From f834babb450ed8e62fe8b2544c253fac1f47af5c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Kn=C3=BCttel?= <daniel.knuettel@daknuett.eu>
Date: Thu, 31 Oct 2019 13:58:45 +0100
Subject: [PATCH] some work on the graph simulator theory

---
 thesis/chapters/graph_simulator.tex |  7 +++++++
 thesis/main.bib                     | 23 +++++++++++++++++++++++
 2 files changed, 30 insertions(+)

diff --git a/thesis/chapters/graph_simulator.tex b/thesis/chapters/graph_simulator.tex
index 4defa10..c9bba99 100644
--- a/thesis/chapters/graph_simulator.tex
+++ b/thesis/chapters/graph_simulator.tex
@@ -1,5 +1,12 @@
 \section{The graph Simulator}
 
+\subsection{Introduction to the Graph Formalism}
+
+The first step towards the simulation in the graph formalism has been
+the discovery of the stabilizer states and stabilizer circuits \cite{gottesman2009}\cite{gottesman1997}.
+They led to the faster simulation using stabilizer tableaux\cite{gottesman_aaronson2008} and later
+to the graph formalism .
+
 \subsection{Graph Storage}
 
 One of the gread advantages of simulating in the graph formalism is a great increase 
diff --git a/thesis/main.bib b/thesis/main.bib
index dce6d16..d9f10b2 100644
--- a/thesis/main.bib
+++ b/thesis/main.bib
@@ -44,3 +44,26 @@
     year=2007,
     publisher={Oxford University Press}
 }
+@article{
+    gottesman2009,
+    title={An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation},
+    year=2009,
+    author={Daniel Gottesman},
+    note={https://arxiv.org/abs/0904.2557v1}
+}
+
+@article{
+    gottesman1997,
+    title={Stabilizer Codes and Quantum Error Correction},
+    year=1997,
+    author={Daniel Gottesman},
+    note={https://arxiv.org/abs/quant-ph/9705052}
+}
+
+@article{
+    gottesman_aaronson2008,
+    title={Improved Simulation of Stabilizer Circuits}
+    year=2008,
+    author={Daniel Gottesman, Scott Aaronson}
+    note={https://arxiv.org/abs/quant-ph/0406196v5}
+}