|
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181 |
- """
- Provides an extremely basic graph structure, based on neighbour lists
- """
-
- from collections import defaultdict
- import itertools as it
- import clifford
- import json
- try:
- import networkx as nx
- except ImportError:
- print "Could not import networkx: layout will not work"
-
-
- class GraphState(object):
-
- def __init__(self):
- self.ngbh = defaultdict(set)
- self.vops = defaultdict(int)
- self.meta = defaultdict(dict)
-
- def add_vertex(self, v):
- """ Add a vertex if it doesn't already exist """
- if not v in self.ngbh:
- self.ngbh[v] = set()
- self.vops[v] = clifford.by_name["hadamard"]
-
- def add_edge(self, v1, v2):
- """ Add an edge between two vertices in the self """
- if not v1 in self.ngbh:
- self.vops[v1] = clifford.by_name["hadamard"]
- if not v2 in self.ngbh:
- self.vops[v2] = clifford.by_name["hadamard"]
- self.ngbh[v1].add(v2)
- self.ngbh[v2].add(v1)
-
- def del_edge(self, v1, v2):
- """ Delete an edge between two vertices in the self """
- self.ngbh[v1].remove(v2)
- self.ngbh[v2].remove(v1)
-
- def has_edge(self, v1, v2):
- """ Test existence of an edge between two vertices in the self """
- return v2 in self.ngbh[v1]
-
- def toggle_edge(self, v1, v2):
- """ Toggle an edge between two vertices in the self """
- if self.has_edge(v1, v2):
- self.del_edge(v1, v2)
- else:
- self.add_edge(v1, v2)
-
- def edgelist(self):
- """ Describe a graph as an edgelist """
- edges = frozenset(tuple(sorted((i, n)))
- for i, v in self.ngbh.items()
- for n in v)
- return [tuple(e) for e in edges]
-
- def remove_vop(self, a, avoid):
- """ Reduces VOP[a] to the identity """
- others = self.ngbh[a] - {avoid}
- swap_qubit = others.pop() if others else avoid
- for v in reversed(clifford.decompositions[self.vops[a]]):
- self.local_complementation(a if v == "x" else swap_qubit)
-
- def local_complementation(self, v):
- """ As defined in LISTING 1 of Anders & Briegel """
- for i, j in it.combinations(self.ngbh[v], 2):
- self.toggle_edge(i, j)
-
- # Update VOPs: TODO check ordering and replace by self.act_local_rotation
- self.vops[v] = clifford.times_table[
- self.vops[v]][clifford.by_name["sqx"]]
- for i in self.ngbh[v]:
- self.vops[i] = clifford.times_table[
- self.vops[i]][clifford.by_name["msqz"]]
-
- def act_local_rotation(self, a, op):
- """ Act a local rotation """
- self.vops[a] = clifford.times_table[op,self.vops[a]]
-
- def act_local_rotation_by_name(self, qubit, name):
- """ Shorthand """
- rotation = clifford.by_name[name]
- self.act_local_rotation(qubit, rotation)
-
- def act_hadamard(self, qubit):
- """ Shorthand """
- self.act_local_rotation(qubit, 10)
-
- def act_cz(self, a, b):
- """ Act a controlled-phase gate on two qubits """
- if self.ngbh[a] - {b}:
- self.remove_vop(a, b)
- if self.ngbh[b] - {a}:
- self.remove_vop(b, a)
- if self.ngbh[a] - {b}:
- self.remove_vop(a, b)
- edge = self.has_edge(a, b)
- new_edge, self.vops[a], self.vops[b] = clifford.cz_table[edge, self.vops[a], self.vops[b]]
- if new_edge != edge:
- self.toggle_edge(a, b)
-
- def measure_x(self, i):
- """ Measure the graph in the X-basis """
- #TODO
- pass
-
- def measure_y(self, i):
- """ Measure the graph in the Y-basis """
- #TODO
- pass
-
- def measure_Z(self, i):
- """ Measure the graph in the Z-basis """
- #TODO
- pass
-
- def order(self):
- """ Get the number of qubits """
- return len(self.vops)
-
- def __str__(self):
- """ Represent as a string for quick debugging """
- return "graph:\n vops: {}\n ngbh: {}\n"\
- .format(str(dict(self.vops)), str(dict(self.ngbh)))
-
- def to_json(self):
- """ Convert the graph to JSON form """
- #ngbh = {key: tuple(value) for key, value in self.ngbh.items()}
- meta = {key: value for key, value in self.meta.items()}
- edge = self.edgelist()
- return json.dumps({"vops": self.vops, "edge": edge, "meta": meta})
-
- def to_networkx(self):
- """ Convert the graph to a networkx graph """
- g = nx.Graph()
- g.edge = {node: {neighbour: {} for neighbour in neighbours}
- for node, neighbours in self.ngbh.items()}
- g.node = {node: {"vop": vop} for node, vop in self.vops.items()}
- for node, metadata in self.meta.items():
- g.node[node].update(metadata)
- return g
-
- def layout(self):
- """ Automatically lay out the graph """
- g = self.to_networkx()
- pos = nx.spring_layout(g, dim=3, scale=10)
- average = lambda axis: sum(p[axis] for p in pos.values())/float(len(pos))
- ax, ay, az = average(0), average(1), average(2)
- for key, (x, y, z) in pos.items():
- self.meta[key]["pos"] = {"x": round(x-ax, 0), "y": round(y-ay, 0), "z": round(z-az, 0)}
-
- def to_stabilizer(self):
- """ Get the stabilizer of this graph """
- # TODO: VOPs are not implemented yet
- output = ""
- for a in self.ngbh:
- for b in self.ngbh:
- if a == b:
- output += " X "
- elif a in self.ngbh[b]:
- output += " Z "
- else:
- output += " I "
- output += "\n"
- return output
-
- def adj_list(self):
- """ For comparison with Anders and Briegel's C++ implementation """
- rows = []
- for key, vop in self.vops.items():
- ngbh = " ".join(map(str, sorted(self.ngbh[key])))
- vop = clifford.ab_names.get(vop, vop)
- s = "Vertex {}: VOp {}, neighbors {}".format(key, vop, ngbh)
- rows.append(s)
- return " \n".join(rows)+ " \n"
-
-
-
|