def test_graph_mapped(self, graph):
"""Test if function returns correctly processed subgraphs given input samples of the list
``quantum_samples``. Note that graph nodes are numbered in this test as [0, 1, 4, 9,
...] (i.e., squares of the usual list) as a simple mapping to explore that the optimised
subgraph returned is still a valid subgraph."""
graph = nx.relabel_nodes(graph, lambda x: x ** 2)
graph_nodes = list(graph.nodes)
subgraphs_mapped = [
sorted([graph_nodes[i] for i in subgraph]) for subgraph in self.subgraphs
]
assert sample.to_subgraphs(self.quantum_samples, graph) == subgraphs_mapped
def test_graph(self, graph):
"""Test if function returns correctly processed subgraphs given input samples of the list
``quantum_samples``."""
assert sample.to_subgraphs(self.quantum_samples,
graph) == self.subgraphs
# In this tutorial, we'll study a 30-node graph with a planted 10-node graph, as considered in # :cite:`arrazola2018using`. The graph is generated by joining two Erdős–Rényi random graphs. The # first graph of 20 nodes is created with edge probability of 0.5. The second planted # graph is generated with edge probability of 0.875. The planted nodes are the last ten nodes in the # graph. The two graphs are joined by selecting 8 nodes at random from both graphs and adding an # edge between them. This graph has the sneaky property that even though the planted subgraph is the # densest of its size, its nodes have a lower average degree than the nodes in the rest of the # graph. # # The :mod:`~.apps.data` module has pre-generated GBS samples from this graph. Let's load them, # postselect on samples with a large number of clicks, and convert them to subgraphs: planted = data.Planted() postselected = sample.postselect(planted, 16, 30) pl_graph = nx.to_networkx_graph(planted.adj) samples = sample.to_subgraphs(postselected, pl_graph) print(len(samples)) ############################################################################## # Not bad! We have more than 2000 samples to play with 😎. The planted subgraph is actually easy to # identify; it even appears clearly from the force-directed Kamada-Kawai algorithm that is used to # plot graphs in Strawberry Fields: sub = list(range(20, 30)) plot_graph = plot.graph(pl_graph, sub) plotly.offline.plot(plot_graph, filename="planted.html") ############################################################################## # .. raw:: html # :file: ../../examples_apps/planted.html # # .. note::
maximal_clique = [4, 11, 12, 18]
maximal_fig = plot.graph(TA_graph, maximal_clique)
plotly.offline.plot(maximal_fig, filename="maximal_clique.html")
##############################################################################
# .. raw:: html
# :file: ../../examples_apps/maximal_clique.html
##############################################################################
# We'll now use the :mod:`~.apps.clique` module to find larger cliques in the graph. We can make
# use of the pre-generated samples from the TACE-AS graph in the :mod:`~.apps.data` module and
# post-select samples with a specific number of clicks. Here we'll look at samples with eight
# clicks, of which there are a total of 1,984:
postselected = sample.postselect(TA, 8, 8)
samples = sample.to_subgraphs(postselected, TA_graph)
print(len(samples))
##############################################################################
# GBS produces samples that correspond to subgraphs of high density. For fun, let's confirm this
# by comparing the average subgraph density in the GBS samples to uniformly generated samples:
GBS_dens = []
u_dens = []
for s in samples:
uniform = list(np.random.choice(24, 8,
replace=False)) # generates uniform sample
GBS_dens.append(nx.density(TA_graph.subgraph(s)))
u_dens.append(nx.density(TA_graph.subgraph(uniform)))
min_clicks = 3 max_clicks = 4 s = sample.postselect(s, min_clicks, max_clicks) print(len(s)) s.append([0, 1, 0, 1, 1, 0]) ############################################################################## # As expected, we have fewer samples than before. The number of samples that survive this # postselection is determined by the mean photon number in GBS. We have also added in our example # sample ``[0, 1, 0, 1, 1, 0]`` to ensure that there is at least one for the following. # # Let's convert our postselected samples to subgraphs: subgraphs = sample.to_subgraphs(s, graph) print(subgraphs) ############################################################################## # We can take a look at one of the sampled subgraphs: plotly.offline.plot(plot.graph(graph, subgraphs[0]), filename="subgraph.html") ############################################################################## # .. raw:: html # :file: ../../examples_apps/subgraph.html # # These sampled subgraphs act as the starting point for some of the applications made available # in Strawberry Fields, including the maximum clique and dense subgraph identification problems. # Go and check out the other tutorials in the applications layer to see what you can do with GBS!
