never ending story of typos

Author: mhjensen

doc/pub/week6/html/week6-bs.html

@@ -382,18 +382,18 @@ <h2 id="single-qubit-gates" class="anchor">Single qubit gates </h2>
 
 <p>The Pauli matrices (and gate operations following therefrom) are defined as</p>
 $$
-	X \equiv \sigma_x = \begin{pmatrix}
+	\boldsymbol{X} \equiv \sigma_x = \begin{bmatrix}
 		0 & 1 \\
 		1 & 0
-	\end{pmatrix}, \quad
-	Y \equiv \sigma_y = \begin{pmatrix}
+	\end{bmatrix}, \quad
+	\boldsymbol{Y} \equiv \sigma_y = \begin{bmatrix}
 		0 & -i \\
 		i & 0
-	\end{pmatrix}, \quad
-	Z \equiv \sigma_z = \begin{pmatrix}
+	\end{bmatrix}, \quad
+	\boldsymbol{Z} \equiv \sigma_z = \begin{bmatrix}
 		1 & 0 \\
 		0 & -1
-	\end{pmatrix}.
+	\end{bmatrix}.
 $$
 
 
@@ -429,10 +429,10 @@ <h2 id="hadamard-gate" class="anchor">Hadamard gate </h2>
 
 <p>The Hadamard gate is defined as</p>
 $$
-	\boldsymbol{H} = \frac{1}{\sqrt{2}} \begin{pmatrix}
+	\boldsymbol{H} = \frac{1}{\sqrt{2}} \begin{bmatrix}
 		1 & 1 \\
 		1 & -1
-	\end{pmatrix}.
+	\end{bmatrix}.
 $$
 
 <p>It creates a superposition of the  \) \vert 0\rangle $ and $ \vert 1\rangle $ states.</p>
@@ -451,10 +451,10 @@ <h2 id="hadamard-gate" class="anchor">Hadamard gate </h2>
 <h2 id="phase-gates" class="anchor">Phase Gates </h2>
 <p>The phase gate is usually denoted as \( S \) and is defined as</p>
 $$
-	\boldsymbol{S} = \begin{pmatrix}
+	\boldsymbol{S} = \begin{bmatrix}
 		1 & 0 \\
 		0 & i
-	\end{pmatrix}.
+	\end{bmatrix}.
 $$
 
 <p>It multiplies only the phase of the $ \vert 1\rangle $ state by $ i $.</p>
@@ -471,10 +471,10 @@ <h2 id="the-inverse-of-the-boldsymbol-s-gate" class="anchor">The  inverse of the
 
 <p>The inverse</p>
 $$
-	\boldsymbol{S}^\dagger = \begin{pmatrix}
+	\boldsymbol{S}^\dagger = \begin{bmatrix}
 		1 & 0 \\
 		0 & -i
-	\end{pmatrix}
+	\end{bmatrix}
 $$
 
 <p>is known as the $ \boldsymbol{S}^\dagger$ gate which applies an \( \imath \) phase shift to \( \vert 1\rangle \).</p>
@@ -490,12 +490,12 @@ <h2 id="two-qubit-gates" class="anchor">Two-qubit gates </h2>
 
 <p>The CNOT gate is a two-qubit gate which acts on two qubits, a control qubit and a target qubit. The CNOT gate is defined as</p>
 $$
-	\text{CNOT} = \begin{pmatrix}
+	\text{CNOT} = \begin{bmatrix}
 		1 & 0 & 0 & 0 \\
 		0 & 1 & 0 & 0 \\
 		0 & 0 & 0 & 1 \\
 		0 & 0 & 1 & 0
-	\end{pmatrix}.
+	\end{bmatrix}.
 $$
 
 <p>It is often used to perform linear entanglement on qubits.</p>
@@ -513,12 +513,12 @@ <h2 id="two-qubit-gates" class="anchor">Two-qubit gates </h2>
 <h2 id="the-swap-gate" class="anchor">The SWAP gate </h2>
 <p>The SWAP gate is a two-qubit gate which swaps the state of two qubits. It is defined as</p>
 $$
-	\text{SWAP} = \begin{pmatrix}
+	\text{SWAP} = \begin{bmatrix}
 		1 & 0 & 0 & 0 \\
 		0 & 0 & 1 & 0 \\
 		0 & 1 & 0 & 0 \\
 		0 & 0 & 0 & 1
-	\end{pmatrix}.
+	\end{bmatrix}.
 $$
 
 $$
@@ -734,10 +734,10 @@ <h2 id="ansatzes" class="anchor">Ansatzes </h2>
 
 <p>Every possible qubit wavefunction \( \left| \psi \right\rangle \) can be presented as a vector: </p>
 $$
-\left| \psi \right\rangle = \begin{pmatrix}
+\left| \psi \right\rangle = \begin{bmatrix}
 \cos{\left( \theta/2 \right)}\\
 e^{i \varphi} \cdot \sin{\left( \theta/2 \right)}
-\end{pmatrix},
+\end{bmatrix},
 $$
 
 <p>where the numbers \( \theta \) and \( \varphi \) define a point on the unit
@@ -1255,14 +1255,14 @@ <h2 id="in-more-detail" class="anchor">In more detail </h2>
 $$
 \begin{align*}
 &\text{Z eigenvectors} \qquad
-\left| 0 \right\rangle = \begin{pmatrix}
+\left| 0 \right\rangle = \begin{bmatrix}
 1\\
 0
-\end{pmatrix},
-&&\left| 1 \right\rangle = \begin{pmatrix}
+\end{bmatrix},
+&&\left| 1 \right\rangle = \begin{bmatrix}
 0\\
 1
-\end{pmatrix},
+\end{bmatrix},
 \end{align*}
 $$
 
@@ -1273,24 +1273,24 @@ <h2 id="for-the-other-two-matrices" class="anchor">For the other two matrices </
 $$
 \begin{align*}
 &\text{X eigenvectors} \qquad
-\left| + \right\rangle = \frac{1}{\sqrt{2}} \begin{pmatrix}
+\left| + \right\rangle = \frac{1}{\sqrt{2}} \begin{bmatrix}
 1\\
 1
-\end{pmatrix},
-&&\left| - \right\rangle = \frac{1}{\sqrt{2}} \begin{pmatrix}
+\end{bmatrix},
+&&\left| - \right\rangle = \frac{1}{\sqrt{2}} \begin{bmatrix}
 1\\
 -1
-\end{pmatrix},
+\end{bmatrix},
 \\
 &\text{Y eigenvectors} \qquad
-\left| +i \right\rangle = \frac{1}{\sqrt{2}} \begin{pmatrix}
+\left| +i \right\rangle = \frac{1}{\sqrt{2}} \begin{bmatrix}
 1\\
 i
-\end{pmatrix}, 
-&&\left| -i \right\rangle = \frac{1}{\sqrt{2}} \begin{pmatrix}
+\end{bmatrix}, 
+&&\left| -i \right\rangle = \frac{1}{\sqrt{2}} \begin{bmatrix}
 1\\
 -i
-\end{pmatrix}.
+\end{bmatrix}.
 \end{align*}
 $$
 
@@ -1334,10 +1334,10 @@ <h2 id="unitary-transformation-of-boldsymbol-x" class="anchor">Unitary transform
 
 <p>If we use the Hadamard gate</p>
 $$
-H = \frac{1}{\sqrt{2}}\begin{pmatrix}
+H = \frac{1}{\sqrt{2}}\begin{bmatrix}
 1 & 1\\
 1 & -1
-\end{pmatrix},
+\end{bmatrix},
 $$
 
 <p>we can rewrite</p>

doc/pub/week6/html/week6-reveal.html

@@ -233,18 +233,18 @@ <h2 id="single-qubit-gates">Single qubit gates </h2>
 <p>The Pauli matrices (and gate operations following therefrom) are defined as</p>
 <p>&nbsp;<br>
 $$
-	X \equiv \sigma_x = \begin{pmatrix}
+	\boldsymbol{X} \equiv \sigma_x = \begin{bmatrix}
 		0 & 1 \\
 		1 & 0
-	\end{pmatrix}, \quad
-	Y \equiv \sigma_y = \begin{pmatrix}
+	\end{bmatrix}, \quad
+	\boldsymbol{Y} \equiv \sigma_y = \begin{bmatrix}
 		0 & -i \\
 		i & 0
-	\end{pmatrix}, \quad
-	Z \equiv \sigma_z = \begin{pmatrix}
+	\end{bmatrix}, \quad
+	\boldsymbol{Z} \equiv \sigma_z = \begin{bmatrix}
 		1 & 0 \\
 		0 & -1
-	\end{pmatrix}.
+	\end{bmatrix}.
 $$
 <p>&nbsp;<br>
 </section>
@@ -289,10 +289,10 @@ <h2 id="hadamard-gate">Hadamard gate </h2>
 <p>The Hadamard gate is defined as</p>
 <p>&nbsp;<br>
 $$
-	\boldsymbol{H} = \frac{1}{\sqrt{2}} \begin{pmatrix}
+	\boldsymbol{H} = \frac{1}{\sqrt{2}} \begin{bmatrix}
 		1 & 1 \\
 		1 & -1
-	\end{pmatrix}.
+	\end{bmatrix}.
 $$
 <p>&nbsp;<br>
 
@@ -316,10 +316,10 @@ <h2 id="phase-gates">Phase Gates </h2>
 <p>The phase gate is usually denoted as \( S \) and is defined as</p>
 <p>&nbsp;<br>
 $$
-	\boldsymbol{S} = \begin{pmatrix}
+	\boldsymbol{S} = \begin{bmatrix}
 		1 & 0 \\
 		0 & i
-	\end{pmatrix}.
+	\end{bmatrix}.
 $$
 <p>&nbsp;<br>
 
@@ -340,10 +340,10 @@ <h2 id="the-inverse-of-the-boldsymbol-s-gate">The  inverse of the \( \boldsymbol
 <p>The inverse</p>
 <p>&nbsp;<br>
 $$
-	\boldsymbol{S}^\dagger = \begin{pmatrix}
+	\boldsymbol{S}^\dagger = \begin{bmatrix}
 		1 & 0 \\
 		0 & -i
-	\end{pmatrix}
+	\end{bmatrix}
 $$
 <p>&nbsp;<br>
 
@@ -364,12 +364,12 @@ <h2 id="two-qubit-gates">Two-qubit gates </h2>
 <p>The CNOT gate is a two-qubit gate which acts on two qubits, a control qubit and a target qubit. The CNOT gate is defined as</p>
 <p>&nbsp;<br>
 $$
-	\text{CNOT} = \begin{pmatrix}
+	\text{CNOT} = \begin{bmatrix}
 		1 & 0 & 0 & 0 \\
 		0 & 1 & 0 & 0 \\
 		0 & 0 & 0 & 1 \\
 		0 & 0 & 1 & 0
-	\end{pmatrix}.
+	\end{bmatrix}.
 $$
 <p>&nbsp;<br>
 
@@ -391,12 +391,12 @@ <h2 id="the-swap-gate">The SWAP gate </h2>
 <p>The SWAP gate is a two-qubit gate which swaps the state of two qubits. It is defined as</p>
 <p>&nbsp;<br>
 $$
-	\text{SWAP} = \begin{pmatrix}
+	\text{SWAP} = \begin{bmatrix}
 		1 & 0 & 0 & 0 \\
 		0 & 0 & 1 & 0 \\
 		0 & 1 & 0 & 0 \\
 		0 & 0 & 0 & 1
-	\end{pmatrix}.
+	\end{bmatrix}.
 $$
 <p>&nbsp;<br>
 
@@ -642,10 +642,10 @@ <h2 id="ansatzes">Ansatzes </h2>
 <p>Every possible qubit wavefunction \( \left| \psi \right\rangle \) can be presented as a vector: </p>
 <p>&nbsp;<br>
 $$
-\left| \psi \right\rangle = \begin{pmatrix}
+\left| \psi \right\rangle = \begin{bmatrix}
 \cos{\left( \theta/2 \right)}\\
 e^{i \varphi} \cdot \sin{\left( \theta/2 \right)}
-\end{pmatrix},
+\end{bmatrix},
 $$
 <p>&nbsp;<br>
 
@@ -1237,14 +1237,14 @@ <h2 id="in-more-detail">In more detail </h2>
 $$
 \begin{align*}
 &\text{Z eigenvectors} \qquad
-\left| 0 \right\rangle = \begin{pmatrix}
+\left| 0 \right\rangle = \begin{bmatrix}
 1\\
 0
-\end{pmatrix},
-&&\left| 1 \right\rangle = \begin{pmatrix}
+\end{bmatrix},
+&&\left| 1 \right\rangle = \begin{bmatrix}
 0\\
 1
-\end{pmatrix},
+\end{bmatrix},
 \end{align*}
 $$
 <p>&nbsp;<br>
@@ -1257,24 +1257,24 @@ <h2 id="for-the-other-two-matrices">For the other two matrices </h2>
 $$
 \begin{align*}
 &\text{X eigenvectors} \qquad
-\left| + \right\rangle = \frac{1}{\sqrt{2}} \begin{pmatrix}
+\left| + \right\rangle = \frac{1}{\sqrt{2}} \begin{bmatrix}
 1\\
 1
-\end{pmatrix},
-&&\left| - \right\rangle = \frac{1}{\sqrt{2}} \begin{pmatrix}
+\end{bmatrix},
+&&\left| - \right\rangle = \frac{1}{\sqrt{2}} \begin{bmatrix}
 1\\
 -1
-\end{pmatrix},
+\end{bmatrix},
 \\
 &\text{Y eigenvectors} \qquad
-\left| +i \right\rangle = \frac{1}{\sqrt{2}} \begin{pmatrix}
+\left| +i \right\rangle = \frac{1}{\sqrt{2}} \begin{bmatrix}
 1\\
 i
-\end{pmatrix}, 
-&&\left| -i \right\rangle = \frac{1}{\sqrt{2}} \begin{pmatrix}
+\end{bmatrix}, 
+&&\left| -i \right\rangle = \frac{1}{\sqrt{2}} \begin{bmatrix}
 1\\
 -i
-\end{pmatrix}.
+\end{bmatrix}.
 \end{align*}
 $$
 <p>&nbsp;<br>
@@ -1324,10 +1324,10 @@ <h2 id="unitary-transformation-of-boldsymbol-x">Unitary transformation of \( \bo
 <p>If we use the Hadamard gate</p>
 <p>&nbsp;<br>
 $$
-H = \frac{1}{\sqrt{2}}\begin{pmatrix}
+H = \frac{1}{\sqrt{2}}\begin{bmatrix}
 1 & 1\\
 1 & -1
-\end{pmatrix},
+\end{bmatrix},
 $$
 <p>&nbsp;<br>