some work

thesis/chapters/conclusion.tex

@@ -82,10 +82,18 @@ and
 CX_{2,1} (h_1 \otimes h_2) CX_{2,1} =  h_1'' \otimes h_2''
 \end{equation}
 
-might be a good step to find new classes of states that can be simulated efficiently
-using this method. This property has to be fulfilled by all elements of a group generated
-by such hermitian matrices.
-How computations and measurements would work using this method
-is not clear at the moment as many basic properties of the stabilizers are lost.
-
+might be a good step to find new classes of states that can be simulated
+efficiently using this method. This property has to be fulfilled by all
+elements of a group generated by such hermitian matrices.  How computations and
+measurements would work using this method is not clear at the moment as many
+basic properties of the stabilizers are lost. One important property is that the
+stabilization: The simulated state is the $+1$ eigenstate of the stabilizers.
+This is another property that will have to be fulfilled by the hermitians as it
+is a key property used in \ref{ref:dynamics_stabilizer}. To ensure that the
+state is well defined one will have to demand that the eigenvalues fulfill
+$\lambda_1 = 1$ and $\lambda_2 < 1$.
 
+One should also note that the sabilizer states do not form a Hilbert (sub)space.
+Linear combinations of stabilizer states are (in general) no stabilizer states.
+The superposition principle is quite essential to many quantum algorithms and
+quantum physics which limits the use of the stabilizer formalism drastically.

thesis/chapters/stabilizer.tex

@@ -144,6 +144,7 @@ In the following discussions for $n$ qbits a set $S = \langle S^{(i)}
 
 
 \subsubsection{Dynamics of Stabilizer States}
+\label{ref:dynamics_stabilizer}
 
 Consider a $n$ qbit state $\ket{\psi}$ that is the $+1$ eigenstate of $S
 = \langle S^{(i)} \rangle_{i=1,...,n}$ and a unitary transformation $U$ that

thesis/main.bib

@@ -174,3 +174,13 @@
     year=2020,
     note={https://docs.python.org/3.5/library/timeit.html}
 }
+
+@online{
+    openqasm,
+    url={https://github.com/QISKit/openqasm},
+    urldate={19.09.2019},
+    title={GitHub - Quiskit/openqasm},
+    author={Jay Gambetta at al.},
+    note={https://github.com/QISKit/openqasm},
+    year=2019
+}