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66 | 66 | None, |
67 | 67 | 'project-2-e-implement-the-phase-estimation-algorithm-for-one-and-two-qubits'), |
68 | 68 | ('Project 2 f): Bringing back the simple Hamiltonians from ' |
69 | | - 'project 1', |
| 69 | + 'project 1. This part is optional', |
70 | 70 | 3, |
71 | 71 | None, |
72 | | - 'project-2-f-bringing-back-the-simple-hamiltonians-from-project-1'), |
| 72 | + 'project-2-f-bringing-back-the-simple-hamiltonians-from-project-1-this-part-is-optional'), |
73 | 73 | ('Project 2 g): This part is optional', |
74 | 74 | 3, |
75 | 75 | None, |
|
162 | 162 | <!-- navigation toc: --> <li><a href="#project-2-c-implementing-the-quantum-fourier-transform-for-one-two-and-three-qubits" style="font-size: 80%;"> Project 2 c): Implementing the Quantum Fourier Transform for one, two and three qubits</a></li> |
163 | 163 | <!-- navigation toc: --> <li><a href="#project-2-d-generalize-the-code-to-an-arbitrary-number-of-qubits" style="font-size: 80%;"> Project 2 d): Generalize the code to an arbitrary number of qubits</a></li> |
164 | 164 | <!-- navigation toc: --> <li><a href="#project-2-e-implement-the-phase-estimation-algorithm-for-one-and-two-qubits" style="font-size: 80%;"> Project 2 e): Implement the phase estimation algorithm for one and two qubits</a></li> |
165 | | - <!-- navigation toc: --> <li><a href="#project-2-f-bringing-back-the-simple-hamiltonians-from-project-1" style="font-size: 80%;"> Project 2 f): Bringing back the simple Hamiltonians from project 1</a></li> |
| 165 | + <!-- navigation toc: --> <li><a href="#project-2-f-bringing-back-the-simple-hamiltonians-from-project-1-this-part-is-optional" style="font-size: 80%;"> Project 2 f): Bringing back the simple Hamiltonians from project 1. This part is optional</a></li> |
166 | 166 | <!-- navigation toc: --> <li><a href="#project-2-g-this-part-is-optional" style="font-size: 80%;"> Project 2 g): This part is optional</a></li> |
167 | 167 | <!-- navigation toc: --> <li><a href="#alternative-two-quantum-machine-learning" style="font-size: 80%;"> Alternative two, Quantum Machine Learning</a></li> |
168 | 168 | <!-- navigation toc: --> <li><a href="#project-2-a-encoding-the-data-into-a-quantum-state" style="font-size: 80%;"> Project 2 a): Encoding the Data Into a Quantum State</a></li> |
@@ -294,7 +294,7 @@ <h3 id="project-2-e-implement-the-phase-estimation-algorithm-for-one-and-two-qub |
294 | 294 | register. Extract the phase and discuss the accuracy of the phase |
295 | 295 | estimation algorithm, see for example Nielsen and Chuang, <b>Quantum Computation and Quantum Information</b>, Oxford, 2000, section 5.2. |
296 | 296 | </p> |
297 | | -<h3 id="project-2-f-bringing-back-the-simple-hamiltonians-from-project-1" class="anchor">Project 2 f): Bringing back the simple Hamiltonians from project 1 </h3> |
| 297 | +<h3 id="project-2-f-bringing-back-the-simple-hamiltonians-from-project-1-this-part-is-optional" class="anchor">Project 2 f): Bringing back the simple Hamiltonians from project 1. This part is optional </h3> |
298 | 298 |
|
299 | 299 | <p>We will now compute the eigenvalues of the simpler matrices from project 1 using the phase estimation algorithm. |
300 | 300 | In project 1 we defined a symmetric matrix \( H\in {\mathbb{R}}^{2\times 2} \) |
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