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8 | 8 | <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> |
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10 | 10 | <meta name="viewport" content="width=device-width, initial-scale=1.0" /> |
11 | | -<meta name="description" content="Measurements, spectral decomposition and Hamiltonians"> |
12 | | -<title>Measurements, spectral decomposition and Hamiltonians</title> |
| 11 | +<meta name="description" content="Measurements, spectral decomposition and HamiltoniansA"> |
| 12 | +<title>Measurements, spectral decomposition and HamiltoniansA</title> |
13 | 13 | <!-- Bootstrap style: bootstrap --> |
14 | 14 | <!-- doconce format html week2.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week2-bs --no_mako --> |
15 | 15 | <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet"> |
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41 | 41 | None, |
42 | 42 | 'summary-from-last-week-and-plans-for-this-week'), |
43 | 43 | ("This week's plans", 2, None, 'this-week-s-plans'), |
44 | | - ('Links to code examples', 2, None, 'links-to-code-examples'), |
45 | 44 | ('Measurements', 2, None, 'measurements'), |
46 | 45 | ('Properties of a measurement', |
47 | 46 | 2, |
|
63 | 62 | 2, |
64 | 63 | None, |
65 | 64 | 'the-spectral-decomposition-from-last-week'), |
| 65 | + ('Bloch sphere', 2, None, 'bloch-sphere'), |
66 | 66 | ('Meet the Bloch sphere', 2, None, 'meet-the-bloch-sphere'), |
| 67 | + ('Bloch sphere exercise', 2, None, 'bloch-sphere-exercise'), |
67 | 68 | ('Measurements', 2, None, 'measurements'), |
68 | 69 | ('Qubit example', 2, None, 'qubit-example'), |
69 | 70 | ('Total probability', 2, None, 'total-probability'), |
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161 | 162 | <span class="icon-bar"></span> |
162 | 163 | <span class="icon-bar"></span> |
163 | 164 | </button> |
164 | | - <a class="navbar-brand" href="week2-bs.html">Measurements, spectral decomposition and Hamiltonians</a> |
| 165 | + <a class="navbar-brand" href="week2-bs.html">Measurements, spectral decomposition and HamiltoniansA</a> |
165 | 166 | </div> |
166 | 167 | <div class="navbar-collapse collapse navbar-responsive-collapse"> |
167 | 168 | <ul class="nav navbar-nav navbar-right"> |
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170 | 171 | <ul class="dropdown-menu"> |
171 | 172 | <!-- navigation toc: --> <li><a href="#summary-from-last-week-and-plans-for-this-week" style="font-size: 80%;">Summary from last week and plans for this week</a></li> |
172 | 173 | <!-- navigation toc: --> <li><a href="#this-week-s-plans" style="font-size: 80%;">This week's plans</a></li> |
173 | | - <!-- navigation toc: --> <li><a href="#links-to-code-examples" style="font-size: 80%;">Links to code examples</a></li> |
174 | 174 | <!-- navigation toc: --> <li><a href="#measurements" style="font-size: 80%;">Measurements</a></li> |
175 | 175 | <!-- navigation toc: --> <li><a href="#properties-of-a-measurement" style="font-size: 80%;">Properties of a measurement</a></li> |
176 | 176 | <!-- navigation toc: --> <li><a href="#entanglement" style="font-size: 80%;">Entanglement</a></li> |
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183 | 183 | <!-- navigation toc: --> <li><a href="#spectral-decomposition" style="font-size: 80%;">Spectral decomposition</a></li> |
184 | 184 | <!-- navigation toc: --> <li><a href="#explicit-results" style="font-size: 80%;">Explicit results</a></li> |
185 | 185 | <!-- navigation toc: --> <li><a href="#the-spectral-decomposition-from-last-week" style="font-size: 80%;">The spectral decomposition, from last week</a></li> |
| 186 | + <!-- navigation toc: --> <li><a href="#bloch-sphere" style="font-size: 80%;">Bloch sphere</a></li> |
186 | 187 | <!-- navigation toc: --> <li><a href="#meet-the-bloch-sphere" style="font-size: 80%;">Meet the Bloch sphere</a></li> |
| 188 | + <!-- navigation toc: --> <li><a href="#bloch-sphere-exercise" style="font-size: 80%;">Bloch sphere exercise</a></li> |
187 | 189 | <!-- navigation toc: --> <li><a href="#measurements" style="font-size: 80%;">Measurements</a></li> |
188 | 190 | <!-- navigation toc: --> <li><a href="#qubit-example" style="font-size: 80%;">Qubit example</a></li> |
189 | 191 | <!-- navigation toc: --> <li><a href="#total-probability" style="font-size: 80%;">Total probability</a></li> |
|
226 | 228 | <!-- ------------------- main content ---------------------- --> |
227 | 229 | <div class="jumbotron"> |
228 | 230 | <center> |
229 | | -<h1>Measurements, spectral decomposition and Hamiltonians</h1> |
| 231 | +<h1>Measurements, spectral decomposition and HamiltoniansA</h1> |
230 | 232 | </center> <!-- document title --> |
231 | 233 |
|
232 | 234 | <!-- author(s): Morten Hjorth-Jensen --> |
@@ -285,10 +287,6 @@ <h2 id="this-week-s-plans" class="anchor">This week's plans </h2> |
285 | 287 |
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286 | 288 | <!-- * <b>Reading recommendation</b>: Scherer, Mathematics of Quantum Computations, chapter 3.1-3.3 and Hundt, Quantum Computing for Programmers, chapter 2.1-2.5. Hundt's text is relevant for the programming part where we build from scratch the ingredients we will need. --> |
287 | 289 |
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288 | | -<!-- !split --> |
289 | | -<h2 id="links-to-code-examples" class="anchor">Links to code examples </h2> |
290 | | - |
291 | | -<p>To be added</p> |
292 | 290 | <!-- The code examples presented by Keran are at --> |
293 | 291 | <!-- <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/pub/week2/ipynb/codeskeran.ipynb" target="_self"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/pub/week2/ipynb/codeskeran.ipynb</tt></a> --> |
294 | 292 |
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@@ -521,6 +519,9 @@ <h2 id="the-spectral-decomposition-from-last-week" class="anchor">The spectral d |
521 | 519 | $$ |
522 | 520 |
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523 | 521 |
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| 522 | +<!-- !split --> |
| 523 | +<h2 id="bloch-sphere" class="anchor">Bloch sphere </h2> |
| 524 | + |
524 | 525 | <!-- !split --> |
525 | 526 | <h2 id="meet-the-bloch-sphere" class="anchor">Meet the Bloch sphere </h2> |
526 | 527 |
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@@ -554,6 +555,11 @@ <h2 id="meet-the-bloch-sphere" class="anchor">Meet the Bloch sphere </h2> |
554 | 555 | </div> |
555 | 556 |
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556 | 557 |
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| 558 | +<!-- !split --> |
| 559 | +<h2 id="bloch-sphere-exercise" class="anchor">Bloch sphere exercise </h2> |
| 560 | + |
| 561 | +<p>Determine the Bloch sphere angles \( \theta \) and \( \phi \) for the eigenstates of each Pauli matrix (see lectures from last week for the definition of Pauli matrices).</p> |
| 562 | + |
557 | 563 | <!-- !split --> |
558 | 564 | <h2 id="measurements" class="anchor">Measurements </h2> |
559 | 565 |
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