Rename intro to brief_intro_to_qec

src/brief_intro_to_qec/MA.bib

@@ -17,7 +17,6 @@
 
 @online{nielsen_quantum_2010,
 	title = {Quantum Computation and Quantum Information: 10th Anniversary Edition},
-	url = {https://www.cambridge.org/highereducation/books/quantum-computation-and-quantum-information/01E10196D0A682A6AEFFEA52D53BE9AE},
 	shorttitle = {Quantum Computation and Quantum Information},
 	abstract = {One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.},
 	titleaddon = {Cambridge Aspire website},

src/brief_intro_to_qec/main.tex

@@ -56,7 +56,7 @@ We call $\ket{\psi}_L$ the logical state.
 We define the codespace as $\mathcal{C} := \text{span}\mleft\{
 \ket{00}, \ket{11} \mright\}$ and the error subspace as $\mathcal{F} :=
 \text{span} \mleft\{\ket{01}, \ket{10} \mright\}$.
-To determine if an error occurred, we want to know
+To determine if an error occurred, we want to measure
 whether a state belongs%
 \footnote{
     It is possible for a state to not completely lie in either subspace.
@@ -70,7 +70,10 @@ described using operators \cite[Section
 1.5]{griffiths_introduction_1995}. Because of the way these operators are
 defined, their eigenvalues correspond to the possible outcomes of
 measuring that observable, and the corresponding
-eigenstates are the determinate states that yield those values as
+eigenstates are the determinate states%
+\todo{Explain determinate states?}
+%
+that yield those values as
 measurements \cite[Section 3.3]{griffiths_introduction_1995}.
 In our case, we need an operator with two eigenvalues, and the corresponding
 eigenspaces should be $\mathcal{C}$ and $\mathcal{F}$ respectively.
@@ -86,7 +89,7 @@ For the two-qubit code, $Z_1Z_2$ is such an operator:%
     .%
 \end{align*}%
 %
-$E$ is an operator describing a possible error and $E
+Here, $E$ is an operator describing a possible error and $E
 \ket{\psi}_\text{L}$ is the resulting state after that error.
 By measuring the corresponding eigenvalue, we can determine if
 $E\ket{\psi}_\text{L}$ lies in $\mathcal{C}$ or $\mathcal{F}$.
@@ -97,7 +100,6 @@ $\ket{\psi}_\text{L}$ in such a way that determining that instead
 indicates the eigenvalue. More specifically, using a syndrome
 extraction circuit as shown in Figure \ref{fig:syndrome extraction}, we
 transform the state of the three-qubit system as%
-
 %
 \begin{align*}
     E\ket{\psi}_\text{L} \ket{0}_\text{A} \hspace*{3mm} \rightarrow
@@ -130,7 +132,8 @@ $\mathcal{F}$. At the same time, because $Z_1Z_2 \ket{\psi}_\text{L}
 = \ket{\psi}_\text{L}$, the projections leave the logical state
 $\ket{\psi}_\text{L}$ untouched.
 \todo{Explain that the collapse of the error superposition enables
-the digitization of arbitrary error operations \cite{nielsen_quantum_2010}}
+    the digitization of arbitrary error operations \cite[p.
+434]{nielsen_quantum_2010}}
 We have thus managed to determine
 whether an error occurred without disturbing the encoded
 quantum information.