|
42 | 42 | 'plans-for-the-week-of-february-10-14'), |
43 | 43 | ('Gates, the whys and hows', 2, None, 'gates-the-whys-and-hows'), |
44 | 44 | ('Structure of the lecture', 2, None, 'structure-of-the-lecture'), |
45 | | - ('Mathematical background', 2, None, 'mathematical-background'), |
| 45 | + ('Part 1: Mathematical background', |
| 46 | + 2, |
| 47 | + None, |
| 48 | + 'part-1-mathematical-background'), |
46 | 49 | ('Unitary transformation', 2, None, 'unitary-transformation'), |
47 | 50 | ('Interaction picture', 2, None, 'interaction-picture'), |
48 | 51 | ('Taking the derivative wrt time', |
|
92 | 95 | None, |
93 | 96 | 'initial-state-preparation'), |
94 | 97 | ('Final expression', 2, None, 'final-expression'), |
95 | | - ('Specific realizations and famous gates', |
| 98 | + ('Part 2: Specific realizations and famous gates', |
96 | 99 | 2, |
97 | 100 | None, |
98 | | - 'specific-realizations-and-famous-gates'), |
99 | | - ('Quantum gates, circuits and simple algorithms (parts from last ' |
100 | | - 'week)', |
| 101 | + 'part-2-specific-realizations-and-famous-gates'), |
| 102 | + ('Part 3: Fanous Quantum gates, circuits and simple algorithms ' |
| 103 | + '(parts from last week)', |
101 | 104 | 2, |
102 | 105 | None, |
103 | | - 'quantum-gates-circuits-and-simple-algorithms-parts-from-last-week'), |
| 106 | + 'part-3-fanous-quantum-gates-circuits-and-simple-algorithms-parts-from-last-week'), |
104 | 107 | ('Quantum circuits', 2, None, 'quantum-circuits'), |
105 | 108 | ('Single-Qubit Gates', 2, None, 'single-qubit-gates'), |
106 | 109 | ('Widely used gates', 2, None, 'widely-used-gates'), |
|
173 | 176 | <!-- navigation toc: --> <li><a href="#plans-for-the-week-of-february-10-14" style="font-size: 80%;">Plans for the week of February 10-14</a></li> |
174 | 177 | <!-- navigation toc: --> <li><a href="#gates-the-whys-and-hows" style="font-size: 80%;">Gates, the whys and hows</a></li> |
175 | 178 | <!-- navigation toc: --> <li><a href="#structure-of-the-lecture" style="font-size: 80%;">Structure of the lecture</a></li> |
176 | | - <!-- navigation toc: --> <li><a href="#mathematical-background" style="font-size: 80%;">Mathematical background</a></li> |
| 179 | + <!-- navigation toc: --> <li><a href="#part-1-mathematical-background" style="font-size: 80%;">Part 1: Mathematical background</a></li> |
177 | 180 | <!-- navigation toc: --> <li><a href="#unitary-transformation" style="font-size: 80%;">Unitary transformation</a></li> |
178 | 181 | <!-- navigation toc: --> <li><a href="#interaction-picture" style="font-size: 80%;">Interaction picture</a></li> |
179 | 182 | <!-- navigation toc: --> <li><a href="#taking-the-derivative-wrt-time" style="font-size: 80%;">Taking the derivative wrt time</a></li> |
|
196 | 199 | <!-- navigation toc: --> <li><a href="#time-evolution" style="font-size: 80%;">Time evolution</a></li> |
197 | 200 | <!-- navigation toc: --> <li><a href="#initial-state-preparation" style="font-size: 80%;">Initial state preparation</a></li> |
198 | 201 | <!-- navigation toc: --> <li><a href="#final-expression" style="font-size: 80%;">Final expression</a></li> |
199 | | - <!-- navigation toc: --> <li><a href="#specific-realizations-and-famous-gates" style="font-size: 80%;">Specific realizations and famous gates</a></li> |
200 | | - <!-- navigation toc: --> <li><a href="#quantum-gates-circuits-and-simple-algorithms-parts-from-last-week" style="font-size: 80%;">Quantum gates, circuits and simple algorithms (parts from last week)</a></li> |
| 202 | + <!-- navigation toc: --> <li><a href="#part-2-specific-realizations-and-famous-gates" style="font-size: 80%;">Part 2: Specific realizations and famous gates</a></li> |
| 203 | + <!-- navigation toc: --> <li><a href="#part-3-fanous-quantum-gates-circuits-and-simple-algorithms-parts-from-last-week" style="font-size: 80%;">Part 3: Fanous Quantum gates, circuits and simple algorithms (parts from last week)</a></li> |
201 | 204 | <!-- navigation toc: --> <li><a href="#quantum-circuits" style="font-size: 80%;">Quantum circuits</a></li> |
202 | 205 | <!-- navigation toc: --> <li><a href="#single-qubit-gates" style="font-size: 80%;">Single-Qubit Gates</a></li> |
203 | 206 | <!-- navigation toc: --> <li><a href="#widely-used-gates" style="font-size: 80%;">Widely used gates</a></li> |
@@ -260,9 +263,9 @@ <h2 id="plans-for-the-week-of-february-10-14" class="anchor">Plans for the week |
260 | 263 | <li> Reminder from last week on gates and circuits</li> |
261 | 264 | <li> One-qubit and two-qubit gates, background and realizations |
262 | 265 | <!-- o Entropy as a measurement of entanglement --></li> |
263 | | -<li> Simple Hamiltonian systems and how to use the density matrix to estimate degrees of entanglement</li> |
| 266 | +<li> Simple Hamiltonian systems</li> |
264 | 267 | <li> <a href="https://youtu.be/" target="_self">Video of lecture to be added</a> |
265 | | -<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2024/NotesFebruary7.pdf" target="_self">Whiteboard notes</a> --></li> |
| 268 | +<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf" target="_self">Whiteboard notes</a> --></li> |
266 | 269 | </ol> |
267 | 270 | <!-- !split --> |
268 | 271 | <h2 id="gates-the-whys-and-hows" class="anchor">Gates, the whys and hows </h2> |
@@ -295,7 +298,7 @@ <h2 id="structure-of-the-lecture" class="anchor">Structure of the lecture </h2> |
295 | 298 | <li> These unitary transformations are then represented as gates. Setting gates together gives us a final circuit which can represent a specific physical system</li> |
296 | 299 | </ol> |
297 | 300 | <!-- !split --> |
298 | | -<h2 id="mathematical-background" class="anchor">Mathematical background </h2> |
| 301 | +<h2 id="part-1-mathematical-background" class="anchor">Part 1: Mathematical background </h2> |
299 | 302 |
|
300 | 303 | <p>The time-dependent Schr\"odinger equation (or equation of motion) reads</p> |
301 | 304 | $$ |
@@ -720,10 +723,14 @@ <h2 id="final-expression" class="anchor">Final expression </h2> |
720 | 723 |
|
721 | 724 |
|
722 | 725 | <!-- !split --> |
723 | | -<h2 id="specific-realizations-and-famous-gates" class="anchor">Specific realizations and famous gates </h2> |
| 726 | +<h2 id="part-2-specific-realizations-and-famous-gates" class="anchor">Part 2: Specific realizations and famous gates </h2> |
| 727 | + |
| 728 | +<p>This part is not yet ready and will be part of the whiteboard notes. |
| 729 | +I will try to get it ready by the end of Tuesday, Feb 11 |
| 730 | +</p> |
724 | 731 |
|
725 | 732 | <!-- !split --> |
726 | | -<h2 id="quantum-gates-circuits-and-simple-algorithms-parts-from-last-week" class="anchor">Quantum gates, circuits and simple algorithms (parts from last week) </h2> |
| 733 | +<h2 id="part-3-fanous-quantum-gates-circuits-and-simple-algorithms-parts-from-last-week" class="anchor">Part 3: Fanous Quantum gates, circuits and simple algorithms (parts from last week) </h2> |
727 | 734 |
|
728 | 735 | <p>Quantum gates are physical actions that are applied to the physical |
729 | 736 | system representing the qubits. Mathematically, they are |
|
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