added something about future work on the sumulator

thesis/chapters/implementation.tex

@@ -301,7 +301,7 @@ states has yet to be implemented but can be done in polynomial time
 
 Writing circuits out by hand can be rather painful. The function\\
 \lstinline{pyqcs.list_to_circuit} Converts a list of circuits to a circuit.
-This is particularely helpful in combination with python's
+This is particularly helpful in combination with python's
 \lstinline{listcomp}:
 
 \begin{lstlisting}[caption={Generating a Large Circuit Efficiently}]
@@ -473,3 +473,26 @@ lengths it is important to account for this virtual performance boost when
 comparing with other simulation methods. This explains why the circuit length
 in Figure \ref{fig:scaling_qbits_linear} had to be scaled with the qbit number.
 
+\subsection{Future Work}
+
+Although the simulator(s) are in a working state and have been tested there is
+still some work that can be done.  A noise model helping to teach and analyze
+noisy execution is one particularly interesting piece of work that should be
+done.  To allow a user to execute circuits on other machines, including both
+real hardware and simulators, a module that exports circuits to OpenQASM
+\cite{openqasm} seems useful. 
+
+The current implementation of some graphical operations can be optimized. While
+clearing VOPs as described in \ref{ref:dynamics_graph} the neighbourhood of
+a vertex is toggled for every $L_a$ transformation. This is the most straight
+forward implementation but often the $L_a$ transformation is performed several
+times on the same vertex. The neighbourhood would have to be toggled either
+once or not at all depending on whether the number of $L_a$ transformations is
+odd or even.
+
+When toggling an edge the simulator uses a series of well tested basic linked
+list operations: Searching an element in the list, inserting an element into
+the list and deleting an element from the list. This is known to have no bugs
+but the performance could be increased by operating directly on the linked
+list. Some initial work to improve this behaviour is already done but does not
+work at the moment.