update p1

Author: mhjensen

doc/Projects/2026/Project1/html/._Project1-bs000.html

@@ -37,12 +37,12 @@
 <!-- tocinfo
 {'highest level': 1,
  'sections': [('Project suggestion', 1, None, 'project-suggestion'),
-              ('Part a) (score 10pt)', 2, None, 'part-a-score-10pt'),
+              ('Part a) (score 15pt)', 2, None, 'part-a-score-15pt'),
               ('Part b) (score 10pt)', 2, None, 'part-b-score-10pt'),
               ('Part c) (score 10pt)', 2, None, 'part-c-score-10pt'),
               ('Part d) (score 15pt)', 2, None, 'part-d-score-15pt'),
               ('Part e) (score 15 pt)', 2, None, 'part-e-score-15-pt'),
-              ('Part f) (score 20 pt)', 2, None, 'part-f-score-20-pt'),
+              ('Part f) (score 15 pt)', 2, None, 'part-f-score-15-pt'),
               ('Part g) (score 20 pt)', 2, None, 'part-g-score-20-pt'),
               ('Introduction to numerical projects',
                2,
@@ -87,12 +87,12 @@
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
      <!-- navigation toc: --> <li><a href="#project-suggestion" style="font-size: 80%;"><b>Project suggestion</b></a></li>
-     <!-- navigation toc: --> <li><a href="#part-a-score-10pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part a) (score 10pt)</a></li>
+     <!-- navigation toc: --> <li><a href="#part-a-score-15pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part a) (score 15pt)</a></li>
      <!-- navigation toc: --> <li><a href="#part-b-score-10pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part b) (score 10pt)</a></li>
      <!-- navigation toc: --> <li><a href="#part-c-score-10pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part c) (score 10pt)</a></li>
      <!-- navigation toc: --> <li><a href="#part-d-score-15pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part d) (score 15pt)</a></li>
      <!-- navigation toc: --> <li><a href="#part-e-score-15-pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part e) (score 15 pt)</a></li>
-     <!-- navigation toc: --> <li><a href="#part-f-score-20-pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part f) (score 20 pt)</a></li>
+     <!-- navigation toc: --> <li><a href="#part-f-score-15-pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part f) (score 15 pt)</a></li>
      <!-- navigation toc: --> <li><a href="#part-g-score-20-pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part g) (score 20 pt)</a></li>
      <!-- navigation toc: --> <li><a href="#introduction-to-numerical-projects" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Introduction to numerical projects</a></li>
      <!-- navigation toc: --> <li><a href="#format-for-electronic-delivery-of-report-and-programs" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Format for electronic delivery of report and programs</a></li>
@@ -131,9 +131,7 @@ <h1 id="project-suggestion" class="anchor">Project suggestion  </h1>
 The total score is 100 points. You can answer each exercise in a sequential way or write a scientific report. Each exercise is given a final score.
 If you plan to write a report, you could use the article in the Physical Review C, volume 106, see <a href="https://journals.aps.org/prc/pdf/10.1103/PhysRevC.106.024319" target="_self"><tt>https://journals.aps.org/prc/pdf/10.1103/PhysRevC.106.024319</tt></a> as a template for your report.
 </p>
-
-<p><b>Note:</b> This is  prelimary version, changes will come and the final version is availbale from February 2.</p>
-<h2 id="part-a-score-10pt" class="anchor">Part a) (score 10pt) </h2>
+<h2 id="part-a-score-15pt" class="anchor">Part a) (score 15pt) </h2>
 
 <p>Write a function which sets up a one-qubit basis and apply the various
 Pauli matrices to these basis states.  Apply the Hadamard and Phase
@@ -146,7 +144,12 @@ <h2 id="part-a-score-10pt" class="anchor">Part a) (score 10pt) </h2>
 which should be discussed and presented.
 </p>
 
-<p>Compare your code with the results obtained using for example software like <b>Qiskit</b>.</p>
+<p>For the Bell states (one of your choice), you should also write a code
+which traces out the density matrix for one subsystem and calculate
+the von Neumann entropy and discuss the results.
+</p>
+
+<!-- You can compare your code with the results obtained using for example software like <b>Qiskit</b>. -->
 <h2 id="part-b-score-10pt" class="anchor">Part b) (score 10pt) </h2>
 
 <p>We define a  symmetric matrix  \( H\in {\mathbb{R}}^{2\times 2} \)</p>
@@ -222,7 +225,7 @@ <h2 id="part-b-score-10pt" class="anchor">Part b) (score 10pt) </h2>
 \( \vert 0 \rangle \) component of more than \( 90\% \).  The character of the
 eigenvectors has therefore been interchanged when passing \( z=2/3 \). The
 value of the parameter \( V_{12} \) represents the strength of the coupling
-between the two states..
+between the two states.
 </p>
 
 <p>Solve <b>by standard eigenvalue solvers</b> (either numerically or analytically) the above eigenvalue problem.
@@ -235,9 +238,9 @@ <h2 id="part-c-score-10pt" class="anchor">Part c) (score 10pt) </h2>
 <p>Implement now the variational quantum eigensolver (VQE) for the above
 Hamiltonian and set up the circuit(s) which is(are) needed in order to find
 the eigenvalues of this system. Discuss the results and compare these
-with those from part b). Feel free to use either <b>Qiskit</b> or your own
-code (based on the setup from part a)) or both approaches. Discuss
-your results.
+with those from part b). You have to write your own code for the VQE but you can compare your code
+with either <b>Qiskit</b> or other software libraries like <b>Pennylane</b> or other.
+Discuss your results.
 </p>
 <h2 id="part-d-score-15pt" class="anchor">Part d) (score 15pt) </h2>
 
@@ -336,7 +339,7 @@ <h2 id="part-d-score-15pt" class="anchor">Part d) (score 15pt) </h2>
 $$
 
 <p>The density matrices for these subsets can be used to compute the
-so-called von Neumann entropy, which is one of the possible measures
+von Neumann entropy discussed in exercise a), which is one of the possible measures
 of entanglement. A pure state has entropy equal zero while entangled
 state have an entropy larger than zero. The von-Neumann entropy is
 defined as
@@ -396,11 +399,12 @@ <h2 id="part-e-score-15-pt" class="anchor">Part e) (score 15 pt) </h2>
 
 <p>Compute now the eigenvalues of this system using the VQE method and
 set up the circuits needed to find the lowest state. Compare these
-results with those from the previous part. Feel free again to either
-use your own code for the circuit and your VQE code or use the
-functionality of <a href="https://qiskit.org/" target="_self">Qiskit</a>, or both.
+results with those from the previous part.
+You have to write your own code for the VQE but you can compare your code
+with either <b>Qiskit</b> or other software libraries like <b>Pennylane</b> or other.
+Discuss your results.
 </p>
-<h2 id="part-f-score-20-pt" class="anchor">Part f) (score 20 pt) </h2>
+<h2 id="part-f-score-15-pt" class="anchor">Part f) (score 15 pt) </h2>
 
 <p>We introduce now the Lipkin Hamiltonian and study this for the
 \( 3\times 3 \) matrix case with total spin \( J=1 \) and the \( 5\times 5 \)

doc/Projects/2026/Project1/html/Project1-bs.html

@@ -37,12 +37,12 @@
 <!-- tocinfo
 {'highest level': 1,
  'sections': [('Project suggestion', 1, None, 'project-suggestion'),
-              ('Part a) (score 10pt)', 2, None, 'part-a-score-10pt'),
+              ('Part a) (score 15pt)', 2, None, 'part-a-score-15pt'),
               ('Part b) (score 10pt)', 2, None, 'part-b-score-10pt'),
               ('Part c) (score 10pt)', 2, None, 'part-c-score-10pt'),
               ('Part d) (score 15pt)', 2, None, 'part-d-score-15pt'),
               ('Part e) (score 15 pt)', 2, None, 'part-e-score-15-pt'),
-              ('Part f) (score 20 pt)', 2, None, 'part-f-score-20-pt'),
+              ('Part f) (score 15 pt)', 2, None, 'part-f-score-15-pt'),
               ('Part g) (score 20 pt)', 2, None, 'part-g-score-20-pt'),
               ('Introduction to numerical projects',
                2,
@@ -87,12 +87,12 @@
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
      <!-- navigation toc: --> <li><a href="#project-suggestion" style="font-size: 80%;"><b>Project suggestion</b></a></li>
-     <!-- navigation toc: --> <li><a href="#part-a-score-10pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part a) (score 10pt)</a></li>
+     <!-- navigation toc: --> <li><a href="#part-a-score-15pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part a) (score 15pt)</a></li>
      <!-- navigation toc: --> <li><a href="#part-b-score-10pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part b) (score 10pt)</a></li>
      <!-- navigation toc: --> <li><a href="#part-c-score-10pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part c) (score 10pt)</a></li>
      <!-- navigation toc: --> <li><a href="#part-d-score-15pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part d) (score 15pt)</a></li>
      <!-- navigation toc: --> <li><a href="#part-e-score-15-pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part e) (score 15 pt)</a></li>
-     <!-- navigation toc: --> <li><a href="#part-f-score-20-pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part f) (score 20 pt)</a></li>
+     <!-- navigation toc: --> <li><a href="#part-f-score-15-pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part f) (score 15 pt)</a></li>
      <!-- navigation toc: --> <li><a href="#part-g-score-20-pt" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Part g) (score 20 pt)</a></li>
      <!-- navigation toc: --> <li><a href="#introduction-to-numerical-projects" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Introduction to numerical projects</a></li>
      <!-- navigation toc: --> <li><a href="#format-for-electronic-delivery-of-report-and-programs" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Format for electronic delivery of report and programs</a></li>
@@ -131,9 +131,7 @@ <h1 id="project-suggestion" class="anchor">Project suggestion  </h1>
 The total score is 100 points. You can answer each exercise in a sequential way or write a scientific report. Each exercise is given a final score.
 If you plan to write a report, you could use the article in the Physical Review C, volume 106, see <a href="https://journals.aps.org/prc/pdf/10.1103/PhysRevC.106.024319" target="_self"><tt>https://journals.aps.org/prc/pdf/10.1103/PhysRevC.106.024319</tt></a> as a template for your report.
 </p>
-
-<p><b>Note:</b> This is  prelimary version, changes will come and the final version is availbale from February 2.</p>
-<h2 id="part-a-score-10pt" class="anchor">Part a) (score 10pt) </h2>
+<h2 id="part-a-score-15pt" class="anchor">Part a) (score 15pt) </h2>
 
 <p>Write a function which sets up a one-qubit basis and apply the various
 Pauli matrices to these basis states.  Apply the Hadamard and Phase
@@ -146,7 +144,12 @@ <h2 id="part-a-score-10pt" class="anchor">Part a) (score 10pt) </h2>
 which should be discussed and presented.
 </p>
 
-<p>Compare your code with the results obtained using for example software like <b>Qiskit</b>.</p>
+<p>For the Bell states (one of your choice), you should also write a code
+which traces out the density matrix for one subsystem and calculate
+the von Neumann entropy and discuss the results.
+</p>
+
+<!-- You can compare your code with the results obtained using for example software like <b>Qiskit</b>. -->
 <h2 id="part-b-score-10pt" class="anchor">Part b) (score 10pt) </h2>
 
 <p>We define a  symmetric matrix  \( H\in {\mathbb{R}}^{2\times 2} \)</p>
@@ -222,7 +225,7 @@ <h2 id="part-b-score-10pt" class="anchor">Part b) (score 10pt) </h2>
 \( \vert 0 \rangle \) component of more than \( 90\% \).  The character of the
 eigenvectors has therefore been interchanged when passing \( z=2/3 \). The
 value of the parameter \( V_{12} \) represents the strength of the coupling
-between the two states..
+between the two states.
 </p>
 
 <p>Solve <b>by standard eigenvalue solvers</b> (either numerically or analytically) the above eigenvalue problem.
@@ -235,9 +238,9 @@ <h2 id="part-c-score-10pt" class="anchor">Part c) (score 10pt) </h2>
 <p>Implement now the variational quantum eigensolver (VQE) for the above
 Hamiltonian and set up the circuit(s) which is(are) needed in order to find
 the eigenvalues of this system. Discuss the results and compare these
-with those from part b). Feel free to use either <b>Qiskit</b> or your own
-code (based on the setup from part a)) or both approaches. Discuss
-your results.
+with those from part b). You have to write your own code for the VQE but you can compare your code
+with either <b>Qiskit</b> or other software libraries like <b>Pennylane</b> or other.
+Discuss your results.
 </p>
 <h2 id="part-d-score-15pt" class="anchor">Part d) (score 15pt) </h2>
 
@@ -336,7 +339,7 @@ <h2 id="part-d-score-15pt" class="anchor">Part d) (score 15pt) </h2>
 $$
 
 <p>The density matrices for these subsets can be used to compute the
-so-called von Neumann entropy, which is one of the possible measures
+von Neumann entropy discussed in exercise a), which is one of the possible measures
 of entanglement. A pure state has entropy equal zero while entangled
 state have an entropy larger than zero. The von-Neumann entropy is
 defined as
@@ -396,11 +399,12 @@ <h2 id="part-e-score-15-pt" class="anchor">Part e) (score 15 pt) </h2>
 
 <p>Compute now the eigenvalues of this system using the VQE method and
 set up the circuits needed to find the lowest state. Compare these
-results with those from the previous part. Feel free again to either
-use your own code for the circuit and your VQE code or use the
-functionality of <a href="https://qiskit.org/" target="_self">Qiskit</a>, or both.
+results with those from the previous part.
+You have to write your own code for the VQE but you can compare your code
+with either <b>Qiskit</b> or other software libraries like <b>Pennylane</b> or other.
+Discuss your results.
 </p>
-<h2 id="part-f-score-20-pt" class="anchor">Part f) (score 20 pt) </h2>
+<h2 id="part-f-score-15-pt" class="anchor">Part f) (score 15 pt) </h2>
 
 <p>We introduce now the Lipkin Hamiltonian and study this for the
 \( 3\times 3 \) matrix case with total spin \( J=1 \) and the \( 5\times 5 \)

doc/Projects/2026/Project1/html/Project1.html

@@ -115,12 +115,12 @@
 <!-- tocinfo
 {'highest level': 1,
  'sections': [('Project suggestion', 1, None, 'project-suggestion'),
-              ('Part a) (score 10pt)', 2, None, 'part-a-score-10pt'),
+              ('Part a) (score 15pt)', 2, None, 'part-a-score-15pt'),
               ('Part b) (score 10pt)', 2, None, 'part-b-score-10pt'),
               ('Part c) (score 10pt)', 2, None, 'part-c-score-10pt'),
               ('Part d) (score 15pt)', 2, None, 'part-d-score-15pt'),
               ('Part e) (score 15 pt)', 2, None, 'part-e-score-15-pt'),
-              ('Part f) (score 20 pt)', 2, None, 'part-f-score-20-pt'),
+              ('Part f) (score 15 pt)', 2, None, 'part-f-score-15-pt'),
               ('Part g) (score 20 pt)', 2, None, 'part-g-score-20-pt'),
               ('Introduction to numerical projects',
                2,
@@ -170,9 +170,7 @@ <h1 id="project-suggestion">Project suggestion  </h1>
 The total score is 100 points. You can answer each exercise in a sequential way or write a scientific report. Each exercise is given a final score.
 If you plan to write a report, you could use the article in the Physical Review C, volume 106, see <a href="https://journals.aps.org/prc/pdf/10.1103/PhysRevC.106.024319" target="_blank"><tt>https://journals.aps.org/prc/pdf/10.1103/PhysRevC.106.024319</tt></a> as a template for your report.
 </p>
-
-<p><b>Note:</b> This is  prelimary version, changes will come and the final version is availbale from February 2.</p>
-<h2 id="part-a-score-10pt">Part a) (score 10pt) </h2>
+<h2 id="part-a-score-15pt">Part a) (score 15pt) </h2>
 
 <p>Write a function which sets up a one-qubit basis and apply the various
 Pauli matrices to these basis states.  Apply the Hadamard and Phase
@@ -185,7 +183,12 @@ <h2 id="part-a-score-10pt">Part a) (score 10pt) </h2>
 which should be discussed and presented.
 </p>
 
-<p>Compare your code with the results obtained using for example software like <b>Qiskit</b>.</p>
+<p>For the Bell states (one of your choice), you should also write a code
+which traces out the density matrix for one subsystem and calculate
+the von Neumann entropy and discuss the results.
+</p>
+
+<!-- You can compare your code with the results obtained using for example software like <b>Qiskit</b>. -->
 <h2 id="part-b-score-10pt">Part b) (score 10pt) </h2>
 
 <p>We define a  symmetric matrix  \( H\in {\mathbb{R}}^{2\times 2} \)</p>
@@ -261,7 +264,7 @@ <h2 id="part-b-score-10pt">Part b) (score 10pt) </h2>
 \( \vert 0 \rangle \) component of more than \( 90\% \).  The character of the
 eigenvectors has therefore been interchanged when passing \( z=2/3 \). The
 value of the parameter \( V_{12} \) represents the strength of the coupling
-between the two states..
+between the two states.
 </p>
 
 <p>Solve <b>by standard eigenvalue solvers</b> (either numerically or analytically) the above eigenvalue problem.
@@ -274,9 +277,9 @@ <h2 id="part-c-score-10pt">Part c) (score 10pt) </h2>
 <p>Implement now the variational quantum eigensolver (VQE) for the above
 Hamiltonian and set up the circuit(s) which is(are) needed in order to find
 the eigenvalues of this system. Discuss the results and compare these
-with those from part b). Feel free to use either <b>Qiskit</b> or your own
-code (based on the setup from part a)) or both approaches. Discuss
-your results.
+with those from part b). You have to write your own code for the VQE but you can compare your code
+with either <b>Qiskit</b> or other software libraries like <b>Pennylane</b> or other.
+Discuss your results.
 </p>
 <h2 id="part-d-score-15pt">Part d) (score 15pt) </h2>
 
@@ -375,7 +378,7 @@ <h2 id="part-d-score-15pt">Part d) (score 15pt) </h2>
 $$
 
 <p>The density matrices for these subsets can be used to compute the
-so-called von Neumann entropy, which is one of the possible measures
+von Neumann entropy discussed in exercise a), which is one of the possible measures
 of entanglement. A pure state has entropy equal zero while entangled
 state have an entropy larger than zero. The von-Neumann entropy is
 defined as
@@ -435,11 +438,12 @@ <h2 id="part-e-score-15-pt">Part e) (score 15 pt) </h2>
 
 <p>Compute now the eigenvalues of this system using the VQE method and
 set up the circuits needed to find the lowest state. Compare these
-results with those from the previous part. Feel free again to either
-use your own code for the circuit and your VQE code or use the
-functionality of <a href="https://qiskit.org/" target="_blank">Qiskit</a>, or both.
+results with those from the previous part.
+You have to write your own code for the VQE but you can compare your code
+with either <b>Qiskit</b> or other software libraries like <b>Pennylane</b> or other.
+Discuss your results.
 </p>
-<h2 id="part-f-score-20-pt">Part f) (score 20 pt) </h2>
+<h2 id="part-f-score-15-pt">Part f) (score 15 pt) </h2>
 
 <p>We introduce now the Lipkin Hamiltonian and study this for the
 \( 3\times 3 \) matrix case with total spin \( J=1 \) and the \( 5\times 5 \)