Update week7.do.txt

Author: mhjensen

doc/src/week7/week7.do.txt

@@ -687,7 +687,8 @@ $4\times 4$ unitary matrices.
 !split
 ===== More terms =====
 
-Let us look at the $\bm{X}\otimes \bm{X}$.
+Let us look at the $\bm{X}\otimes \bm{X}$ term in the simpler two-qubit Hamiltonian.
+
 This term can be rewritten as
 
 !bt
@@ -703,10 +704,10 @@ which results in
 		0 & 1 & 0 & 0 \\
 		0 & 0 & -1 & 0 \\
 		0 & 0 & 0 & -1
-	\end{bmatrix},
+	\end{bmatrix}.
 \]
 !et
-which we recognize as our $\bm{Z}\otimes\bm{I}$ tensor product. 
+We recognize this result as our $\bm{Z}\otimes\bm{I}$ tensor product. 
 
 !split
 ===== Explicit expressions =====
@@ -740,22 +741,30 @@ For a two qubit system we list here the possible transformations
 !split
 ===== Additional remarks =====
 
-Here, the CNOT operation appears for the following reason. Each Pauli measurement that doesn't include the 
- matrix is equivalent up to a unitary to 
- by the earlier reasoning. The eigenvalues of 
- only depend on the parity of the qubits that comprise each computational basis vector, and the controlled-not operations serve to compute this parity and store it in the first bit. Then once the first bit is measured, you can recover the identity of the resultant half-space, which is equivalent to measuring the Pauli operator.
-
-Also, while it can be tempting to assume that measuring 
- is the same as sequentially measuring 𝟙
- and then 𝟙
-, this assumption would be false. The reason is that measuring 
- projects the quantum state into either the 
- or 
- eigenstate of these operators. Measuring 𝟙
- and then 𝟙
- projects the quantum state vector first onto a half space of 𝟙
- and then onto a half space of 𝟙
-. As there are four computational basis vectors, performing both measurements reduces the state to a quarter-space and hence reduces it to a single computational basis vector.
+Here, the CNOT (CX10) operation appears for the following reason. Each Pauli
+measurement that does not include the matrix is equivalent up to a
+unitary to by the earlier reasoning. The eigenvalues of only depend on
+the parity of the qubits that comprise each computational basis
+vector, and the controlled-not operations serve to compute this parity
+and store it in the first bit. Then once the first bit is measured,
+you can recover the identity of the resultant half-space, which is
+equivalent to measuring the Pauli operator.
+
+Also, while it can be tempting to assume that measuring is the same as
+sequentially measuring 𝟙 and then 𝟙 , this assumption would be
+false. The reason is that measuring projects the quantum state into
+either the or eigenstate of these operators. Measuring 𝟙 and then 𝟙
+projects the quantum state vector first onto a half space of 𝟙 and
+then onto a half space of 𝟙 . As there are four computational basis
+vectors, performing both measurements reduces the state to a
+quarter-space and hence reduces it to a single computational basis
+vector.
+
+!split
+===== Two-qubit Hamiltonian =====
+!bc pycod
+
+!ec
 
 
 !split