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doc/Projects/2025/Project2/html/._Project2-bs000.html

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'project-2-e-implement-the-phase-estimation-algorithm-for-one-and-two-qubits'),
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('Project 2 f): Bringing back the simple Hamiltonians from '
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'project 1',
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'project 1. This part is optional',
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'project-2-f-bringing-back-the-simple-hamiltonians-from-project-1-this-part-is-optional'),
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('Project 2 g): This part is optional',
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<!-- navigation toc: --> <li><a href="#project-2-c-implementing-the-quantum-fourier-transform-for-one-two-and-three-qubits" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 c): Implementing the Quantum Fourier Transform for one, two and three qubits</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-d-generalize-the-code-to-an-arbitrary-number-of-qubits" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 d): Generalize the code to an arbitrary number of qubits</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-e-implement-the-phase-estimation-algorithm-for-one-and-two-qubits" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 e): Implement the phase estimation algorithm for one and two qubits</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-f-bringing-back-the-simple-hamiltonians-from-project-1" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 f): Bringing back the simple Hamiltonians from project 1</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-f-bringing-back-the-simple-hamiltonians-from-project-1-this-part-is-optional" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 f): Bringing back the simple Hamiltonians from project 1. This part is optional</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-g-this-part-is-optional" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 g): This part is optional</a></li>
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<!-- navigation toc: --> <li><a href="#alternative-two-quantum-machine-learning" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Alternative two, Quantum Machine Learning</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-a-encoding-the-data-into-a-quantum-state" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 a): Encoding the Data Into a Quantum State</a></li>
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register. Extract the phase and discuss the accuracy of the phase
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estimation algorithm, see for example Nielsen and Chuang, <b>Quantum Computation and Quantum Information</b>, Oxford, 2000, section 5.2.
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</p>
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<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>
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<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>
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<p>We will now compute the eigenvalues of the simpler matrices from project 1 using the phase estimation algorithm.
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In project 1 we defined a symmetric matrix \( H\in {\mathbb{R}}^{2\times 2} \)

doc/Projects/2025/Project2/html/Project2-bs.html

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'project-2-e-implement-the-phase-estimation-algorithm-for-one-and-two-qubits'),
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('Project 2 f): Bringing back the simple Hamiltonians from '
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('Project 2 g): This part is optional',
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<!-- navigation toc: --> <li><a href="#project-2-c-implementing-the-quantum-fourier-transform-for-one-two-and-three-qubits" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 c): Implementing the Quantum Fourier Transform for one, two and three qubits</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-d-generalize-the-code-to-an-arbitrary-number-of-qubits" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 d): Generalize the code to an arbitrary number of qubits</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-e-implement-the-phase-estimation-algorithm-for-one-and-two-qubits" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 e): Implement the phase estimation algorithm for one and two qubits</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-f-bringing-back-the-simple-hamiltonians-from-project-1" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 f): Bringing back the simple Hamiltonians from project 1</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-f-bringing-back-the-simple-hamiltonians-from-project-1-this-part-is-optional" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 f): Bringing back the simple Hamiltonians from project 1. This part is optional</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-g-this-part-is-optional" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 g): This part is optional</a></li>
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<!-- navigation toc: --> <li><a href="#alternative-two-quantum-machine-learning" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Alternative two, Quantum Machine Learning</a></li>
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<!-- navigation toc: --> <li><a href="#project-2-a-encoding-the-data-into-a-quantum-state" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Project 2 a): Encoding the Data Into a Quantum State</a></li>
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register. Extract the phase and discuss the accuracy of the phase
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estimation algorithm, see for example Nielsen and Chuang, <b>Quantum Computation and Quantum Information</b>, Oxford, 2000, section 5.2.
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</p>
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<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>
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<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>
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<p>We will now compute the eigenvalues of the simpler matrices from project 1 using the phase estimation algorithm.
300300
In project 1 we defined a symmetric matrix \( H\in {\mathbb{R}}^{2\times 2} \)

doc/Projects/2025/Project2/html/Project2.html

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'project-2-e-implement-the-phase-estimation-algorithm-for-one-and-two-qubits'),
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('Project 2 f): Bringing back the simple Hamiltonians from '
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'project 1. This part is optional',
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('Project 2 g): This part is optional',
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register. Extract the phase and discuss the accuracy of the phase
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estimation algorithm, see for example Nielsen and Chuang, <b>Quantum Computation and Quantum Information</b>, Oxford, 2000, section 5.2.
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</p>
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<h3 id="project-2-f-bringing-back-the-simple-hamiltonians-from-project-1">Project 2 f): Bringing back the simple Hamiltonians from project 1 </h3>
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<h3 id="project-2-f-bringing-back-the-simple-hamiltonians-from-project-1-this-part-is-optional">Project 2 f): Bringing back the simple Hamiltonians from project 1. This part is optional </h3>
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<p>We will now compute the eigenvalues of the simpler matrices from project 1 using the phase estimation algorithm.
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In project 1 we defined a symmetric matrix \( H\in {\mathbb{R}}^{2\times 2} \)

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