diff --git a/abp/graphstate.py b/abp/graphstate.py
index b2e7bb9..9c5f705 100644
--- a/abp/graphstate.py
+++ b/abp/graphstate.py
@@ -5,7 +5,7 @@ This module implements Anders and Briegel's method for fast simulation of Cliffo
 import itertools as it
 import json, random
 import qi, clifford, util
-
+from stabilizer import Stabilizer
 
 class GraphState(object):
 
@@ -361,6 +361,9 @@ class GraphState(object):
             >>> with open("graph.json") as f:
                     json.dump(graph.to_json(True), f)
 
+        .. todo::
+            Implement ``from_json()``!
+
         """
         if stringify:
             node = {str(key): value for key, value in self.node.items()}
@@ -370,11 +373,6 @@ class GraphState(object):
         else:
             return {"node": self.node, "adj": self.adj}
 
-    def from_json(self, data):
-        """ Reconstruct from JSON """
-        self.__init__([])
-        # TODO
-
     def to_state_vector(self):
         """ Get the full state vector corresponding to this stabilizer state. Useful for debugging, interface with other simulators.
             This method becomes very slow for more than about ten qubits!
@@ -401,6 +399,10 @@ class GraphState(object):
             state.act_local_rotation(mapping[i], clifford.unitaries[n["vop"]])
         return state
 
+    def to_stabilizer(self):
+        """ Get the stabilizer representation of the state. """
+        return Stabilizer(self)
+
     def __eq__(self, other):
         """ Check equality between GraphStates """
         return self.adj == other.adj and self.node == other.node
diff --git a/abp/stabilizer.py b/abp/stabilizer.py
index 6c4f02d..426cf45 100644
--- a/abp/stabilizer.py
+++ b/abp/stabilizer.py
@@ -1,18 +1,47 @@
+"""
+Implements a simple Stabilizer object.
+"""
+
+import itertools as it
+from abp import clifford
+
+I = clifford.by_name["identity"]
+X = clifford.by_name["px"]
+Z = clifford.by_name["pz"]
+
 class Stabilizer(object):
     def __init__(self, g):
         """ Construct a Stabilizer from a Graphstate """
-        pass
-
-    def to_stabilizer(self):
-        """ Get the stabilizer tableau.  Work in progress!
-        """
-        for a, b in it.product(self.node, self.node):
-            output[a]["sign"] = 1
+        self.tableau = {i:{j: I for j in g.node} for i in g.node}
+        self.phases = {i: 1 for i in g.node}
+        for a, b in it.product(g.node, g.node):
             if a == b:
-                output[a][b] = "X"
-            elif a in self.adj[b]:
-                output[a][b] = "Z"
-            else:
-                output[a][b] = "I"
-        return output
+                self.tableau[a][b] = X
+            elif a in g.adj[b]:
+                self.tableau[a][b] = Z
+            self.conjugate(a, b, g.node[b]["vop"])
+
+    def conjugate(self, a, b, vop):
+        """ Do a little conjugation """
+        op, phase = clifford.conjugate(self.tableau[a][b], vop)
+        self.tableau[a][b] = op
+        self.phases[a] *= phase
+
+    def to_dictionary(self):
+        """ For comparison with old A&B code """
+        m = {1: 0, 1j:1, -1: 2, -1j: 3}
+        return {"paulis": self.tableau,
+                "phases": {key: m[value] for key, value in self.phases.items()}}
+
+    def __str__(self):
+        """ Represent as a string """
+        s = ""
+        for i in sorted(self.phases):
+            sign = self.phases[i]
+            sign = {1: "  ", -1: " -", 1j: " i", -1j: "-i"}[sign]
+            row = (self.tableau[i][j] for j in sorted(self.phases))
+            row = ("IXYZ"[i] for i in row)
+            row = " ".join(row)
+            s += "{} {}\n".format(sign, row)
+        return s
 
diff --git a/tests/mock.py b/tests/mock.py
index ee034f0..a801c23 100644
--- a/tests/mock.py
+++ b/tests/mock.py
@@ -50,6 +50,9 @@ class ABPWrapper(GraphState):
     def __init__(self, nodes=[]):
         super(ABPWrapper, self).__init__(nodes, deterministic=True)
 
+    def print_stabilizer(self):
+        print self.to_stabilizer()
+
     def __eq__(self, other):
         return self.to_json() == other.to_json()
 
diff --git a/tests/test_graphstate.py b/tests/test_graphstate.py
index b63f053..c582e1c 100644
--- a/tests/test_graphstate.py
+++ b/tests/test_graphstate.py
@@ -74,13 +74,6 @@ def test_cz():
     assert g.has_edge(0, 1)
 
 
-def test_stabilizer():
-    """ Test that we can generate stabilizers okay """
-    g = mock.simple_graph()
-    stab = g.to_stabilizer()
-    # TODO
-
-
 def test_local_complementation():
     """ Test that local complementation works okay """
     pairs = (0, 1), (0, 3), (1, 3), (1, 2), 
diff --git a/tests/mercedes.py b/tests/test_mercedes.py
similarity index 100%
rename from tests/mercedes.py
rename to tests/test_mercedes.py
diff --git a/tests/test_stabilizer.py b/tests/test_stabilizer.py
new file mode 100644
index 0000000..4d97b0d
--- /dev/null
+++ b/tests/test_stabilizer.py
@@ -0,0 +1,21 @@
+from abp import GraphState
+from tqdm import tqdm
+import mock
+
+REPEATS = 1000
+
+def test_stabilizers_against_anders_and_briegel(n=10):
+    """ Test that stabilizers are line-for-line equivalent """
+    
+    for i in tqdm(range(REPEATS), "Stabilizer representation VS A&B"):
+        c = mock.random_stabilizer_circuit(n)
+        g = mock.AndersWrapper(range(n))
+        g.act_circuit(c)
+        da = g.get_full_stabilizer().to_dictionary()
+
+        g = mock.ABPWrapper(range(n))
+        g.act_circuit(c)
+        db = g.to_stabilizer().to_dictionary()
+
+        assert da == db
+