Local complementation

TODO

@@ -0,0 +1,4 @@
+Next things to do:
+    - Read A&B code which expresses C(1) as products of sqrt(iX), sqrt(iY)
+    - Read A&B code which exposes LC API
+    - Implement the above

cz.py

@@ -0,0 +1,29 @@
+from graph import Graph
+from matplotlib import pyplot as plt
+
+class GraphState(Graph):
+
+    def __init__(self, n):
+        Graph.__init__(self, n)
+
+    def local_complementation(self, a):
+        for i in self.neighbours[a]:
+            for j in self.neighbours[a]:
+                if i<j:
+                    self.toggle_edge(i, j)
+
+if __name__ == '__main__':
+    g = GraphState(10)
+    g.add_edge(0, 1)
+    g.add_edge(1, 3)
+    g.add_edge(3, 2)
+    g.add_edge(3, 0)
+    g.add_edge(2, 0)
+    g.add_edge(0, 5)
+    g.vops[0]=1
+    g.draw()
+
+    plt.clf()
+    g.local_complementation(0)
+    g.draw("out2.pdf")
+

graph.py

@@ -1,36 +1,46 @@
 import networkx as nx
 from matplotlib import pyplot as plt
 
+vop_colors = ["red", "green", "blue"]
+
 class Graph(object):
 
     def __init__(self, n):
-        self.vertices = [set() for i in xrange(n)]
-        self.vops = ["hadamard" for i in xrange(n)]
+        self.neighbours = [set() for i in xrange(n)]
+        self.vops = [0 for i in xrange(n)]
 
     def add_edge(self, v1, v2):
-        self.vertices[v1].add(v2)
-        self.vertices[v2].add(v1)
+        self.neighbours[v1].add(v2)
+        self.neighbours[v2].add(v1)
 
     def del_edge(self, v1, v2):
-        self.vertices[v1].remove(v2)
-        self.vertices[v2].remove(v1)
+        self.neighbours[v1].remove(v2)
+        self.neighbours[v2].remove(v1)
+
+    def has_edge(self, v1, v2):
+        return v2 in self.neighbours[v1]
+
+    def toggle_edge(self, v1, v2):
+        if self.has_edge(v1, v2):
+            self.del_edge(v1, v2)
+        else:
+            self.add_edge(v1, v2)
+
 
     def edgelist(self):
         edges = frozenset(frozenset((i, n))
-                for i, v in enumerate(self.vertices)
+                for i, v in enumerate(self.neighbours)
                 for n in v)
         return [tuple(e) for e in edges]
 
-    def draw(self, filename="out.pdf"):
+    def draw(self, filename="out.pdf", ns=500):
         g = nx.from_edgelist(self.edgelist())
         pos = nx.spring_layout(g)
-        nx.draw_networkx_nodes(g, pos, node_color="white", node_size=1000)
+        colors = [vop_colors[vop] for vop in self.vops]
+        nx.draw_networkx_nodes(g, pos, node_color="white", node_size=ns)
+        nx.draw_networkx_nodes(g, pos, node_color=colors, node_size=ns, alpha=.4)
         nx.draw_networkx_labels(g, pos)
         nx.draw_networkx_edges(g, pos)
-        for i, vop in enumerate(self.vops):
-            if not i in pos: continue
-            x, y = pos[i]
-            plt.text(x, y+0.1, "hadamard", ha="center")
 
         plt.axis('off')
         plt.savefig(filename)

tests/test_graph.py

@@ -5,11 +5,14 @@ def test_graph():
     g.add_edge(0,1)
     g.add_edge(1,2)
     g.add_edge(2,0)
-    assert g.vertices[0]==set([1,2])
+    assert g.neighbours[0]==set([1,2])
 
     g.del_edge(0,1)
-    assert g.vertices[0]==set([2])
+    assert g.neighbours[0]==set([2])
     el = g.edgelist()
     assert (1,2) in el
     assert not (0,1) in el
     assert len(el)==2
+
+    assert g.has_edge(1,2)
+    assert not g.has_edge(0,1)