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corrected exercise numbering
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‎doc/pub/week1/html/week1-bs.html‎

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@@ -188,32 +188,23 @@
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218209

219210
<body>
@@ -319,14 +310,14 @@
319310
<!-- navigation toc: --> <li><a href="#explicit-results" style="font-size: 80%;">Explicit results</a></li>
320311
<!-- navigation toc: --> <li><a href="#the-spectral-decomposition" style="font-size: 80%;">The spectral decomposition</a></li>
321312
<!-- navigation toc: --> <li><a href="#first-exercise-set" style="font-size: 80%;">First exercise set</a></li>
322-
<!-- navigation toc: --> <li><a href="#exercise-1-bell-states" style="font-size: 80%;">Exercise 1: Bell states</a></li>
313+
<!-- navigation toc: --> <li><a href="#ex1-bell-states" style="font-size: 80%;">Ex1: Bell states</a></li>
323314
<!-- navigation toc: --> <li><a href="#and-the-next-two" style="font-size: 80%;">And the next two</a></li>
324-
<!-- navigation toc: --> <li><a href="#exercise-2-entangled-state" style="font-size: 80%;">Exercise 2: Entangled state</a></li>
325-
<!-- navigation toc: --> <li><a href="#exercise-3-commutator-identities" style="font-size: 80%;">Exercise 3: Commutator identities</a></li>
326-
<!-- navigation toc: --> <li><a href="#exercise-4-pauli-matrices" style="font-size: 80%;">Exercise 4: Pauli matrices</a></li>
327-
<!-- navigation toc: --> <li><a href="#exercise-5-shared-eigenvectors" style="font-size: 80%;">Exercise 5: Shared eigenvectors</a></li>
328-
<!-- 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>
329-
<!-- navigation toc: --> <li><a href="#exercise-7-hadamard-and-phase-gates" style="font-size: 80%;">Exercise 7: Hadamard and Phase gates</a></li>
315+
<!-- navigation toc: --> <li><a href="#ex2-entangled-state" style="font-size: 80%;">Ex2: Entangled state</a></li>
316+
<!-- navigation toc: --> <li><a href="#ex3-commutator-identities" style="font-size: 80%;">Ex3: Commutator identities</a></li>
317+
<!-- navigation toc: --> <li><a href="#ex4-pauli-matrices" style="font-size: 80%;">Ex4: Pauli matrices</a></li>
318+
<!-- navigation toc: --> <li><a href="#ex5-shared-eigenvectors" style="font-size: 80%;">Ex5: Shared eigenvectors</a></li>
319+
<!-- navigation toc: --> <li><a href="#ex6-one-qubit-basis-and-pauli-matrices" style="font-size: 80%;">Ex6: One-qubit basis and Pauli matrices</a></li>
320+
<!-- navigation toc: --> <li><a href="#ex7-hadamard-and-phase-gates" style="font-size: 80%;">Ex7: Hadamard and Phase gates</a></li>
330321

331322
</ul>
332323
</li>
@@ -1578,7 +1569,7 @@ <h2 id="first-exercise-set" class="anchor">First exercise set </h2>
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</p>
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15801571
<!-- !split -->
1581-
<h2 id="exercise-1-bell-states" class="anchor">Exercise 1: Bell states </h2>
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<h2 id="ex1-bell-states" class="anchor">Ex1: Bell states </h2>
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15831574
<p>Show that the so-called Bell states listed here (and to be encountered many times in this course) form an orthogonal basis</p>
15841575
$$
@@ -1605,37 +1596,37 @@ <h2 id="and-the-next-two" class="anchor">And the next two </h2>
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<!-- !split -->
1608-
<h2 id="exercise-2-entangled-state" class="anchor">Exercise 2: Entangled state </h2>
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<h2 id="ex2-entangled-state" class="anchor">Ex2: Entangled state </h2>
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16101601
<p>Show that the state \( \alpha \vert 00\rangle+\beta\vert 11\rangle \) cannot be written as the product of the tensor product of two states and is thus entangle. The constants \( \alpha \) and \( \beta \) are both nonzero.</p>
16111602

16121603
<!-- !split -->
1613-
<h2 id="exercise-3-commutator-identities" class="anchor">Exercise 3: Commutator identities </h2>
1604+
<h2 id="ex3-commutator-identities" class="anchor">Ex3: Commutator identities </h2>
16141605
<p>Prove the following commutator relations for different operators (marked with a hat)</p>
16151606
<ol>
16161607
<li> \( [\hat{A}+\hat{B},\hat{C}]= [\hat{A},\hat{C}]+[\hat{B},\hat{C}] \);</li>
16171608
<li> \( [\hat{A},\hat{B}\hat{C}]= [\hat{A},\hat{B}]\hat{C}+\hat{B}[\hat{A},\hat{C}] \); and</li>
16181609
<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>
16191610
</ol>
16201611
<!-- !split -->
1621-
<h2 id="exercise-4-pauli-matrices" class="anchor">Exercise 4: Pauli matrices </h2>
1612+
<h2 id="ex4-pauli-matrices" class="anchor">Ex4: Pauli matrices </h2>
16221613
<ol>
16231614
<li> Set up the commutation rules for Pauli matrices, that is find \( [\sigma_i,\sigma_j] \) where \( i,j=x,y,z \).</li>
16241615
<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>
16251616
<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>
16261617
</ol>
16271618
<!-- !split -->
1628-
<h2 id="exercise-5-shared-eigenvectors" class="anchor">Exercise 5: Shared eigenvectors </h2>
1619+
<h2 id="ex5-shared-eigenvectors" class="anchor">Ex5: Shared eigenvectors </h2>
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16301621
<p>Prove that if two operators \( \hat{A} \) and \( \hat{B} \) commute they will share a basis of eigenstates</p>
16311622

16321623
<!-- !split -->
1633-
<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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<h2 id="ex6-one-qubit-basis-and-pauli-matrices" class="anchor">Ex6: One-qubit basis and Pauli matrices </h2>
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16351626
<p>Write a function which sets up a one-qubit basis and apply the various Pauli matrices to these basis states.</p>
16361627

16371628
<!-- !split -->
1638-
<h2 id="exercise-7-hadamard-and-phase-gates" class="anchor">Exercise 7: Hadamard and Phase gates </h2>
1629+
<h2 id="ex7-hadamard-and-phase-gates" class="anchor">Ex7: Hadamard and Phase gates </h2>
16391630

16401631
<p>Apply the Hadamard and Phase gates to the same one-qubit basis states and study their actions on these states.</p>
16411632
<!-- ------------------- end of main content --------------- -->

‎doc/pub/week1/html/week1-reveal.html‎

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@@ -1666,7 +1666,7 @@ <h2 id="first-exercise-set">First exercise set </h2>
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</section>
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<section>
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<h2 id="exercise-1-bell-states">Exercise 1: Bell states </h2>
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<h2 id="ex1-bell-states">Ex1: Bell states </h2>
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<p>Show that the so-called Bell states listed here (and to be encountered many times in this course) form an orthogonal basis</p>
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<p>&nbsp;<br>
@@ -1700,13 +1700,13 @@ <h2 id="and-the-next-two">And the next two </h2>
17001700
</section>
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<section>
1703-
<h2 id="exercise-2-entangled-state">Exercise 2: Entangled state </h2>
1703+
<h2 id="ex2-entangled-state">Ex2: Entangled state </h2>
17041704

17051705
<p>Show that the state \( \alpha \vert 00\rangle+\beta\vert 11\rangle \) cannot be written as the product of the tensor product of two states and is thus entangle. The constants \( \alpha \) and \( \beta \) are both nonzero.</p>
17061706
</section>
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17081708
<section>
1709-
<h2 id="exercise-3-commutator-identities">Exercise 3: Commutator identities </h2>
1709+
<h2 id="ex3-commutator-identities">Ex3: Commutator identities </h2>
17101710
<p>Prove the following commutator relations for different operators (marked with a hat)</p>
17111711
<ol>
17121712
<p><li> \( [\hat{A}+\hat{B},\hat{C}]= [\hat{A},\hat{C}]+[\hat{B},\hat{C}] \);</li>
@@ -1716,7 +1716,7 @@ <h2 id="exercise-3-commutator-identities">Exercise 3: Commutator identities </h
17161716
</section>
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17181718
<section>
1719-
<h2 id="exercise-4-pauli-matrices">Exercise 4: Pauli matrices </h2>
1719+
<h2 id="ex4-pauli-matrices">Ex4: Pauli matrices </h2>
17201720
<ol>
17211721
<p><li> Set up the commutation rules for Pauli matrices, that is find \( [\sigma_i,\sigma_j] \) where \( i,j=x,y,z \).</li>
17221722
<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>
@@ -1725,19 +1725,19 @@ <h2 id="exercise-4-pauli-matrices">Exercise 4: Pauli matrices </h2>
17251725
</section>
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17271727
<section>
1728-
<h2 id="exercise-5-shared-eigenvectors">Exercise 5: Shared eigenvectors </h2>
1728+
<h2 id="ex5-shared-eigenvectors">Ex5: Shared eigenvectors </h2>
17291729

17301730
<p>Prove that if two operators \( \hat{A} \) and \( \hat{B} \) commute they will share a basis of eigenstates</p>
17311731
</section>
17321732

17331733
<section>
1734-
<h2 id="exercise-6-one-qubit-basis-and-pauli-matrices">Exercise 6: One-qubit basis and Pauli matrices </h2>
1734+
<h2 id="ex6-one-qubit-basis-and-pauli-matrices">Ex6: One-qubit basis and Pauli matrices </h2>
17351735

17361736
<p>Write a function which sets up a one-qubit basis and apply the various Pauli matrices to these basis states.</p>
17371737
</section>
17381738

17391739
<section>
1740-
<h2 id="exercise-7-hadamard-and-phase-gates">Exercise 7: Hadamard and Phase gates </h2>
1740+
<h2 id="ex7-hadamard-and-phase-gates">Ex7: Hadamard and Phase gates </h2>
17411741

17421742
<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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</p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
1492-
<h2 id="exercise-1-bell-states">Exercise 1: Bell states </h2>
1483+
<h2 id="ex1-bell-states">Ex1: Bell states </h2>
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<p>Show that the so-called Bell states listed here (and to be encountered many times in this course) form an orthogonal basis</p>
14951486
$$
@@ -1516,37 +1507,37 @@ <h2 id="and-the-next-two">And the next two </h2>
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15171508

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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
1519-
<h2 id="exercise-2-entangled-state">Exercise 2: Entangled state </h2>
1510+
<h2 id="ex2-entangled-state">Ex2: Entangled state </h2>
15201511

15211512
<p>Show that the state \( \alpha \vert 00\rangle+\beta\vert 11\rangle \) cannot be written as the product of the tensor product of two states and is thus entangle. The constants \( \alpha \) and \( \beta \) are both nonzero.</p>
15221513

15231514
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
1524-
<h2 id="exercise-3-commutator-identities">Exercise 3: Commutator identities </h2>
1515+
<h2 id="ex3-commutator-identities">Ex3: Commutator identities </h2>
15251516
<p>Prove the following commutator relations for different operators (marked with a hat)</p>
15261517
<ol>
15271518
<li> \( [\hat{A}+\hat{B},\hat{C}]= [\hat{A},\hat{C}]+[\hat{B},\hat{C}] \);</li>
15281519
<li> \( [\hat{A},\hat{B}\hat{C}]= [\hat{A},\hat{B}]\hat{C}+\hat{B}[\hat{A},\hat{C}] \); and</li>
15291520
<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>
15301521
</ol>
15311522
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
1532-
<h2 id="exercise-4-pauli-matrices">Exercise 4: Pauli matrices </h2>
1523+
<h2 id="ex4-pauli-matrices">Ex4: Pauli matrices </h2>
15331524
<ol>
15341525
<li> Set up the commutation rules for Pauli matrices, that is find \( [\sigma_i,\sigma_j] \) where \( i,j=x,y,z \).</li>
15351526
<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>
15361527
<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>
15371528
</ol>
15381529
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
1539-
<h2 id="exercise-5-shared-eigenvectors">Exercise 5: Shared eigenvectors </h2>
1530+
<h2 id="ex5-shared-eigenvectors">Ex5: Shared eigenvectors </h2>
15401531

15411532
<p>Prove that if two operators \( \hat{A} \) and \( \hat{B} \) commute they will share a basis of eigenstates</p>
15421533

15431534
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
1544-
<h2 id="exercise-6-one-qubit-basis-and-pauli-matrices">Exercise 6: One-qubit basis and Pauli matrices </h2>
1535+
<h2 id="ex6-one-qubit-basis-and-pauli-matrices">Ex6: One-qubit basis and Pauli matrices </h2>
15451536

15461537
<p>Write a function which sets up a one-qubit basis and apply the various Pauli matrices to these basis states.</p>
15471538

15481539
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
1549-
<h2 id="exercise-7-hadamard-and-phase-gates">Exercise 7: Hadamard and Phase gates </h2>
1540+
<h2 id="ex7-hadamard-and-phase-gates">Ex7: Hadamard and Phase gates </h2>
15501541

15511542
<p>Apply the Hadamard and Phase gates to the same one-qubit basis states and study their actions on these states.</p>
15521543
<!-- ------------------- end of main content --------------- -->

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