def test_empty_list(self):
# Set up fragmentation function
pg = pegasus_graph(3)
fragment_tuple = get_tuple_fragmentation_fn(pg)
# Fragment pegasus coordinates
fragments = fragment_tuple([])
self.assertEqual([], fragments)
def test_valid_clique_ints(self):
k = nx.complete_graph(15)
m = 4
# Find embedding
pg = pegasus_graph(m)
embedding = find_clique_embedding(k, target_graph=pg)
self.assertTrue(is_valid_embedding(embedding, k, pg))
def test_k_parameter_int(self):
k_int = 5
m = 3
# Find embedding
pg = pegasus_graph(m, coordinates=True)
embedding = find_clique_embedding(k_int, target_graph=pg)
self.assertTrue(is_valid_embedding(embedding, nx.complete_graph(k_int), pg))
def test_k_parameter_list(self):
k_nodes = ['one', 'two', 'three']
m = 4
# Find embedding
pg = pegasus_graph(m, coordinates=True)
embedding = find_clique_embedding(k_nodes, target_graph=pg)
self.assertTrue(is_valid_embedding(embedding, nx.complete_graph(k_nodes), pg))
def test_one_clique(self):
k = 1
m = 4
# Find embedding
pg = pegasus_graph(m, coordinates=True)
embedding = find_clique_embedding(k, target_graph=pg)
self.assertTrue(is_valid_embedding(embedding, nx.complete_graph(k), pg))
def test_valid_clique_coord(self):
k = nx.complete_graph(55)
m = 6
# Find embedding
pg = pegasus_graph(m, coordinates=True)
embedding = find_clique_embedding(k, target_graph=pg)
self.assertTrue(is_valid_embedding(embedding, k, pg))
def test_impossible_clique(self):
k = 55
m = 2
# Find embedding
pg = pegasus_graph(m)
with self.assertRaises(ValueError):
find_clique_embedding(k, target_graph=pg)
def test_empty_list(self):
# Set up defragmentation function
pg = pegasus_graph(2)
defragment_tuple = get_tuple_defragmentation_fn(pg)
# De-fragment chimera coordinates
chimera_coords = []
pegasus_coords = defragment_tuple(chimera_coords)
self.assertEqual([], pegasus_coords)
def test_zero_clique(self):
k = 0
m = 3
# Find embedding
pg = pegasus_graph(m)
embedding = find_clique_embedding(k, target_graph=pg)
self.assertEqual(k, len(embedding))
self.assertEqual({}, embedding)
def test_single_fragment(self):
# Set up defragmentation function
pg = pegasus_graph(4)
defragment_tuple = get_tuple_defragmentation_fn(pg)
# De-fragment chimera coordinates
chimera_coords = [(3, 7, 0, 0)]
pegasus_coords = defragment_tuple(chimera_coords)
expected_pegasus_coords = [(0, 1, 2, 0)]
self.assertEqual(expected_pegasus_coords, pegasus_coords)
def test_mixed_fragments(self):
# Set up defragmenation function
pg = pegasus_graph(8)
defragment_tuple = get_tuple_defragmentation_fn(pg)
# De-fragment chimera coordinates
chimera_coords = [(17, 14, 0, 0), (22, 14, 0, 0), (24, 32, 1, 0), (1, 31, 0, 0)]
pegasus_coords = defragment_tuple(chimera_coords)
expected_pegasus_coords = {(0, 2, 4, 2), (1, 4, 0, 4), (0, 5, 2, 0)}
self.assertEqual(expected_pegasus_coords, set(pegasus_coords))
def _pegasus_fragment_helper(m=None, target_graph=None):
# This is a function that takes m or a target_graph and produces a
# `processor` object for the corresponding Pegasus graph, and a function
# that translates embeddings produced by that object back to the original
# pegasus graph. Consumed by `find_clique_embedding` and
# `find_biclique_embedding`.
# Organize parameter values
if target_graph is None:
if m is None:
raise TypeError("m and target_graph cannot both be None.")
target_graph = pegasus_graph(m)
m = target_graph.graph['rows'] # We only support square Pegasus graphs
# Deal with differences in ints vs coordinate target_graphs
if target_graph.graph['labels'] == 'nice':
back_converter = pegasus_coordinates.pegasus_to_nice
back_translate = lambda embedding: {
key: [back_converter(p) for p in chain]
for key, chain in embedding.items()
}
elif target_graph.graph['labels'] == 'int':
# Convert nodes in terms of Pegasus coordinates
coord_converter = pegasus_coordinates(m)
# A function to convert our final coordinate embedding to an ints embedding
back_translate = lambda embedding: {
key: list(coord_converter.iter_pegasus_to_linear(chain))
for key, chain in embedding.items()
}
else:
back_translate = lambda embedding: embedding
# collect edges of the graph produced by splitting each Pegasus qubit into six pieces
fragment_edges = list(fragmented_edges(target_graph))
# Find clique embedding in K2,2 Chimera graph
embedding_processor = processor(fragment_edges,
M=m * 6,
N=m * 6,
L=2,
linear=False)
# Convert chimera fragment embedding in terms of Pegasus coordinates
defragment_tuple = get_tuple_defragmentation_fn(target_graph)
def embedding_to_pegasus(nodes, emb):
emb = map(defragment_tuple, emb)
emb = dict(zip(nodes, emb))
emb = back_translate(emb)
return emb
return embedding_processor, embedding_to_pegasus
def test_multiple_fragments_from_same_qubit(self):
# Set up defragmentation function
pg = pegasus_graph(3)
defragment_tuple = get_tuple_defragmentation_fn(pg)
# De-fragment chimera coordinates
chimera_coords = [(9, 8, 1, 1), (9, 11, 1, 1)]
pegasus_coords = defragment_tuple(chimera_coords)
expected_pegasus_coords = [(1, 1, 7, 1)]
self.assertEqual(expected_pegasus_coords, pegasus_coords)
def test_single_vertical_coordinate(self):
# Set up fragmentation function
pg = pegasus_graph(6)
fragment_tuple = get_tuple_fragmentation_fn(pg)
pegasus_coord = (0, 1, 3, 1)
fragments = fragment_tuple([pegasus_coord])
expected_fragments = {(7, 7, 0, 1), (8, 7, 0, 1), (9, 7, 0, 1),
(10, 7, 0, 1), (11, 7, 0, 1), (12, 7, 0, 1)}
self.assertEqual(expected_fragments, set(fragments))
def test_nice_coordinates(self):
p = pegasus_graph(3, nice_coordinates=True)
c = chimera_graph(24, coordinates=True)
num_edges = 0
for u, v in fragmented_edges(p):
self.assertTrue(c.has_edge(u, v))
num_edges += 1
#This is a weird edgecount: each node produces 5 extra edges for the internal connections
#between fragments corresponding to a pegasus qubit. But then we need to delete the odd
#couplers, which aren't included in the chimera graph -- odd couplers make a perfect
#matching, so thats 1/2 an edge per node.
self.assertEqual(p.number_of_edges() + 9 * p.number_of_nodes()//2, num_edges)
def test_single_horizontal_coordinate(self):
# Set up fragmentation function
pg = pegasus_graph(2)
fragment_tuple = get_tuple_fragmentation_fn(pg)
# Fragment pegasus coordinates
pegasus_coord = (1, 0, 0, 0)
fragments = fragment_tuple([pegasus_coord])
expected_fragments = {(0, 3, 1, 0), (0, 4, 1, 0), (0, 5, 1, 0),
(0, 6, 1, 0), (0, 7, 1, 0), (0, 8, 1, 0)}
self.assertEqual(expected_fragments, set(fragments))
def test_list_of_coordinates(self):
# Set up fragmentation function
pg = pegasus_graph(6)
fragment_tuple = get_tuple_fragmentation_fn(pg)
# Fragment pegasus coordinates
pegasus_coords = [(1, 5, 11, 4), (0, 2, 2, 3)]
fragments = fragment_tuple(pegasus_coords)
expected_fragments = {(35, 29, 1, 1), (35, 30, 1, 1), (35, 31, 1, 1),
(35, 32, 1, 1), (35, 33, 1, 1), (35, 34, 1, 1),
(19, 13, 0, 0), (20, 13, 0, 0), (21, 13, 0, 0),
(22, 13, 0, 0), (23, 13, 0, 0), (24, 13, 0, 0)}
self.assertEqual(expected_fragments, set(fragments))
def test_clique_incomplete_graph(self):
k = 5
m = 2
# Nodes in a known K5 embedding
# Note: {0: [14, 32], 1: [33, 15], 2: [16, 34], 3: [35, 17], 4: [36, 12]}
known_embedding_nodes = {14, 32, 33, 15, 16, 34, 35, 17, 36, 12}
# Create graph with missing nodes
incomplete_pg = pegasus_graph(m)
removed_nodes = set(incomplete_pg.nodes) - known_embedding_nodes
incomplete_pg.remove_nodes_from(removed_nodes)
# See if clique embedding is found
embedding = find_clique_embedding(k, target_graph=incomplete_pg)
self.assertTrue(is_valid_embedding(embedding, nx.complete_graph(k), incomplete_pg))
def draw_pegasus_yield(G, **kwargs):
"""Draws the given graph G with highlighted faults, according to layout.
Parameters
----------
G : NetworkX graph
The graph to be parsed for faults
unused_color : tuple or color string (optional, default (0.9,0.9,0.9,1.0))
The color to use for nodes and edges of G which are not faults.
If unused_color is None, these nodes and edges will not be shown at all.
fault_color : tuple or color string (optional, default (1.0,0.0,0.0,1.0))
A color to represent nodes absent from the graph G. Colors should be
length-4 tuples of floats between 0 and 1 inclusive.
fault_shape : string, optional (default='x')
The shape of the fault nodes. Specification is as matplotlib.scatter
marker, one of 'so^>v<dph8'.
fault_style : string, optional (default='dashed')
Edge fault line style (solid|dashed|dotted,dashdot)
kwargs : optional keywords
See networkx.draw_networkx() for a description of optional keywords,
with the exception of the `pos` parameter which is not used by this
function. If `linear_biases` or `quadratic_biases` are provided,
any provided `node_color` or `edge_color` arguments are ignored.
"""
try:
assert (G.graph["family"] == "pegasus")
m = G.graph['columns']
offset_lists = (G.graph['vertical_offsets'],
G.graph['horizontal_offsets'])
coordinates = G.graph["labels"] == "coordinate"
# Can't interpret fabric_only from graph attributes
except:
raise ValueError("Target pegasus graph needs to have columns, rows, \
tile, and label attributes to be able to identify faulty qubits.")
perfect_graph = pegasus_graph(m,
offset_lists=offset_lists,
coordinates=coordinates)
draw_yield(G, pegasus_layout(perfect_graph), perfect_graph, **kwargs)
def test_clique_missing_edges(self):
k = 9
m = 2
pg = pegasus_graph(m)
#pick a random ordering of the edges
edges = list(pg.edges())
shuffle(edges)
K = nx.complete_graph(k)
#now delete edges, one at a time, until we can no longer embed K
with self.assertRaises(ValueError):
while 1:
(u, v) = edges.pop()
pg.remove_edge(u, v)
# See if clique embedding is found
embedding = find_clique_embedding(k, target_graph=pg)
self.assertTrue(is_valid_embedding(embedding, K, pg))
def find_clique_embedding(k, m=None, target_graph=None):
"""Find an embedding for a clique in a Pegasus graph.
Given a clique (fully connected graph) and target Pegasus graph, attempts
to find an embedding by transforming the Pegasus graph into a :math:`K_{2,2}`
Chimera graph and then applying a Chimera clique-finding algorithm. Results
are converted back to Pegasus coordinates.
Args:
k (int/iterable/:obj:`networkx.Graph`): A complete graph to embed,
formatted as a number of nodes, node labels, or a NetworkX graph.
m (int): Number of tiles in a row of a square Pegasus graph. Required to
generate an m-by-m Pegasus graph when `target_graph` is None.
target_graph (:obj:`networkx.Graph`): A Pegasus graph. Required when `m`
is None.
Returns:
dict: An embedding as a dict, where keys represent the clique's nodes and
values, formatted as lists, represent chains of pegasus coordinates.
Examples:
This example finds an embedding for a :math:`K_3` complete graph in a
2-by-2 Pegaus graph.
>>> from dwave.embedding.pegasus import find_clique_embedding
...
>>> print(find_clique_embedding(3, 2)) # doctest: +SKIP
{0: [10, 34], 1: [35, 11], 2: [32, 12]}
"""
# Organize parameter values
if target_graph is None:
if m is None:
raise TypeError("m and target_graph cannot both be None.")
target_graph = pegasus_graph(m)
m = target_graph.graph['rows'] # We only support square Pegasus graphs
_, nodes = k
# Deal with differences in ints vs coordinate target_graphs
if target_graph.graph['labels'] == 'nice':
fwd_converter = get_nice_to_pegasus_fn()
back_converter = get_pegasus_to_nice_fn()
pegasus_coords = [fwd_converter(*p) for p in target_graph.nodes]
back_translate = lambda embedding: {key: [back_converter(*p) for p in chain]
for key, chain in embedding.items()}
elif target_graph.graph['labels'] == 'int':
# Convert nodes in terms of Pegasus coordinates
coord_converter = pegasus_coordinates(m)
pegasus_coords = map(coord_converter.tuple, target_graph.nodes)
# A function to convert our final coordinate embedding to an ints embedding
back_translate = lambda embedding: {key: list(coord_converter.ints(chain))
for key, chain in embedding.items()}
else:
pegasus_coords = target_graph.nodes
back_translate = lambda embedding: embedding
# Break each Pegasus qubits into six Chimera fragments
# Note: By breaking the graph in this way, you end up with a K2,2 Chimera graph
fragment_tuple = get_tuple_fragmentation_fn(target_graph)
fragments = fragment_tuple(pegasus_coords)
# Create a K2,2 Chimera graph
# Note: 6 * m because Pegasus qubits split into six pieces, so the number of rows and columns
# get multiplied by six
chim_m = 6 * m
chim_graph = chimera_graph(chim_m, t=2, coordinates=True)
# Determine valid fragment couplers in a K2,2 Chimera graph
edges = chim_graph.subgraph(fragments).edges()
# Find clique embedding in K2,2 Chimera graph
embedding_processor = processor(edges, M=chim_m, N=chim_m, L=2, linear=False)
chimera_clique_embedding = embedding_processor.tightestNativeClique(len(nodes))
# Convert chimera fragment embedding in terms of Pegasus coordinates
defragment_tuple = get_tuple_defragmentation_fn(target_graph)
pegasus_clique_embedding = map(defragment_tuple, chimera_clique_embedding)
pegasus_clique_embedding = dict(zip(nodes, pegasus_clique_embedding))
pegasus_clique_embedding = back_translate(pegasus_clique_embedding)
if len(pegasus_clique_embedding) != len(nodes):
raise ValueError("No clique embedding found")
return pegasus_clique_embedding
def find_clique_embedding(k, m=None, target_graph=None):
"""Find an embedding of a k-sized clique on a Pegasus graph (target_graph).
This clique is found by transforming the Pegasus graph into a K2,2 Chimera graph and then
applying a Chimera clique finding algorithm. The results are then converted back in terms of
Pegasus coordinates.
Note: If target_graph is None, m will be used to generate a m-by-m Pegasus graph. Hence m and
target_graph cannot both be None.
Args:
k (int/iterable/:obj:`networkx.Graph`): Number of members in the requested clique; list of nodes;
a complete graph that you want to embed onto the target_graph
m (int): Number of tiles in a row of a square Pegasus graph
target_graph (:obj:`networkx.Graph`): A Pegasus graph
Returns:
dict: A dictionary representing target_graphs's clique embedding. Each dictionary key
represents a node in said clique. Each corresponding dictionary value is a list of pegasus
coordinates that should be chained together to represent said node.
"""
# Organize parameter values
if target_graph is None:
if m is None:
raise TypeError("m and target_graph cannot both be None.")
target_graph = pegasus_graph(m)
m = target_graph.graph['rows'] # We only support square Pegasus graphs
_, nodes = k
# Deal with differences in ints vs coordinate target_graphs
if target_graph.graph['labels'] == 'nice':
fwd_converter = get_nice_to_pegasus_fn(m=m)
back_converter = get_pegasus_to_nice_fn(m=m)
pegasus_coords = [fwd_converter(*p) for p in target_graph.nodes]
back_translate = lambda embedding: {
key: [back_converter(*p) for p in chain]
for key, chain in embedding.items()
}
elif target_graph.graph['labels'] == 'int':
# Convert nodes in terms of Pegasus coordinates
coord_converter = pegasus_coordinates(m)
pegasus_coords = map(coord_converter.tuple, target_graph.nodes)
# A function to convert our final coordinate embedding to an ints embedding
back_translate = lambda embedding: {
key: list(coord_converter.ints(chain))
for key, chain in embedding.items()
}
else:
pegasus_coords = target_graph.nodes
back_translate = lambda embedding: embedding
# Break each Pegasus qubits into six Chimera fragments
# Note: By breaking the graph in this way, you end up with a K2,2 Chimera graph
fragment_tuple = get_tuple_fragmentation_fn(target_graph)
fragments = fragment_tuple(pegasus_coords)
# Create a K2,2 Chimera graph
# Note: 6 * m because Pegasus qubits split into six pieces, so the number of rows and columns
# get multiplied by six
chim_m = 6 * m
chim_graph = chimera_graph(chim_m, t=2, coordinates=True)
# Determine valid fragment couplers in a K2,2 Chimera graph
edges = chim_graph.subgraph(fragments).edges()
# Find clique embedding in K2,2 Chimera graph
embedding_processor = processor(edges,
M=chim_m,
N=chim_m,
L=2,
linear=False)
chimera_clique_embedding = embedding_processor.tightestNativeClique(
len(nodes))
# Convert chimera fragment embedding in terms of Pegasus coordinates
defragment_tuple = get_tuple_defragmentation_fn(target_graph)
pegasus_clique_embedding = map(defragment_tuple, chimera_clique_embedding)
pegasus_clique_embedding = dict(zip(nodes, pegasus_clique_embedding))
pegasus_clique_embedding = back_translate(pegasus_clique_embedding)
if len(pegasus_clique_embedding) != len(nodes):
raise ValueError("No clique embedding found")
return pegasus_clique_embedding