11/html/week11-reveal.html‎

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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b> [1, 2]
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<b>Morten Hjorth-Jensen</b>
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</center>
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<!-- institution(s) -->
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<!-- institution -->
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<center>
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[1] <b>Department of Physics, University of Oslo</b>
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</center>
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<center>
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[2] <b>Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University</b>
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<b>Department of Physics, University of Oslo, Norway</b>
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</center>
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<br>
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<center>
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<center style="font-size:80%">
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<!-- copyright --> &copy; 1999-2024, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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<!-- copyright --> &copy; 1999-2025, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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</center>
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</section>
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<b></b>
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<p>
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<ol>
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<p><li> Discrete Fourier transforms (DFTs) and the fast Fourier Transform (FFT)</li>
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<p><li> Quantum Fourier transforms (QFTs), basic mathematical expressions</li>
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<p><li> Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (additional slides)</li>
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<p><li> Quantum Fourier transforms (QFTs), reminder from last week</li>
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<p><li> Setting up circuits for QFT</li>
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<p><li> Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT.</li>
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<p><li> <a href="https://youtu.be/" target="_blank">Video of lecture TBA</a>
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<p><li> Quantum phase estimation algorithm</li>
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<p><li> Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT.
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<!-- o <a href="https://youtu.be/" target="_blank">Video of lecture TBA</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2024/NotesApril3.pdf" target="_blank">Whiteboard notes</a> --></li>
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</ol>
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</div>
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</section>
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<section>
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<h2 id="possible-paths-for-project-2">Possible paths for project 2 </h2>
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<ul>
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<p><li> Implement QFTs</li>
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<p><li> Study other algorithms
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<ol type="a"></li>
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<p><li> Deutsch-Jozsa algorithm: Determine if a function is constant or balance using the fewest number of queries.</li>
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<p><li> SImon's algorithm: Determine if a function (Oracle) is one-to-one or two-to-one</li>
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<p><li> Grover's algorithm: Search unstructured list of data fast</li>
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<p><li> Possibly: Shor's algorithm and how to Factorize integers efficiently</li>
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</ol>
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<p>
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<p><li> Study the solution of quantum mechanical eigenvalue problems with systems from atomic/molecular physics and quantum chemistry</li>
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<p><li> Quantum machine learning projects, quantum boltzmann machines or related topics
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<!-- For project 2, in order to be time efficient, you can use software like Qiskit, Pennylane, qBraid and/or other --></li>
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</ul>
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</section>
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<section>
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<h2 id="brief-reminder-on-fourier-transforms">Brief reminder on Fourier transforms </h2>
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<p>Last week we reviewed some basic properties of Fourier transforms. We restate some of these results here.
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<p>Last week we reviewed some basic properties of Fourier transforms and derived the expressions for the quantum Fourier variant.
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We restate some of these results here.
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<a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/pub/week10/ipynb/week10.ipynb" target="_blank">For more information, see slides from previous week</a>
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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>
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</p>
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<p>Our emphasis is on the link between discrete Fourier transforms and quantum Fourier transforms. We will not discuss FFT in this course.</p>
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<p>For a discussion of FFT, see additional slides at (address to be added)</p>
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<p>&nbsp;<br>
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<h2 id="fast-fourier-transform-and-polynomial-multiplication">Fast Fourier transform and polynomial multiplication </h2>
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<p>The FFT algorithm is an \( O(n\log{n}) \) divide and conquer algorithm for DFT, used by
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Gauss circa 1805, and popularized by Cooley and Turkey and 1965. Gauss used the
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algorithm to determine periodic asteroid orbits, while Cooley and Turkey used it to
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detect Soviet nuclear tests from o&#64256;shore readings.
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A practical implementation of FFT is FFTW, which was described by Frigo and
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Johnson at MIT. The algorithm is often implemented directly in hardware, for fixed \( n \).
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<h2 id="from-dft-to-qft">From DFT to QFT </h2>
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‎doc/pub/week11/html/week11-solarized.html‎

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'plans-for-the-week-of-march-31-april-4-2025'),
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('Fast Fourier transform and polynomial multiplication',
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'fast-fourier-transform-and-polynomial-multiplication'),
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('From DFT to QFT', 2, None, 'from-dft-to-qft'),
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('In terms of arbitrary states',
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<!-- author(s): Morten Hjorth-Jensen -->
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<b>Morten Hjorth-Jensen</b> [1, 2]
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</center>
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<!-- institution(s) -->
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<center>
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[1] <b>Department of Physics, University of Oslo</b>
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<b>Morten Hjorth-Jensen</b>
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</center>
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<!-- institution -->
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[2] <b>Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University</b>
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<b>Department of Physics, University of Oslo, Norway</b>
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<b></b>
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<p>
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<ol>
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<li> Discrete Fourier transforms (DFTs) and the fast Fourier Transform (FFT)</li>
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<li> Quantum Fourier transforms (QFTs), basic mathematical expressions</li>
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<li> Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (additional slides)</li>
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<li> Quantum Fourier transforms (QFTs), reminder from last week</li>
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<li> Setting up circuits for QFT</li>
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<li> Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT.</li>
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<li> <a href="https://youtu.be/" target="_blank">Video of lecture TBA</a>
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<li> Quantum phase estimation algorithm</li>
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<li> Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT.
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<!-- o <a href="https://youtu.be/" target="_blank">Video of lecture TBA</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2024/NotesApril3.pdf" target="_blank">Whiteboard notes</a> --></li>
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</ol>
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</div>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="possible-paths-for-project-2">Possible paths for project 2 </h2>
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<ul>
239-
<li> Implement QFTs</li>
240-
<li> Study other algorithms
241-
<ol type="a"></li>
242-
<li> Deutsch-Jozsa algorithm: Determine if a function is constant or balance using the fewest number of queries.</li>
243-
<li> SImon's algorithm: Determine if a function (Oracle) is one-to-one or two-to-one</li>
244-
<li> Grover's algorithm: Search unstructured list of data fast</li>
245-
<li> Possibly: Shor's algorithm and how to Factorize integers efficiently</li>
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</ol>
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<li> Study the solution of quantum mechanical eigenvalue problems with systems from atomic/molecular physics and quantum chemistry</li>
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<li> Quantum machine learning projects, quantum boltzmann machines or related topics
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<!-- For project 2, in order to be time efficient, you can use software like Qiskit, Pennylane, qBraid and/or other --></li>
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</ul>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="brief-reminder-on-fourier-transforms">Brief reminder on Fourier transforms </h2>
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<p>Last week we reviewed some basic properties of Fourier transforms. We restate some of these results here.
228+
<p>Last week we reviewed some basic properties of Fourier transforms and derived the expressions for the quantum Fourier variant.
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We restate some of these results here.
255230
<a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/pub/week10/ipynb/week10.ipynb" target="_blank">For more information, see slides from previous week</a>
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</p>
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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>
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</p>
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<p>Our emphasis is on the link between discrete Fourier transforms and quantum Fourier transforms. We will not discuss FFT in this course.</p>
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<p>For a discussion of FFT, see additional slides at (address to be added)</p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="the-discrete-fourier-transform-dft">The discrete Fourier transform (DFT) </h2>
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$$
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="fast-fourier-transform-and-polynomial-multiplication">Fast Fourier transform and polynomial multiplication </h2>
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<p>The FFT algorithm is an \( O(n\log{n}) \) divide and conquer algorithm for DFT, used by
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Gauss circa 1805, and popularized by Cooley and Turkey and 1965. Gauss used the
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algorithm to determine periodic asteroid orbits, while Cooley and Turkey used it to
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detect Soviet nuclear tests from o&#64256;shore readings.
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A practical implementation of FFT is FFTW, which was described by Frigo and
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Johnson at MIT. The algorithm is often implemented directly in hardware, for fixed \( n \).
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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="from-dft-to-qft">From DFT to QFT </h2>
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<!-- ------------------- end of main content --------------- -->
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<center style="font-size:80%">
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<!-- copyright --> &copy; 1999-2024, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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<!-- copyright --> &copy; 1999-2025, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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</center>
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</body>
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</html>

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