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‎doc/pub/week1/html/week1-bs.html‎

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<body>
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<!-- navigation toc: --> <li><a href="#and-the-next-two" style="font-size: 80%;">And the next two</a></li>
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<!-- navigation toc: --> <li><a href="#exercise-2-entangled-state" style="font-size: 80%;">Exercise 2: Entangled state</a></li>
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<!-- navigation toc: --> <li><a href="#exercise-3-commutator-identities" style="font-size: 80%;">Exercise 3: Commutator identities</a></li>
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<!-- navigation toc: --> <li><a href="#exercise-4-shared-eigenvectors" style="font-size: 80%;">Exercise 4: Shared eigenvectors</a></li>
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<!-- navigation toc: --> <li><a href="#exercise-5-one-qubit-basis-and-pauli-matrices" style="font-size: 80%;">Exercise 5: One-qubit basis and Pauli matrices</a></li>
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<!-- navigation toc: --> <li><a href="#exercise-6-hadamard-and-phase-gates" style="font-size: 80%;">Exercise 6: Hadamard and Phase gates</a></li>
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<!-- navigation toc: --> <li><a href="#exercise-4-pauli-matrices" style="font-size: 80%;">Exercise 4: Pauli matrices</a></li>
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<!-- navigation toc: --> <li><a href="#exercise-5-shared-eigenvectors" style="font-size: 80%;">Exercise 5: Shared eigenvectors</a></li>
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<!-- navigation toc: --> <li><a href="#exercise-6-one-qubit-basis-and-pauli-matrices" style="font-size: 80%;">Exercise 6: One-qubit basis and Pauli matrices</a></li>
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<!-- navigation toc: --> <li><a href="#exercise-7-hadamard-and-phase-gates" style="font-size: 80%;">Exercise 7: Hadamard and Phase gates</a></li>
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</ul>
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</li>
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<li> \( [\hat{A},[\hat{B}\hat{C}]]= [\hat{B},[\hat{C},\hat{A}]]+[\hat{C},[\hat{A},\hat{B}]]=0 \) (the so-called Jacobi identity).</li>
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</ol>
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<!-- !split -->
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<h2 id="exercise-4-shared-eigenvectors" class="anchor">Exercise 4: Shared eigenvectors </h2>
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<h2 id="exercise-4-pauli-matrices" class="anchor">Exercise 4: Pauli matrices </h2>
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<ol>
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<li> Set up the commutation rules for Pauli matrices, that is find \( [\sigma_i,\sigma_j] \) where \( i,j=x,y,z \).</li>
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<li> We define \( \boldsymbol{X}=\sigma_x \), \( \boldsymbol{Y}=\sigma_y \) and \( \boldsymbol{Z}=\sigma_z \). Show that \( \boldsymbol{XX}=\boldsymbol{YY}=\boldsymbol{ZZ}=\boldsymbol{I} \).</li>
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<li> Which one of the Pauli matrices has the qubit basis \( \vert 0\rangle \) and \( \vert 1\rangle \) as eigenbasis? What are the eigenvalues?</li>
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</ol>
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<!-- !split -->
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<h2 id="exercise-5-shared-eigenvectors" class="anchor">Exercise 5: Shared eigenvectors </h2>
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<p>Prove that if two operators \( \hat{A} \) and \( \hat{B} \) commute they will share a basis of eigenstates</p>
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<!-- !split -->
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<h2 id="exercise-5-one-qubit-basis-and-pauli-matrices" class="anchor">Exercise 5: One-qubit basis and Pauli matrices </h2>
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<h2 id="exercise-6-one-qubit-basis-and-pauli-matrices" class="anchor">Exercise 6: One-qubit basis and Pauli matrices </h2>
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<p>Write a function which sets up a one-qubit basis and apply the various Pauli matrices to these basis states.</p>
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<!-- !split -->
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<h2 id="exercise-6-hadamard-and-phase-gates" class="anchor">Exercise 6: Hadamard and Phase gates </h2>
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<h2 id="exercise-7-hadamard-and-phase-gates" class="anchor">Exercise 7: Hadamard and Phase gates </h2>
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<p>Apply the Hadamard and Phase gates to the same one-qubit basis states and study their actions on these states.</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/week1/html/week1-reveal.html‎

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</section>
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<section>
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<h2 id="exercise-4-shared-eigenvectors">Exercise 4: Shared eigenvectors </h2>
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<h2 id="exercise-4-pauli-matrices">Exercise 4: Pauli matrices </h2>
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<ol>
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<p><li> Set up the commutation rules for Pauli matrices, that is find \( [\sigma_i,\sigma_j] \) where \( i,j=x,y,z \).</li>
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<p><li> We define \( \boldsymbol{X}=\sigma_x \), \( \boldsymbol{Y}=\sigma_y \) and \( \boldsymbol{Z}=\sigma_z \). Show that \( \boldsymbol{XX}=\boldsymbol{YY}=\boldsymbol{ZZ}=\boldsymbol{I} \).</li>
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<p><li> Which one of the Pauli matrices has the qubit basis \( \vert 0\rangle \) and \( \vert 1\rangle \) as eigenbasis? What are the eigenvalues?</li>
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</ol>
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</section>
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<section>
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<h2 id="exercise-5-shared-eigenvectors">Exercise 5: Shared eigenvectors </h2>
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<p>Prove that if two operators \( \hat{A} \) and \( \hat{B} \) commute they will share a basis of eigenstates</p>
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</section>
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<section>
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<h2 id="exercise-5-one-qubit-basis-and-pauli-matrices">Exercise 5: One-qubit basis and Pauli matrices </h2>
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<h2 id="exercise-6-one-qubit-basis-and-pauli-matrices">Exercise 6: One-qubit basis and Pauli matrices </h2>
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<p>Write a function which sets up a one-qubit basis and apply the various Pauli matrices to these basis states.</p>
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</section>
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<section>
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<h2 id="exercise-6-hadamard-and-phase-gates">Exercise 6: Hadamard and Phase gates </h2>
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<h2 id="exercise-7-hadamard-and-phase-gates">Exercise 7: Hadamard and Phase gates </h2>
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<p>Apply the Hadamard and Phase gates to the same one-qubit basis states and study their actions on these states.</p>
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</section>

‎doc/pub/week1/html/week1-solarized.html‎

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<body>
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<li> \( [\hat{A},[\hat{B}\hat{C}]]= [\hat{B},[\hat{C},\hat{A}]]+[\hat{C},[\hat{A},\hat{B}]]=0 \) (the so-called Jacobi identity).</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="exercise-4-shared-eigenvectors">Exercise 4: Shared eigenvectors </h2>
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<h2 id="exercise-4-pauli-matrices">Exercise 4: Pauli matrices </h2>
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<ol>
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<li> Set up the commutation rules for Pauli matrices, that is find \( [\sigma_i,\sigma_j] \) where \( i,j=x,y,z \).</li>
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<li> We define \( \boldsymbol{X}=\sigma_x \), \( \boldsymbol{Y}=\sigma_y \) and \( \boldsymbol{Z}=\sigma_z \). Show that \( \boldsymbol{XX}=\boldsymbol{YY}=\boldsymbol{ZZ}=\boldsymbol{I} \).</li>
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<li> Which one of the Pauli matrices has the qubit basis \( \vert 0\rangle \) and \( \vert 1\rangle \) as eigenbasis? What are the eigenvalues?</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="exercise-5-shared-eigenvectors">Exercise 5: Shared eigenvectors </h2>
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<p>Prove that if two operators \( \hat{A} \) and \( \hat{B} \) commute they will share a basis of eigenstates</p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="exercise-5-one-qubit-basis-and-pauli-matrices">Exercise 5: One-qubit basis and Pauli matrices </h2>
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<h2 id="exercise-6-one-qubit-basis-and-pauli-matrices">Exercise 6: One-qubit basis and Pauli matrices </h2>
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<p>Write a function which sets up a one-qubit basis and apply the various Pauli matrices to these basis states.</p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="exercise-6-hadamard-and-phase-gates">Exercise 6: Hadamard and Phase gates </h2>
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<h2 id="exercise-7-hadamard-and-phase-gates">Exercise 7: Hadamard and Phase gates </h2>
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<p>Apply the Hadamard and Phase gates to the same one-qubit basis states and study their actions on these states.</p>
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<!-- ------------------- end of main content --------------- -->
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<center style="font-size:80%">
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<!-- copyright --> &copy; 1999-2025, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license

‎doc/pub/week1/html/week1.html‎

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<body>
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<li> \( [\hat{A},[\hat{B}\hat{C}]]= [\hat{B},[\hat{C},\hat{A}]]+[\hat{C},[\hat{A},\hat{B}]]=0 \) (the so-called Jacobi identity).</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="exercise-4-shared-eigenvectors">Exercise 4: Shared eigenvectors </h2>
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<h2 id="exercise-4-pauli-matrices">Exercise 4: Pauli matrices </h2>
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<ol>
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<li> Set up the commutation rules for Pauli matrices, that is find \( [\sigma_i,\sigma_j] \) where \( i,j=x,y,z \).</li>
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<li> We define \( \boldsymbol{X}=\sigma_x \), \( \boldsymbol{Y}=\sigma_y \) and \( \boldsymbol{Z}=\sigma_z \). Show that \( \boldsymbol{XX}=\boldsymbol{YY}=\boldsymbol{ZZ}=\boldsymbol{I} \).</li>
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<li> Which one of the Pauli matrices has the qubit basis \( \vert 0\rangle \) and \( \vert 1\rangle \) as eigenbasis? What are the eigenvalues?</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="exercise-5-shared-eigenvectors">Exercise 5: Shared eigenvectors </h2>
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<p>Prove that if two operators \( \hat{A} \) and \( \hat{B} \) commute they will share a basis of eigenstates</p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="exercise-5-one-qubit-basis-and-pauli-matrices">Exercise 5: One-qubit basis and Pauli matrices </h2>
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<h2 id="exercise-6-one-qubit-basis-and-pauli-matrices">Exercise 6: One-qubit basis and Pauli matrices </h2>
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<p>Write a function which sets up a one-qubit basis and apply the various Pauli matrices to these basis states.</p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="exercise-6-hadamard-and-phase-gates">Exercise 6: Hadamard and Phase gates </h2>
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<h2 id="exercise-7-hadamard-and-phase-gates">Exercise 7: Hadamard and Phase gates </h2>
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<p>Apply the Hadamard and Phase gates to the same one-qubit basis states and study their actions on these states.</p>
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<!-- ------------------- end of main content --------------- -->
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<center style="font-size:80%">
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<!-- copyright --> &copy; 1999-2025, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license

‎doc/pub/week1/ipynb/ipynb-week1-src.tar.gz‎

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