update

Author: mhjensen

doc/pub/week7/html/week7-bs.html

@@ -441,19 +441,19 @@ <h2 id="pauli-x-reminder" class="anchor">Pauli \( X \) reminder </h2>
 
 <p>with eigenvalues \( 1 \) in both cases. The latter two equations tell us
 that the computational basis we have chosen, and in which we will
-prepare our states, is not an eigenbasis of the \( \sigma_x \) matrix.
+prepare our states, is not an eigenbasis of the \( \boldsymbol{X} \) matrix.
 </p>
 
 <!-- !split -->
 <h2 id="rewriting-the-pauli-x-matrix" class="anchor">Rewriting the Pauli \( X \) matrix </h2>
 
 <p>We rewrite the Pauli \( X \) matrix in terms of a Pauli
-\( Z \) matrixcusing the Hadamard matrix
+\( Z \) matrix using the Hadamard matrix
 twice, that is
 </p>
 
 $$
-\boldsymbol{X}=\boldsymbol{\sigma}_x=\boldsymbol{H}\boldsymbol{Z}\boldsymbol{H}.
+\boldsymbol{X}=\boldsymbol{H}\boldsymbol{Z}\boldsymbol{H}.
 $$
 
 
@@ -463,7 +463,7 @@ <h2 id="the-pauli-y-matrix" class="anchor">The Pauli \( Y \) matrix </h2>
 <p>The Pauli \( Y \) matrix can be written as</p>
 
 $$
-\boldsymbol{Y}=\boldsymbol{\sigma}_y=\boldsymbol{H}\boldsymbol{S}^{\dagger}\boldsymbol{Z}\boldsymbol{H}\boldsymbol{S},
+\boldsymbol{Y}=\boldsymbol{H}\boldsymbol{S}^{\dagger}\boldsymbol{Z}\boldsymbol{H}\boldsymbol{S},
 $$
 
 <p>where \( S \) is the phase matrix</p>
@@ -635,35 +635,18 @@ <h2 id="preparing-the-states" class="anchor">Preparing the states </h2>
 gates on the \( \left| 0 \right\rangle \) initial state
 </p>
 $$
-R_y(t_2)R_x(t_1) \left| 0 \right\rangle = \left| \psi\right\rangle.
+R_y(\phi)R_x(\theta) \left| 0 \right\rangle = \left| \psi\right\rangle.
 $$
 
-<p>The rotation \( R_x(t_1) \)
+<p>The rotation \( R_x(\theta) \)
 corresponds to the rotation in the Bloch
-sphere around the \( x \)-axis and \( R_y(t_2) \) the rotation around the \( y \)-axis.
+sphere around the \( x \)-axis and \( R_y(\phi) \) the rotation around the \( y \)-axis.
 </p>
 
 <!-- !split -->
 <h2 id="rotations-used" class="anchor">Rotations used </h2>
 
-<p>With these two rotations, one can have access to any point in
-the Bloch sphere. Here we show the matrix forms of \( R_x(t_1) \) and
-\( R_y(t_2) \) gates:
-</p>
-
-$$
-R_x(t_1) = \begin{pmatrix}
-cos(\frac{t_1}{2}) & -i \cdot sin(\frac{t_1}{2})\\
--i \cdot sin(\frac{t_1}{2}) & cos(\frac{t_1}{2})
-\end{pmatrix},
-\qquad
-R_y(t_2) = \begin{pmatrix}
-cos(\frac{t_2}{2}) & -sin(\frac{t_2}{2})\\
-sin(\frac{t_2}{2}) & cos(\frac{t_2}{2})
-\end{pmatrix}.
-$$
-
-<p>These two gates with there parameters (\( t_1 \) and \( t_2 \)) will generate
+<p>These two gates with there parameters (\( \theta \) and \( \phi \)) will generate
 for us the trial (ansatz) wavefunctions. The two parameters will be in
 control of the Classical Computer and its optimization model.
 </p>

doc/pub/week7/html/week7-reveal.html

@@ -355,21 +355,21 @@ <h2 id="pauli-x-reminder">Pauli \( X \) reminder </h2>
 
 <p>with eigenvalues \( 1 \) in both cases. The latter two equations tell us
 that the computational basis we have chosen, and in which we will
-prepare our states, is not an eigenbasis of the \( \sigma_x \) matrix.
+prepare our states, is not an eigenbasis of the \( \boldsymbol{X} \) matrix.
 </p>
 </section>
 
 <section>
 <h2 id="rewriting-the-pauli-x-matrix">Rewriting the Pauli \( X \) matrix </h2>
 
 <p>We rewrite the Pauli \( X \) matrix in terms of a Pauli
-\( Z \) matrixcusing the Hadamard matrix
+\( Z \) matrix using the Hadamard matrix
 twice, that is
 </p>
 
 <p>&nbsp;<br>
 $$
-\boldsymbol{X}=\boldsymbol{\sigma}_x=\boldsymbol{H}\boldsymbol{Z}\boldsymbol{H}.
+\boldsymbol{X}=\boldsymbol{H}\boldsymbol{Z}\boldsymbol{H}.
 $$
 <p>&nbsp;<br>
 </section>
@@ -381,7 +381,7 @@ <h2 id="the-pauli-y-matrix">The Pauli \( Y \) matrix </h2>
 
 <p>&nbsp;<br>
 $$
-\boldsymbol{Y}=\boldsymbol{\sigma}_y=\boldsymbol{H}\boldsymbol{S}^{\dagger}\boldsymbol{Z}\boldsymbol{H}\boldsymbol{S},
+\boldsymbol{Y}=\boldsymbol{H}\boldsymbol{S}^{\dagger}\boldsymbol{Z}\boldsymbol{H}\boldsymbol{S},
 $$
 <p>&nbsp;<br>
 
@@ -576,39 +576,20 @@ <h2 id="preparing-the-states">Preparing the states </h2>
 </p>
 <p>&nbsp;<br>
 $$
-R_y(t_2)R_x(t_1) \left| 0 \right\rangle = \left| \psi\right\rangle.
+R_y(\phi)R_x(\theta) \left| 0 \right\rangle = \left| \psi\right\rangle.
 $$
 <p>&nbsp;<br>
 
-<p>The rotation \( R_x(t_1) \)
+<p>The rotation \( R_x(\theta) \)
 corresponds to the rotation in the Bloch
-sphere around the \( x \)-axis and \( R_y(t_2) \) the rotation around the \( y \)-axis.
+sphere around the \( x \)-axis and \( R_y(\phi) \) the rotation around the \( y \)-axis.
 </p>
 </section>
 
 <section>
 <h2 id="rotations-used">Rotations used </h2>
 
-<p>With these two rotations, one can have access to any point in
-the Bloch sphere. Here we show the matrix forms of \( R_x(t_1) \) and
-\( R_y(t_2) \) gates:
-</p>
-
-<p>&nbsp;<br>
-$$
-R_x(t_1) = \begin{pmatrix}
-cos(\frac{t_1}{2}) & -i \cdot sin(\frac{t_1}{2})\\
--i \cdot sin(\frac{t_1}{2}) & cos(\frac{t_1}{2})
-\end{pmatrix},
-\qquad
-R_y(t_2) = \begin{pmatrix}
-cos(\frac{t_2}{2}) & -sin(\frac{t_2}{2})\\
-sin(\frac{t_2}{2}) & cos(\frac{t_2}{2})
-\end{pmatrix}.
-$$
-<p>&nbsp;<br>
-
-<p>These two gates with there parameters (\( t_1 \) and \( t_2 \)) will generate
+<p>These two gates with there parameters (\( \theta \) and \( \phi \)) will generate
 for us the trial (ansatz) wavefunctions. The two parameters will be in
 control of the Classical Computer and its optimization model.
 </p>

doc/pub/week7/html/week7-solarized.html

@@ -376,19 +376,19 @@ <h2 id="pauli-x-reminder">Pauli \( X \) reminder </h2>
 
 <p>with eigenvalues \( 1 \) in both cases. The latter two equations tell us
 that the computational basis we have chosen, and in which we will
-prepare our states, is not an eigenbasis of the \( \sigma_x \) matrix.
+prepare our states, is not an eigenbasis of the \( \boldsymbol{X} \) matrix.
 </p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="rewriting-the-pauli-x-matrix">Rewriting the Pauli \( X \) matrix </h2>
 
 <p>We rewrite the Pauli \( X \) matrix in terms of a Pauli
-\( Z \) matrixcusing the Hadamard matrix
+\( Z \) matrix using the Hadamard matrix
 twice, that is
 </p>
 
 $$
-\boldsymbol{X}=\boldsymbol{\sigma}_x=\boldsymbol{H}\boldsymbol{Z}\boldsymbol{H}.
+\boldsymbol{X}=\boldsymbol{H}\boldsymbol{Z}\boldsymbol{H}.
 $$
 
 
@@ -398,7 +398,7 @@ <h2 id="the-pauli-y-matrix">The Pauli \( Y \) matrix </h2>
 <p>The Pauli \( Y \) matrix can be written as</p>
 
 $$
-\boldsymbol{Y}=\boldsymbol{\sigma}_y=\boldsymbol{H}\boldsymbol{S}^{\dagger}\boldsymbol{Z}\boldsymbol{H}\boldsymbol{S},
+\boldsymbol{Y}=\boldsymbol{H}\boldsymbol{S}^{\dagger}\boldsymbol{Z}\boldsymbol{H}\boldsymbol{S},
 $$
 
 <p>where \( S \) is the phase matrix</p>
@@ -570,35 +570,18 @@ <h2 id="preparing-the-states">Preparing the states </h2>
 gates on the \( \left| 0 \right\rangle \) initial state
 </p>
 $$
-R_y(t_2)R_x(t_1) \left| 0 \right\rangle = \left| \psi\right\rangle.
+R_y(\phi)R_x(\theta) \left| 0 \right\rangle = \left| \psi\right\rangle.
 $$
 
-<p>The rotation \( R_x(t_1) \)
+<p>The rotation \( R_x(\theta) \)
 corresponds to the rotation in the Bloch
-sphere around the \( x \)-axis and \( R_y(t_2) \) the rotation around the \( y \)-axis.
+sphere around the \( x \)-axis and \( R_y(\phi) \) the rotation around the \( y \)-axis.
 </p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="rotations-used">Rotations used </h2>
 
-<p>With these two rotations, one can have access to any point in
-the Bloch sphere. Here we show the matrix forms of \( R_x(t_1) \) and
-\( R_y(t_2) \) gates:
-</p>
-
-$$
-R_x(t_1) = \begin{pmatrix}
-cos(\frac{t_1}{2}) & -i \cdot sin(\frac{t_1}{2})\\
--i \cdot sin(\frac{t_1}{2}) & cos(\frac{t_1}{2})
-\end{pmatrix},
-\qquad
-R_y(t_2) = \begin{pmatrix}
-cos(\frac{t_2}{2}) & -sin(\frac{t_2}{2})\\
-sin(\frac{t_2}{2}) & cos(\frac{t_2}{2})
-\end{pmatrix}.
-$$
-
-<p>These two gates with there parameters (\( t_1 \) and \( t_2 \)) will generate
+<p>These two gates with there parameters (\( \theta \) and \( \phi \)) will generate
 for us the trial (ansatz) wavefunctions. The two parameters will be in
 control of the Classical Computer and its optimization model.
 </p>

doc/pub/week7/html/week7.html

@@ -453,19 +453,19 @@ <h2 id="pauli-x-reminder">Pauli \( X \) reminder </h2>
 
 <p>with eigenvalues \( 1 \) in both cases. The latter two equations tell us
 that the computational basis we have chosen, and in which we will
-prepare our states, is not an eigenbasis of the \( \sigma_x \) matrix.
+prepare our states, is not an eigenbasis of the \( \boldsymbol{X} \) matrix.
 </p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="rewriting-the-pauli-x-matrix">Rewriting the Pauli \( X \) matrix </h2>
 
 <p>We rewrite the Pauli \( X \) matrix in terms of a Pauli
-\( Z \) matrixcusing the Hadamard matrix
+\( Z \) matrix using the Hadamard matrix
 twice, that is
 </p>
 
 $$
-\boldsymbol{X}=\boldsymbol{\sigma}_x=\boldsymbol{H}\boldsymbol{Z}\boldsymbol{H}.
+\boldsymbol{X}=\boldsymbol{H}\boldsymbol{Z}\boldsymbol{H}.
 $$
 
 
@@ -475,7 +475,7 @@ <h2 id="the-pauli-y-matrix">The Pauli \( Y \) matrix </h2>
 <p>The Pauli \( Y \) matrix can be written as</p>
 
 $$
-\boldsymbol{Y}=\boldsymbol{\sigma}_y=\boldsymbol{H}\boldsymbol{S}^{\dagger}\boldsymbol{Z}\boldsymbol{H}\boldsymbol{S},
+\boldsymbol{Y}=\boldsymbol{H}\boldsymbol{S}^{\dagger}\boldsymbol{Z}\boldsymbol{H}\boldsymbol{S},
 $$
 
 <p>where \( S \) is the phase matrix</p>
@@ -647,35 +647,18 @@ <h2 id="preparing-the-states">Preparing the states </h2>
 gates on the \( \left| 0 \right\rangle \) initial state
 </p>
 $$
-R_y(t_2)R_x(t_1) \left| 0 \right\rangle = \left| \psi\right\rangle.
+R_y(\phi)R_x(\theta) \left| 0 \right\rangle = \left| \psi\right\rangle.
 $$
 
-<p>The rotation \( R_x(t_1) \)
+<p>The rotation \( R_x(\theta) \)
 corresponds to the rotation in the Bloch
-sphere around the \( x \)-axis and \( R_y(t_2) \) the rotation around the \( y \)-axis.
+sphere around the \( x \)-axis and \( R_y(\phi) \) the rotation around the \( y \)-axis.
 </p>
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="rotations-used">Rotations used </h2>
 
-<p>With these two rotations, one can have access to any point in
-the Bloch sphere. Here we show the matrix forms of \( R_x(t_1) \) and
-\( R_y(t_2) \) gates:
-</p>
-
-$$
-R_x(t_1) = \begin{pmatrix}
-cos(\frac{t_1}{2}) & -i \cdot sin(\frac{t_1}{2})\\
--i \cdot sin(\frac{t_1}{2}) & cos(\frac{t_1}{2})
-\end{pmatrix},
-\qquad
-R_y(t_2) = \begin{pmatrix}
-cos(\frac{t_2}{2}) & -sin(\frac{t_2}{2})\\
-sin(\frac{t_2}{2}) & cos(\frac{t_2}{2})
-\end{pmatrix}.
-$$
-
-<p>These two gates with there parameters (\( t_1 \) and \( t_2 \)) will generate
+<p>These two gates with there parameters (\( \theta \) and \( \phi \)) will generate
 for us the trial (ansatz) wavefunctions. The two parameters will be in
 control of the Classical Computer and its optimization model.
 </p>