typos

Author: mhjensen

doc/pub/week4/html/week4-bs.html

@@ -864,13 +864,13 @@ <h2 id="time-evolution" class="anchor">Time evolution </h2>
 \vert \psi(t) \rangle=\exp{\imath\omega_L t\sigma_z/2}\cos{(\frac{\theta}{2})}\vert 0\rangle +\exp{\imath\omega_L t\sigma_z/2}\exp{\imath\phi}\sin{(\frac{\theta}{2})}\vert 1\rangle.
 $$
 
-<p>The specific hamiltonian we have chosen here serves to exemplify how can represent physical operations in terms of specifc gates, here a one-qubit gate (see whiteboard notes at <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf" target="_self"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf</tt></a>for more details).</p>
+<p>The specific hamiltonian we have chosen here serves to exemplify how can represent physical operations in terms of specific gates, here a one-qubit gate (see whiteboard notes at <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf" target="_self"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf</tt></a>for more details).</p>
 
 <!-- !split -->
 <h2 id="final-expression" class="anchor">Final expression </h2>
-<p>In exercise 4 from the second week, we showed that, given \( \boldsymbol{A} \) an operator on a vector space satisfying \( \boldsymbol{A}^2=1 \) and \( \alpha \) any real constant, we had</p>
+<p>Assume we have a given operator \( \boldsymbol{A} \) acting on a  vector space \( \vert a\rangle \) with eigenvalues \( a \) </p>
 $$
-\exp{\imath\alpha \boldsymbol{A}}=\sum_{n=0}^{\infty} \frac{(i\alpha)^n}{n!}\boldsymbol{A}^n=\boldsymbol{I}\cos{\alpha}+\imath\boldsymbol{A}\sin{\alpha}.
+\exp{\boldsymbol{A}}\vert a\rangle=\sum_{n=0}^{\infty} \frac{1}{n!}\boldsymbol{A}^n\vert a\rangle=\sum_{n=0}^{\infty} \frac{a^n}{n!}\vert a\rangle=\exp{a}\vert a\rangle.
 $$
 
 <p>Using this result, we obtain</p>

doc/pub/week4/html/week4-reveal.html

@@ -878,15 +878,15 @@ <h2 id="time-evolution">Time evolution </h2>
 $$
 <p>&nbsp;<br>
 
-<p>The specific hamiltonian we have chosen here serves to exemplify how can represent physical operations in terms of specifc gates, here a one-qubit gate (see whiteboard notes at <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf" target="_blank"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf</tt></a>for more details).</p>
+<p>The specific hamiltonian we have chosen here serves to exemplify how can represent physical operations in terms of specific gates, here a one-qubit gate (see whiteboard notes at <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf" target="_blank"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf</tt></a>for more details).</p>
 </section>
 
 <section>
 <h2 id="final-expression">Final expression </h2>
-<p>In exercise 4 from the second week, we showed that, given \( \boldsymbol{A} \) an operator on a vector space satisfying \( \boldsymbol{A}^2=1 \) and \( \alpha \) any real constant, we had</p>
+<p>Assume we have a given operator \( \boldsymbol{A} \) acting on a  vector space \( \vert a\rangle \) with eigenvalues \( a \) </p>
 <p>&nbsp;<br>
 $$
-\exp{\imath\alpha \boldsymbol{A}}=\sum_{n=0}^{\infty} \frac{(i\alpha)^n}{n!}\boldsymbol{A}^n=\boldsymbol{I}\cos{\alpha}+\imath\boldsymbol{A}\sin{\alpha}.
+\exp{\boldsymbol{A}}\vert a\rangle=\sum_{n=0}^{\infty} \frac{1}{n!}\boldsymbol{A}^n\vert a\rangle=\sum_{n=0}^{\infty} \frac{a^n}{n!}\vert a\rangle=\exp{a}\vert a\rangle.
 $$
 <p>&nbsp;<br>
 

doc/pub/week4/html/week4-solarized.html

@@ -769,13 +769,13 @@ <h2 id="time-evolution">Time evolution </h2>
 \vert \psi(t) \rangle=\exp{\imath\omega_L t\sigma_z/2}\cos{(\frac{\theta}{2})}\vert 0\rangle +\exp{\imath\omega_L t\sigma_z/2}\exp{\imath\phi}\sin{(\frac{\theta}{2})}\vert 1\rangle.
 $$
 
-<p>The specific hamiltonian we have chosen here serves to exemplify how can represent physical operations in terms of specifc gates, here a one-qubit gate (see whiteboard notes at <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf" target="_blank"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf</tt></a>for more details).</p>
+<p>The specific hamiltonian we have chosen here serves to exemplify how can represent physical operations in terms of specific gates, here a one-qubit gate (see whiteboard notes at <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf" target="_blank"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf</tt></a>for more details).</p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="final-expression">Final expression </h2>
-<p>In exercise 4 from the second week, we showed that, given \( \boldsymbol{A} \) an operator on a vector space satisfying \( \boldsymbol{A}^2=1 \) and \( \alpha \) any real constant, we had</p>
+<p>Assume we have a given operator \( \boldsymbol{A} \) acting on a  vector space \( \vert a\rangle \) with eigenvalues \( a \) </p>
 $$
-\exp{\imath\alpha \boldsymbol{A}}=\sum_{n=0}^{\infty} \frac{(i\alpha)^n}{n!}\boldsymbol{A}^n=\boldsymbol{I}\cos{\alpha}+\imath\boldsymbol{A}\sin{\alpha}.
+\exp{\boldsymbol{A}}\vert a\rangle=\sum_{n=0}^{\infty} \frac{1}{n!}\boldsymbol{A}^n\vert a\rangle=\sum_{n=0}^{\infty} \frac{a^n}{n!}\vert a\rangle=\exp{a}\vert a\rangle.
 $$
 
 <p>Using this result, we obtain</p>

doc/pub/week4/html/week4.html

@@ -846,13 +846,13 @@ <h2 id="time-evolution">Time evolution </h2>
 \vert \psi(t) \rangle=\exp{\imath\omega_L t\sigma_z/2}\cos{(\frac{\theta}{2})}\vert 0\rangle +\exp{\imath\omega_L t\sigma_z/2}\exp{\imath\phi}\sin{(\frac{\theta}{2})}\vert 1\rangle.
 $$
 
-<p>The specific hamiltonian we have chosen here serves to exemplify how can represent physical operations in terms of specifc gates, here a one-qubit gate (see whiteboard notes at <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf" target="_blank"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf</tt></a>for more details).</p>
+<p>The specific hamiltonian we have chosen here serves to exemplify how can represent physical operations in terms of specific gates, here a one-qubit gate (see whiteboard notes at <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf" target="_blank"><tt>https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesFebruary12.pdf</tt></a>for more details).</p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="final-expression">Final expression </h2>
-<p>In exercise 4 from the second week, we showed that, given \( \boldsymbol{A} \) an operator on a vector space satisfying \( \boldsymbol{A}^2=1 \) and \( \alpha \) any real constant, we had</p>
+<p>Assume we have a given operator \( \boldsymbol{A} \) acting on a  vector space \( \vert a\rangle \) with eigenvalues \( a \) </p>
 $$
-\exp{\imath\alpha \boldsymbol{A}}=\sum_{n=0}^{\infty} \frac{(i\alpha)^n}{n!}\boldsymbol{A}^n=\boldsymbol{I}\cos{\alpha}+\imath\boldsymbol{A}\sin{\alpha}.
+\exp{\boldsymbol{A}}\vert a\rangle=\sum_{n=0}^{\infty} \frac{1}{n!}\boldsymbol{A}^n\vert a\rangle=\sum_{n=0}^{\infty} \frac{a^n}{n!}\vert a\rangle=\exp{a}\vert a\rangle.
 $$
 
 <p>Using this result, we obtain</p>