update

Author: mhjensen

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

@@ -327,9 +327,11 @@ <h2 id="plans-for-the-week-of-february-10-14" class="anchor">Plans for the week
 <!-- !split -->
 <h2 id="readings" class="anchor">Readings </h2>
 
-<ol>
-<li> For the discussion of one-qubit, two-qubit and other gates, sections 2.6-2.11 and 3.1-3.4 of Hundt's book <b>Quantum Computing for Programmers</b>, contain most of the relevant information.</li> 
-</ol>
+<p>For the discussion of one-qubit, two-qubit and other gates, sections
+2.6-2.11 and 3.1-3.4 of Hundt's book <b>Quantum Computing for Programmers</b>,
+contain most of the relevant information.
+</p>
+
 <!-- !split -->
 <h2 id="gates-the-whys-and-hows" class="anchor">Gates, the whys and hows </h2>
 
@@ -356,19 +358,19 @@ <h2 id="gates-the-whys-and-hows" class="anchor">Gates, the whys and hows </h2>
 <h2 id="structure-of-the-lecture" class="anchor">Structure of the lecture </h2>
 
 <ol>
-<li> First we review some of the basic ways of representing the solution to the Schr\"odinger equation, introducing the so-called Interaction, Heisenberg and Schr\"odinger prictures and unitary transformations.</li>
+<li> First we review some of the basic ways of representing the solution to the Schr&#246;dinger equation, introducing the so-called Interaction, Heisenberg and Schr&#246;dinger prictures and unitary transformations.</li>
 <li> Secondly, we present examples of physical processes and how they can be represented as unitary operations on a given state.</li>
 <li> These unitary transformations are then represented as gates. Setting gates together gives us a final circuit which can represent a specific physical system</li>
 </ol>
 <!-- !split -->
 <h2 id="part-1-mathematical-background" class="anchor">Part 1: Mathematical background </h2>
 
-<p>The time-dependent Schr\"odinger equation (or equation of motion) reads</p>
+<p>The time-dependent Schr&#246;dinger equation (or equation of motion) reads</p>
 $$
 \imath \hbar\frac{\partial }{\partial t}|\Psi_S(t)\rangle = \hat{H}\Psi_S(t)\rangle,
 $$
 
-<p>where the subscript \( S \) stands for Schr\"odinger here.
+<p>where the subscript \( S \) stands for Schr&#246;dinger here.
 A formal solution is given by 
 </p>
 $$
@@ -407,7 +409,7 @@ <h2 id="interaction-picture" class="anchor">Interaction picture  </h2>
 $$
 
 <p>which is again a unitary transformation carried out now at the time \( t \) on the 
-wave function in the Schr\"odinger picture. 
+wave function in the Schr&#246;dinger picture. 
 </p>
 
 <!-- !split -->
@@ -422,7 +424,7 @@ <h2 id="taking-the-derivative-wrt-time" class="anchor">Taking the derivative wrt
 <!-- !split -->
 <h2 id="expression-using-the-interaction-picture" class="anchor">Expression using the interaction picture  </h2>
 
-<p>Using the definition of the Schr\"odinger equation, we can rewrite the last equation as </p>
+<p>Using the definition of the Schr&#246;dinger equation, we can rewrite the last equation as </p>
 $$
 \imath \hbar\frac{\partial }{\partial t}|\Psi_I(t)\rangle = \exp{(\imath\hat{H}_0t/\hbar)}\left[-\hat{H}_0+\hat{H}_0+\hat{H}_I\right]\exp{(-\imath\hat{H}_0t/\hbar)}\Psi_I(t)\rangle,
 $$
@@ -474,7 +476,7 @@ <h2 id="interaction-picture-and-equation-of-motion" class="anchor">Interaction p
 \imath \hbar\frac{\partial }{\partial t}\hat{O}_I(t) = \exp{(\imath\hat{H}_0t/\hbar)}\left[\hat{O}_S\hat{H}_0-\hat{H}_0\hat{O}_S\right]\exp{(-\imath\hat{H}_0t/\hbar)}=\left[\hat{O}_I(t),\hat{H}_0\right].
 $$
 
-<p>Here we have used the time-independence of the Schr\"odinger equation
+<p>Here we have used the time-independence of the Schr&#246;dinger equation
 together with the observation that any function of an operator commutes with the operator itself. 
 </p>
 
@@ -527,7 +529,7 @@ <h2 id="time-development-operator" class="anchor">Time-development operator  </h
 <!-- !split -->
 <h2 id="properties-of-the-operator-u" class="anchor">Properties of the operator \( U \)  </h2>
 
-<p>Using our definition of Schr\"odinger's equation in the interaction picture, we can then construct the operator \( \hat{U} \). We have defined</p>
+<p>Using our definition of Schr&#246;dinger's equation in the interaction picture, we can then construct the operator \( \hat{U} \). We have defined</p>
 $$
 |\Psi_I(t)\rangle = \exp{(\imath\hat{H}_0t/\hbar)}|\Psi_S(t)\rangle,
 $$
@@ -650,8 +652,8 @@ <h2 id="heisenberg-picture-as-alternative" class="anchor">Heisenberg  picture as
 $$
 
 <p>which is again a unitary transformation carried out now at the time \( t \) on the 
-wave function in the Schr\"odinger picture. If we combine this equation with 
-Schr\"odinger's equation we obtain the following equation of motion
+wave function in the Schr&#246;dinger picture. If we combine this equation with 
+Schr&#246;dinger's equation we obtain the following equation of motion
 </p>
 $$
 \imath \hbar\frac{\partial }{\partial t}|\Psi_H(t)\rangle = 0,
@@ -748,7 +750,7 @@ <h2 id="time-evolution" class="anchor">Time evolution </h2>
 <!-- !split -->
 <h2 id="initial-state-preparation" class="anchor">Initial state preparation  </h2>
 
-<p>In the limit \( t_0\rightarrow -\infty \), the solution ot Schr\"odinger's equation is
+<p>In the limit \( t_0\rightarrow -\infty \), the solution ot Schr&#246;dinger's equation is
 \( |\Phi_0\rangle \), and the eigenenergies are given by 
 </p>
 $$

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

@@ -209,9 +209,10 @@ <h2 id="plans-for-the-week-of-february-10-14">Plans for the week of February 10-
 <section>
 <h2 id="readings">Readings </h2>
 
-<ol>
-<p><li> For the discussion of one-qubit, two-qubit and other gates, sections 2.6-2.11 and 3.1-3.4 of Hundt's book <b>Quantum Computing for Programmers</b>, contain most of the relevant information.</li> 
-</ol>
+<p>For the discussion of one-qubit, two-qubit and other gates, sections
+2.6-2.11 and 3.1-3.4 of Hundt's book <b>Quantum Computing for Programmers</b>,
+contain most of the relevant information.
+</p>
 </section>
 
 <section>
@@ -241,7 +242,7 @@ <h2 id="gates-the-whys-and-hows">Gates, the whys and hows </h2>
 <h2 id="structure-of-the-lecture">Structure of the lecture </h2>
 
 <ol>
-<p><li> First we review some of the basic ways of representing the solution to the Schr\"odinger equation, introducing the so-called Interaction, Heisenberg and Schr\"odinger prictures and unitary transformations.</li>
+<p><li> First we review some of the basic ways of representing the solution to the Schr&#246;dinger equation, introducing the so-called Interaction, Heisenberg and Schr&#246;dinger prictures and unitary transformations.</li>
 <p><li> Secondly, we present examples of physical processes and how they can be represented as unitary operations on a given state.</li>
 <p><li> These unitary transformations are then represented as gates. Setting gates together gives us a final circuit which can represent a specific physical system</li>
 </ol>
@@ -250,14 +251,14 @@ <h2 id="structure-of-the-lecture">Structure of the lecture </h2>
 <section>
 <h2 id="part-1-mathematical-background">Part 1: Mathematical background </h2>
 
-<p>The time-dependent Schr\"odinger equation (or equation of motion) reads</p>
+<p>The time-dependent Schr&#246;dinger equation (or equation of motion) reads</p>
 <p>&nbsp;<br>
 $$
 \imath \hbar\frac{\partial }{\partial t}|\Psi_S(t)\rangle = \hat{H}\Psi_S(t)\rangle,
 $$
 <p>&nbsp;<br>
 
-<p>where the subscript \( S \) stands for Schr\"odinger here.
+<p>where the subscript \( S \) stands for Schr&#246;dinger here.
 A formal solution is given by 
 </p>
 <p>&nbsp;<br>
@@ -304,7 +305,7 @@ <h2 id="interaction-picture">Interaction picture  </h2>
 <p>&nbsp;<br>
 
 <p>which is again a unitary transformation carried out now at the time \( t \) on the 
-wave function in the Schr\"odinger picture. 
+wave function in the Schr&#246;dinger picture. 
 </p>
 </section>
 
@@ -323,7 +324,7 @@ <h2 id="taking-the-derivative-wrt-time">Taking the derivative wrt time  </h2>
 <section>
 <h2 id="expression-using-the-interaction-picture">Expression using the interaction picture  </h2>
 
-<p>Using the definition of the Schr\"odinger equation, we can rewrite the last equation as </p>
+<p>Using the definition of the Schr&#246;dinger equation, we can rewrite the last equation as </p>
 <p>&nbsp;<br>
 $$
 \imath \hbar\frac{\partial }{\partial t}|\Psi_I(t)\rangle = \exp{(\imath\hat{H}_0t/\hbar)}\left[-\hat{H}_0+\hat{H}_0+\hat{H}_I\right]\exp{(-\imath\hat{H}_0t/\hbar)}\Psi_I(t)\rangle,
@@ -390,7 +391,7 @@ <h2 id="interaction-picture-and-equation-of-motion">Interaction picture and equa
 $$
 <p>&nbsp;<br>
 
-<p>Here we have used the time-independence of the Schr\"odinger equation
+<p>Here we have used the time-independence of the Schr&#246;dinger equation
 together with the observation that any function of an operator commutes with the operator itself. 
 </p>
 </section>
@@ -457,7 +458,7 @@ <h2 id="time-development-operator">Time-development operator  </h2>
 <section>
 <h2 id="properties-of-the-operator-u">Properties of the operator \( U \)  </h2>
 
-<p>Using our definition of Schr\"odinger's equation in the interaction picture, we can then construct the operator \( \hat{U} \). We have defined</p>
+<p>Using our definition of Schr&#246;dinger's equation in the interaction picture, we can then construct the operator \( \hat{U} \). We have defined</p>
 <p>&nbsp;<br>
 $$
 |\Psi_I(t)\rangle = \exp{(\imath\hat{H}_0t/\hbar)}|\Psi_S(t)\rangle,
@@ -617,8 +618,8 @@ <h2 id="heisenberg-picture-as-alternative">Heisenberg  picture as alternative </
 <p>&nbsp;<br>
 
 <p>which is again a unitary transformation carried out now at the time \( t \) on the 
-wave function in the Schr\"odinger picture. If we combine this equation with 
-Schr\"odinger's equation we obtain the following equation of motion
+wave function in the Schr&#246;dinger picture. If we combine this equation with 
+Schr&#246;dinger's equation we obtain the following equation of motion
 </p>
 <p>&nbsp;<br>
 $$
@@ -740,7 +741,7 @@ <h2 id="time-evolution">Time evolution </h2>
 <section>
 <h2 id="initial-state-preparation">Initial state preparation  </h2>
 
-<p>In the limit \( t_0\rightarrow -\infty \), the solution ot Schr\"odinger's equation is
+<p>In the limit \( t_0\rightarrow -\infty \), the solution ot Schr&#246;dinger's equation is
 \( |\Phi_0\rangle \), and the eigenenergies are given by 
 </p>
 <p>&nbsp;<br>

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

@@ -232,9 +232,11 @@ <h2 id="plans-for-the-week-of-february-10-14">Plans for the week of February 10-
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="readings">Readings </h2>
 
-<ol>
-<li> For the discussion of one-qubit, two-qubit and other gates, sections 2.6-2.11 and 3.1-3.4 of Hundt's book <b>Quantum Computing for Programmers</b>, contain most of the relevant information.</li> 
-</ol>
+<p>For the discussion of one-qubit, two-qubit and other gates, sections
+2.6-2.11 and 3.1-3.4 of Hundt's book <b>Quantum Computing for Programmers</b>,
+contain most of the relevant information.
+</p>
+
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="gates-the-whys-and-hows">Gates, the whys and hows </h2>
 
@@ -261,19 +263,19 @@ <h2 id="gates-the-whys-and-hows">Gates, the whys and hows </h2>
 <h2 id="structure-of-the-lecture">Structure of the lecture </h2>
 
 <ol>
-<li> First we review some of the basic ways of representing the solution to the Schr\"odinger equation, introducing the so-called Interaction, Heisenberg and Schr\"odinger prictures and unitary transformations.</li>
+<li> First we review some of the basic ways of representing the solution to the Schr&#246;dinger equation, introducing the so-called Interaction, Heisenberg and Schr&#246;dinger prictures and unitary transformations.</li>
 <li> Secondly, we present examples of physical processes and how they can be represented as unitary operations on a given state.</li>
 <li> These unitary transformations are then represented as gates. Setting gates together gives us a final circuit which can represent a specific physical system</li>
 </ol>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="part-1-mathematical-background">Part 1: Mathematical background </h2>
 
-<p>The time-dependent Schr\"odinger equation (or equation of motion) reads</p>
+<p>The time-dependent Schr&#246;dinger equation (or equation of motion) reads</p>
 $$
 \imath \hbar\frac{\partial }{\partial t}|\Psi_S(t)\rangle = \hat{H}\Psi_S(t)\rangle,
 $$
 
-<p>where the subscript \( S \) stands for Schr\"odinger here.
+<p>where the subscript \( S \) stands for Schr&#246;dinger here.
 A formal solution is given by 
 </p>
 $$
@@ -312,7 +314,7 @@ <h2 id="interaction-picture">Interaction picture  </h2>
 $$
 
 <p>which is again a unitary transformation carried out now at the time \( t \) on the 
-wave function in the Schr\"odinger picture. 
+wave function in the Schr&#246;dinger picture. 
 </p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -327,7 +329,7 @@ <h2 id="taking-the-derivative-wrt-time">Taking the derivative wrt time  </h2>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="expression-using-the-interaction-picture">Expression using the interaction picture  </h2>
 
-<p>Using the definition of the Schr\"odinger equation, we can rewrite the last equation as </p>
+<p>Using the definition of the Schr&#246;dinger equation, we can rewrite the last equation as </p>
 $$
 \imath \hbar\frac{\partial }{\partial t}|\Psi_I(t)\rangle = \exp{(\imath\hat{H}_0t/\hbar)}\left[-\hat{H}_0+\hat{H}_0+\hat{H}_I\right]\exp{(-\imath\hat{H}_0t/\hbar)}\Psi_I(t)\rangle,
 $$
@@ -379,7 +381,7 @@ <h2 id="interaction-picture-and-equation-of-motion">Interaction picture and equa
 \imath \hbar\frac{\partial }{\partial t}\hat{O}_I(t) = \exp{(\imath\hat{H}_0t/\hbar)}\left[\hat{O}_S\hat{H}_0-\hat{H}_0\hat{O}_S\right]\exp{(-\imath\hat{H}_0t/\hbar)}=\left[\hat{O}_I(t),\hat{H}_0\right].
 $$
 
-<p>Here we have used the time-independence of the Schr\"odinger equation
+<p>Here we have used the time-independence of the Schr&#246;dinger equation
 together with the observation that any function of an operator commutes with the operator itself. 
 </p>
 
@@ -432,7 +434,7 @@ <h2 id="time-development-operator">Time-development operator  </h2>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="properties-of-the-operator-u">Properties of the operator \( U \)  </h2>
 
-<p>Using our definition of Schr\"odinger's equation in the interaction picture, we can then construct the operator \( \hat{U} \). We have defined</p>
+<p>Using our definition of Schr&#246;dinger's equation in the interaction picture, we can then construct the operator \( \hat{U} \). We have defined</p>
 $$
 |\Psi_I(t)\rangle = \exp{(\imath\hat{H}_0t/\hbar)}|\Psi_S(t)\rangle,
 $$
@@ -555,8 +557,8 @@ <h2 id="heisenberg-picture-as-alternative">Heisenberg  picture as alternative </
 $$
 
 <p>which is again a unitary transformation carried out now at the time \( t \) on the 
-wave function in the Schr\"odinger picture. If we combine this equation with 
-Schr\"odinger's equation we obtain the following equation of motion
+wave function in the Schr&#246;dinger picture. If we combine this equation with 
+Schr&#246;dinger's equation we obtain the following equation of motion
 </p>
 $$
 \imath \hbar\frac{\partial }{\partial t}|\Psi_H(t)\rangle = 0,
@@ -653,7 +655,7 @@ <h2 id="time-evolution">Time evolution </h2>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="initial-state-preparation">Initial state preparation  </h2>
 
-<p>In the limit \( t_0\rightarrow -\infty \), the solution ot Schr\"odinger's equation is
+<p>In the limit \( t_0\rightarrow -\infty \), the solution ot Schr&#246;dinger's equation is
 \( |\Phi_0\rangle \), and the eigenenergies are given by 
 </p>
 $$