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‎doc/pub/week15/html/week15-bs.html‎

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<!-- tocinfo
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{'highest level': 2,
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'sections': [('Plan for the week of May 6-10',
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'sections': [('Plan for the week of May 5-9',
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('Some history', 2, None, 'some-history'),
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('What is the algorithm doing?',
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("Other algorithms: Simon's algorithm",
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'other-algorithms-simon-s-algorithm')]}
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'plan-for-the-week-of-may-5-9')]}
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<body>
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<script type="text/x-mathjax-config">
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MathJax.Hub.Config({
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<!-- Bootstrap navigation bar -->
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<div class="navbar navbar-default navbar-fixed-top">
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<div class="navbar-header">
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<li class="dropdown">
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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="#plan-for-the-week-of-may-6-10" style="font-size: 80%;">Plan for the week of May 6-10</a></li>
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<!-- navigation toc: --> <li><a href="#qpe-and-shor-s-algorithm" style="font-size: 80%;">QPE and Shor's algorithm</a></li>
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<!-- navigation toc: --> <li><a href="#some-history" style="font-size: 80%;">Some history</a></li>
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<!-- navigation toc: --> <li><a href="#what-is-the-algorithm-doing" style="font-size: 80%;">What is the algorithm doing?</a></li>
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<!-- navigation toc: --> <li><a href="#other-algorithms-simon-s-algorithm" style="font-size: 80%;">Other algorithms: Simon's algorithm</a></li>
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<!-- navigation toc: --> <li><a href="#plan-for-the-week-of-may-5-9" style="font-size: 80%;">Plan for the week of May 5-9</a></li>
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</ul>
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</li>
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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</b>
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</center>
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<br>
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<center>
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<h4>May 8, 2024</h4>
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<h4>May 7, 2025</h4>
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</center> <!-- date -->
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<br>
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<!-- potential-jumbotron-button -->
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</div> <!-- end jumbotron -->
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<!-- !split -->
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<h2 id="plan-for-the-week-of-may-6-10" class="anchor">Plan for the week of May 6-10 </h2>
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<h2 id="plan-for-the-week-of-may-5-9" class="anchor">Plan for the week of May 5-9 </h2>
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<div class="panel panel-default">
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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> Discussion of Shor's algorithm and order finding</li>
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<li> Reading suggestions: Hundt sections 6.4-6.6 and Nielsen and Chuang, sections 5.2-5.3
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<li> TBA
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<!-- o <a href="https://youtu.be/OZdyky8UYdk" target="_self">Video of lecture at</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2024/NotesMay8.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="qpe-and-shor-s-algorithm" class="anchor">QPE and Shor's algorithm </h2>
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<p>The crucial observation of Shor was that there is an efficient quantum
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algorithm for the problem of period-finding and that factoring can be
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reduced to this, in the sense that an efficient algorithm for
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period-finding implies an efficient algorithm for factoring. The
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quantum phase estimation algorithm discussed earlier plays a central
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role in Shor's algorithm as well.
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</p>
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<!-- !split -->
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<h2 id="some-history" class="anchor">Some history </h2>
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<p>In 1994 Peter Shor found a polynomial time algorithm for the
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factorization of \( n \)-bit numbers on quantum computers, see
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<a href="https://arxiv.org/abs/quant-ph/9508027" target="_self"><tt>https://arxiv.org/abs/quant-ph/9508027</tt></a>.
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</p>
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<p>The discovery generated a wave of enthusiasm for quantum
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computing. There are at least two reasons for this. One is the
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mathematical and intellectual challenge of the algorithm. Secondly,
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factorization plays an important role for the security of
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cryptographic protocols, which are based on factoring large integers.
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</p>
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<!-- !split -->
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<h2 id="what-is-the-algorithm-doing" class="anchor">What is the algorithm doing? </h2>
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<p>In essence, Shor's algorithm reduces the factorization problem to the problem of finding the period of a function (to be discussed below). In addition, it uses quantum parallelism to find a superposition of all values of the function in one single step. </p>
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<!-- !split -->
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<!-- !split -->
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<h2 id="other-algorithms-simon-s-algorithm" class="anchor">Other algorithms: Simon's algorithm </h2>
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<p>More material will be added here</p>
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<!-- ------------------- end of main content --------------- -->
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</div> <!-- end container -->
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<!-- include javascript, jQuery *first* -->

‎doc/pub/week15/html/week15-reveal.html‎

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<!-- ------------------- main content ---------------------- -->
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<center>
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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</b>
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</center>
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<br>
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<center>
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<h4>May 8, 2024</h4>
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<h4>May 7, 2025</h4>
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</center> <!-- date -->
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<br>
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</section>
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<section>
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<h2 id="plan-for-the-week-of-may-6-10">Plan for the week of May 6-10 </h2>
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<h2 id="plan-for-the-week-of-may-5-9">Plan for the week of May 5-9 </h2>
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<div class="alert alert-block alert-block alert-text-normal">
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<b></b>
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<p>
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<ol>
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<p><li> Discussion of Shor's algorithm and order finding</li>
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<p><li> Reading suggestions: Hundt sections 6.4-6.6 and Nielsen and Chuang, sections 5.2-5.3
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<p><li> TBA
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<!-- o <a href="https://youtu.be/OZdyky8UYdk" target="_blank">Video of lecture at</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2024/NotesMay8.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="qpe-and-shor-s-algorithm">QPE and Shor's algorithm </h2>
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<p>The crucial observation of Shor was that there is an efficient quantum
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algorithm for the problem of period-finding and that factoring can be
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reduced to this, in the sense that an efficient algorithm for
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period-finding implies an efficient algorithm for factoring. The
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quantum phase estimation algorithm discussed earlier plays a central
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role in Shor's algorithm as well.
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</p>
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</section>
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<section>
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<h2 id="some-history">Some history </h2>
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<p>In 1994 Peter Shor found a polynomial time algorithm for the
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factorization of \( n \)-bit numbers on quantum computers, see
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<a href="https://arxiv.org/abs/quant-ph/9508027" target="_blank"><tt>https://arxiv.org/abs/quant-ph/9508027</tt></a>.
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</p>
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<p>The discovery generated a wave of enthusiasm for quantum
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computing. There are at least two reasons for this. One is the
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mathematical and intellectual challenge of the algorithm. Secondly,
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factorization plays an important role for the security of
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cryptographic protocols, which are based on factoring large integers.
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</p>
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</section>
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<section>
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<h2 id="what-is-the-algorithm-doing">What is the algorithm doing? </h2>
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<p>In essence, Shor's algorithm reduces the factorization problem to the problem of finding the period of a function (to be discussed below). In addition, it uses quantum parallelism to find a superposition of all values of the function in one single step. </p>
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</section>
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<section>
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</section>
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<section>
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<h2 id="other-algorithms-simon-s-algorithm">Other algorithms: Simon's algorithm </h2>
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<p>More material will be added here</p>
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</section>
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</div> <!-- class="slides" -->

‎doc/pub/week15/html/week15-solarized.html‎

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<!-- tocinfo
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{'highest level': 2,
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'sections': [('Plan for the week of May 6-10',
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'sections': [('Plan for the week of May 5-9',
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2,
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None,
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'plan-for-the-week-of-may-6-10'),
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("QPE and Shor's algorithm", 2, None, 'qpe-and-shor-s-algorithm'),
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('Some history', 2, None, 'some-history'),
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('What is the algorithm doing?',
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2,
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None,
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'what-is-the-algorithm-doing'),
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("Other algorithms: Simon's algorithm",
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2,
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None,
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'other-algorithms-simon-s-algorithm')]}
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'plan-for-the-week-of-may-5-9')]}
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end of tocinfo -->
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<body>
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<script type="text/x-mathjax-config">
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MathJax.Hub.Config({
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equationNumbers: { autoNumber: "AMS" },
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extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
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<script type="text/javascript" async
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src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
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</script>
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<!-- ------------------- main content ---------------------- -->
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<center>
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<h1>Quantum Computing, Quantum Machine Learning and Quantum Information Theories</h1>
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</center> <!-- document title -->
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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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<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</b>
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</center>
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<br>
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<h4>May 8, 2024</h4>
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<h4>May 7, 2025</h4>
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</center> <!-- date -->
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<br>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="plan-for-the-week-of-may-6-10">Plan for the week of May 6-10 </h2>
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<h2 id="plan-for-the-week-of-may-5-9">Plan for the week of May 5-9 </h2>
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<div class="alert alert-block alert-block alert-text-normal">
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<b></b>
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<p>
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<ol>
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<li> Discussion of Shor's algorithm and order finding</li>
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<li> Reading suggestions: Hundt sections 6.4-6.6 and Nielsen and Chuang, sections 5.2-5.3
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<li> TBA
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<!-- o <a href="https://youtu.be/OZdyky8UYdk" target="_blank">Video of lecture at</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2024/NotesMay8.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="qpe-and-shor-s-algorithm">QPE and Shor's algorithm </h2>
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<p>The crucial observation of Shor was that there is an efficient quantum
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algorithm for the problem of period-finding and that factoring can be
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reduced to this, in the sense that an efficient algorithm for
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period-finding implies an efficient algorithm for factoring. The
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quantum phase estimation algorithm discussed earlier plays a central
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role in Shor's algorithm as well.
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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="some-history">Some history </h2>
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<p>In 1994 Peter Shor found a polynomial time algorithm for the
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factorization of \( n \)-bit numbers on quantum computers, see
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<a href="https://arxiv.org/abs/quant-ph/9508027" target="_blank"><tt>https://arxiv.org/abs/quant-ph/9508027</tt></a>.
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</p>
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<p>The discovery generated a wave of enthusiasm for quantum
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computing. There are at least two reasons for this. One is the
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mathematical and intellectual challenge of the algorithm. Secondly,
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factorization plays an important role for the security of
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cryptographic protocols, which are based on factoring large integers.
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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="what-is-the-algorithm-doing">What is the algorithm doing? </h2>
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<p>In essence, Shor's algorithm reduces the factorization problem to the problem of finding the period of a function (to be discussed below). In addition, it uses quantum parallelism to find a superposition of all values of the function in one single step. </p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="other-algorithms-simon-s-algorithm">Other algorithms: Simon's algorithm </h2>
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<p>More material will be added here</p>
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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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