Update week6.do.txt

Author: mhjensen

doc/src/week6/week6.do.txt

@@ -21,12 +21,34 @@ DATE: February 25, 2026
 
 FIGURE: [figures/vqe.png, width=700 frac=1.0]
 
+!split
+===== One-qubit Hamiltonian =====
+
+Last week we simply computed the expectations values of the various
+Pauli matrices by evaluating expressions like
+!bt
+\[
+\langle \psi(\theta)\vert \bm{X} \vert \psi(\theta)\rangle,
+\]
+!et
+for the Pauli-$\bm{X}$ matrix and similarly for the other Pauli matrices and
+the $2\times 2$ identity matrix $\bm{I}$.  This is however not the way
+we end up evaluating such expectation values on an actual quantum
+computer. We have to transform the set of measurements to be performed to the computational basis we have chosen.
+
+!split
+===== Our computational basis =====
+
+The computational basis we have chosen is given by the eigenvectors of
+the Pauli-$\bm{Z}$ matrix, namely $\vert 0 \rangle$ and $\vert
+1\rangle$.
+
 
 
 !split
 ===== Two-qubit Hamiltonian =====
 
-We end this review from last week with a discussion on how to rewrite the two-qubit Hamiltonian rom last week (and project 1)
+Here we discuss  how to rewrite the two-qubit Hamiltonian defined by the following Hamiltonian matrix (project 1)
 !bt
 \[
 \mathcal{H}=\begin{bmatrix} \epsilon_{1}+V_z & 0 & 0 & V_x \\