def test_sample_to_orbit(dim):
"""Test if function ``similarity.sample_to_orbit`` correctly returns the original orbit after
taking all permutations over the orbit. The starting orbits are all orbits for a fixed photon
number ``dim``."""
orb = all_orbits[dim]
checks = []
for o in orb:
sorted_sample = o.copy()
sorted_sample_len = len(sorted_sample)
if sorted_sample_len != dim:
sorted_sample += [0] * sorted_sample_len
permutations = itertools.permutations(sorted_sample)
checks.append(all([similarity.sample_to_orbit(p) == o for p in permutations]))
assert all(checks)
# # Following :cite:`schuld2019quantum`, we can create a *feature vector* to describe each graph. # These feature vectors contain information about the graphs and can be viewed as a mapping to a # high-dimensional feature space, a technique often used in machine learning that allows us to # employ properties of the feature space to separate and classify the vectors. # # The feature vector of a graph can be composed in a variety of ways. One approach is to # associate features with the relative frequencies of certain types of measurements being # recorded from a GBS device configured to sample from the graph, as we now discuss. # # We begin by defining the concept of an *orbit*, which is the set of all GBS samples that are # equivalent under permutation of the modes. A sample can be converted to its corresponding orbit # using the :func:`~.sample_to_orbit` function. For example, the first sample of ``m0`` is ``[0, # 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]`` and has orbit: print(similarity.sample_to_orbit(m0[0])) ############################################################################## # Here, ``[1, 1]`` means that two photons were detected, each in a separate mode. Other samples # can be randomly generated from the ``[1, 1]`` orbit using: print(similarity.orbit_to_sample([1, 1], modes=m0.modes)) ############################################################################## # Orbits provide a useful way to coarse-grain the samples from GBS into outcomes that are # statistically more likely to be observed. However, we are interested in coarse-graining further # into *events*, which correspond to a combination of orbits with the same photon number such # that the number of photons counted in each mode does not exceed a fixed value # ``max_count_per_mode``. To understand this, let's look at all of the orbits with a photon # number of 5: