def draw_tiling(sampler, t=4):
"""Draw Chimera graph of sampler with colored tiles.
Args:
sampler (:class:`dwave_micro_client_dimod.TilingComposite`): A tiled dimod sampler to be drawn.
t (int): The size of the shore within each Chimera cell.
Uses `dwave_networkx.draw_chimera` (see draw_chimera_).
Linear biases are overloaded to color the graph according to which tile each Chimera cell belongs to.
.. _draw_chimera: http://dwave-networkx.readthedocs.io/en/latest/reference/generated/dwave_networkx.drawing.chimera_layout.draw_chimera.html
"""
child = sampler.child
nodes_per_cell = t * 2
m = n = int(
ceil(sqrt(ceil(len(child.structure.nodelist) /
nodes_per_cell)))) # assume square lattice shape
system = dnx.chimera_graph(m,
n,
t,
node_list=child.structure.nodelist,
edge_list=child.structure.edgelist)
labels = {node: -len(sampler.embeddings)
for node in system.nodes} # unused cells are blue
labels.update({
node: i
for i, embedding in enumerate(sampler.embeddings)
for s in embedding.values() for node in s
})
dnx.draw_chimera(system, linear_biases=labels)
def plotBipartite(self, left=[], right=[]):
G = dnx.chimera_graph(
1, 1, max(max([i for i, j in left]), max([i for i, j in right])))
dnx.draw_chimera(G, width=4.6, edge_color="purple", node_size=480)
answer = []
labelDict = {}
for i in range(len(left)):
answer.append((0, 0, 0, i))
labelDict[(0, 0, 0, i)] = "{}".format(left[i][1])
for i in range(len(right)):
answer.append((0, 0, 1, i))
labelDict[(0, 0, 1, i)] = "{}".format(right[i][1])
x = dnx.generators.chimera_graph(1,
1,
max(max([i for i, j in left]),
max([i for i, j in right])),
node_list=answer,
coordinates=True)
dnx.draw_chimera(x,
node_color="red",
labels=labelDict,
node_size=480,
width=5,
with_labels=True,
edge_color="red",
font_weight="bold",
font_size="medium")
plt.show()
def plotChimera(self, l, m, n, *, biPartite=None):
assert (biPartite != None and len(biPartite) >= 2
), "A bipartite graph w/ >= 2 nodes must be provided."
if len(self.theGraph) == 0:
raise emptyGraphException()
H = nx.Graph()
H.add_nodes_from([x for x, y in biPartite] + [y for x, y in biPartite])
H.add_edges_from(biPartite)
# need to find correct dimensions
# first need L and R sizes
# assuming this bipartite set is the one provided in the args
LSet, RSet, OCTSet = self.greedyBipartiteSets(getOCT=True)
left, right, OCT = len(LSet), len(RSet), len(OCTSet)
G = dnx.chimera_graph(l, m, n)
dnx.draw_chimera(G, width=3, edge_color="purple")
# abstracting built in exceptions
try:
dnx.draw_chimera(H,
node_color='r',
style='dashed',
edge_color='r',
width=3,
with_labels=True,
font_weight="bold")
except:
print("QEmbed Error: provided graph is not bi-partite. Exiting...")
return
plt.show()
def test_draw_pegasus_biases(self):
G = dnx.chimera_graph(8)
h = {v: v % 12 for v in G}
J = {(u, v) if u % 2 else (v, u): (u + v) % 24 for u, v in G.edges()}
for v in G:
J[v, v] = .1
dnx.draw_chimera(G, linear_biases=h, quadratic_biases=J)
def draw_architecture(target_graph, **kwargs):
""" Draws graph G according to G's family layout.
"""
family = target_graph.graph['family']
if family == 'chimera':
dnx.draw_chimera(target_graph, **kwargs)
elif family == 'pegasus':
dnx.draw_pegasus(target_graph, **kwargs)
else:
nx.draw_spring(target_graph)
warnings.warn(
"Graph family not available. Using NetworkX spring layout")
def draw_tiling(sampler, t=4):
"""Draw Chimera graph of sampler with colored tiles.
Args:
sampler (:class:`dwave_micro_client_dimod.TilingComposite`): A tiled dimod
sampler to be drawn.
t (int): The size of the shore within each
:std:doc:`Chimera <system:reference/intro>` cell.
Uses :std:doc:`dwave_networkx.draw_chimera <networkx:index>`.
Linear biases are overloaded to color the graph according to which tile each Chimera cell belongs to.
See `Ocean Glossary <https://docs.ocean.dwavesys.com/en/latest/glossary.html>`_
for explanations of technical terms in descriptions of Ocean tools.
"""
child = sampler.child
nodes_per_cell = t * 2
m = n = int(
ceil(sqrt(ceil(len(child.structure.nodelist) /
nodes_per_cell)))) # assume square lattice shape
system = dnx.chimera_graph(m,
n,
t,
node_list=child.structure.nodelist,
edge_list=child.structure.edgelist)
labels = {node: -len(sampler.embeddings)
for node in system.nodes} # unused cells are blue
labels.update({
node: i
for i, embedding in enumerate(sampler.embeddings)
for s in embedding.values() for node in s
})
dnx.draw_chimera(system, linear_biases=labels)
def draw_chimera_bqm(bqm, width=None, height=None):
"""Draws a Chimera Graph representation of a Binary Quadratic Model.
If cell width and height not provided assumes square cell dimensions.
Throws an error if drawing onto a Chimera graph of the given dimensions fails.
Args:
bqm (:obj:`dimod.BinaryQuadraticModel`):
Should be equivalent to a Chimera graph or a subgraph of a Chimera graph produced by dnx.chimera_graph.
The nodes and edges should have integer variables as in the dnx.chimera_graph.
width (int, optional):
An integer representing the number of cells of the Chimera graph will be in width.
height (int, optional):
An integer representing the number of cells of the Chimera graph will be in height.
Examples:
>>> from dwave.embedding.drawing import draw_chimera_bqm
>>> from dimod import BinaryQuadraticModel
>>> Q={(0, 0): 2, (1, 1): 1, (2, 2): 0, (3, 3): -1, (4, 4): -2, (5, 5): -2, (6, 6): -2, (7, 7): -2,
... (0, 4): 2, (0, 4): -1, (1, 7): 1, (1, 5): 0, (2, 5): -2, (2, 6): -2, (3, 4): -2, (3, 7): -2}
>>> draw_chimera_bqm(BinaryQuadraticModel.from_qubo(Q), width=1, height=1)
"""
linear = bqm.linear.keys()
quadratic = bqm.quadratic.keys()
if width is None and height is None:
# Create a graph large enough to fit the input networkx graph.
graph_size = ceil(sqrt((max(linear) + 1) / 8.0))
width = graph_size
height = graph_size
if not width or not height:
raise Exception("Both dimensions must be defined, not just one.")
# A background image of the same size is created to show the complete graph.
G0 = chimera_graph(height, width, 4)
G = chimera_graph(height, width, 4)
# Check if input graph is chimera graph shaped, by making sure that no edges are invalid.
# Invalid edges can also appear if the size of the chimera graph is incompatible with the input graph in cell dimensions.
non_chimera_nodes = []
non_chimera_edges = []
for node in linear:
if not node in G.nodes:
non_chimera_nodes.append(node)
for edge in quadratic:
if not edge in G.edges:
non_chimera_edges.append(edge)
linear_set = set(linear)
g_node_set = set(G.nodes)
quadratic_set = set(map(frozenset, quadratic))
g_edge_set = set(map(frozenset, G.edges))
non_chimera_nodes = linear_set - g_node_set
non_chimera_edges = quadratic_set - g_edge_set
if non_chimera_nodes or non_chimera_edges:
raise Exception("Input graph is not a chimera graph: Nodes: %s Edges: %s" % (non_chimera_nodes, non_chimera_edges))
# Get lists of nodes and edges to remove from the complete graph to turn the complete graph into your graph.
remove_nodes = list(g_node_set - linear_set)
remove_edges = list(g_edge_set - quadratic_set)
# Remove the nodes and edges from the graph.
for edge in remove_edges:
G.remove_edge(*edge)
for node in remove_nodes:
G.remove_node(node)
node_size = 100
# Draw the complete chimera graph as the background.
draw_chimera(G0, node_size=node_size*0.5, node_color='black', edge_color='black')
# Draw your graph over the complete graph to show the connectivity.
draw_chimera(G, node_size=node_size, linear_biases=bqm.linear, quadratic_biases=bqm.quadratic,
width=3)
return
# Copyright 2018 D-Wave Systems Inc. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # # ================================================================================================ import matplotlib.pyplot as plt import dwave_networkx as dnx import networkx as nx G = dnx.chimera_graph(2, 2, 4) dnx.draw_chimera(G) plt.show()
def plotChimeraFromBipartite(self,
showMappings=False,
L=2,
M=2,
N=2,
*,
left=[],
right=[],
isBipartite=False):
assert (left != None and
right != None), "Must provide non-empty left and right sets."
assert (L >= 1 and M >= 1
and N >= 1), "Chimera L,M,N topologies must be at least 1."
if (left == [] or right == []):
print("Warning: empty left or right sets.")
answer = []
labelDict = {}
if isBipartite == True:
for i in range(len(left)):
answer.append((0, 0, 0, i))
labelDict[(0, 0, 0, i)] = "v{}".format(left[i][1])
for i in range(len(right)):
answer.append((0, 0, 1, i))
labelDict[(0, 0, 1, i)] = "h{}".format(left[i][1])
# Mapping bipartite sets. First left set
else:
for i, end in left:
for j in range(1, L + 1):
t = (j, math.ceil((i) / N), 1,
((i) % N)) if ((i) % N) > 0 else (j, math.ceil(
(i) / N), 1, N)
answer.append(tuple(k - 1 for k in t))
if (showMappings == True):
print("Mapping v{} to {}.".format(
end, tuple(k - 1 for k in t)))
labelDict[tuple(k - 1 for k in t)] = "h{}".format(end)
for i, end in right:
for j in range(1, M + 1):
t = (math.ceil((i) / N), j, 2,
((i) % N)) if ((i) % N) > 0 else (math.ceil(
(i) / N), j, 2, N)
answer.append(tuple(k - 1 for k in t))
if (showMappings == True):
print("Mapping h{} to {}.".format(
end, tuple(k - 1 for k in t)))
labelDict[tuple(k - 1 for k in t)] = "v{}".format(end)
G = dnx.chimera_graph(L, M, N)
dnx.draw_chimera(G, width=4.6, edge_color="purple", node_size=480)
x = dnx.generators.chimera_graph(L,
M,
N,
node_list=answer,
coordinates=True)
dnx.draw_chimera(x,
node_color="red",
labels=labelDict,
node_size=480,
width=5,
with_labels=True,
edge_color="red",
font_weight="bold",
font_size="medium")
plt.show()
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import minorminer
import networkx as nx
import dwave_networkx as dnx
import matplotlib.pyplot as plt
K3 = nx.Graph([('A', 'B'), ('B', 'C'), ('C', 'A')])
plt.subplot(2, 2, 1)
nx.draw(K3, with_labels=True)
C = dnx.chimera_graph(1, 2, coordinates=False)
plt.subplot(2, 2, 2)
dnx.draw_chimera(C, with_labels=True)
# Example with one blob for one node. Source node will use at least one.
blob = [4, 5, 12, 13]
suspend_chains = {'A': [blob]}
embedding = minorminer.find_embedding(K3, C, suspend_chains=suspend_chains)
plt.subplot(2, 2, 3)
dnx.draw_chimera_embedding(C, embedding, with_labels=True)
# Example with one blob for one node, and two blobs for another.
# Second source node is forced to use at least one in each blob.
blob_A0 = [4, 5]
blob_A1 = [12, 13]
blob_C0 = [6, 7, 14, 15]
suspend_chains = {'A': [blob_A0, blob_A1], 'C': [blob_C0]}
embedding = minorminer.find_embedding(K3, C, suspend_chains=suspend_chains)
# Look at a minor embedding problem. It's still NP-hard
# Usually need probablistic heuristics to find an embedding
# D-Wave has unit cells containing K4,4 bipartite fully connected graph
# with two remote connections from each qubit going to qubits in neighbouring unit cells. A unit
# cell is with its local and remote connections including indicated
# Chimera graph, largest hardware has 2048 qubits consisting of 16 by 16 unit cells of 8 qubits
# Chimera graph is available as a networkx graph in the package dwave_networkx
# draw a smaller one of 2 by 2 cells
import matplotlib.pyplot as plt
import dwave_networkx as dnx
connectivity_structure = dnx.chimera_graph(2, 2)
dnx.draw_chimera(connectivity_structure)
plt.show()
# Now create a graph that does not fit the connectivity structure. The complete Kn on nine nodes
import networkx as nx
G = nx.complete_graph(9)
plt.axis('off')
nx.draw_networkx(G, with_labels=False)
import minorminer
embedded_graph = minorminer.find_embedding(G.edges(), connectivity_structure.edges())
dnx.draw_chimera_embedding(connectivity_structure, embedded_graph)
plt.show()
classical_sampler = neal.SimulatedAnnealingSampler() sampler = dimod.StructureComposite(classical_sampler, P6.nodes, P6.edges) # %% # Working With Embeddings # 全結合の40ノードを作りたい num_variables = 40 embedding = dwave.embedding.chimera.find_clique_embedding(num_variables, 16) max(len(chain) for chain in embedding.values()) # チェーン数は11 # %% # 680 node Pegasus num_variables = 40 embedding = dwave.embedding.pegasus.find_clique_embedding(num_variables, 6) max(len(chain) for chain in embedding.values()) # チェーン数は6 # %% # https://qiita.com/YuichiroMinato/items/dbc142ecb1efbebd6adf chimera = dnx.chimera_graph(2, 2, 4) dnx.draw_chimera(chimera) plt.show() # %% P3 = dnx.pegasus_graph(2) dnx.draw_pegasus(P3) plt.show() # %%
