Samplesets and Solutions#
Samplers sample from low-energy states of a problem’s objective function—BQM samplers sample from low-energy states in models such as those defined by an Ising equation or a QUBO problem—and return an iterable of samples, in order of increasing energy.
When a D-Wave quantum computer solves a problem, it uses quantum phenomena such as superposition and tunneling to explore all possible solutions simultaneously and find a set of the best ones. At the end of the computation (anneal), a single solution is sampled from a set of good solutions, with some probability, and returned. Because the sampled solution is probabilistic, different solutions may be returned in different runs. The standard way of submitting a problem to the system requests many samples, not just one. This not only returns multiple “best” answers but also reduces the probability of settling on a suboptimal answer.
Some classical samplers might return
non-probabilistic solutions; for example, the dimod
package’s ExactSolver class deterministically returns the best
solution or solutions to small problems by calculating the result for every
configuration of variable values. Such samplers are called
solvers.
Some Ocean software functions might return a single best solution; for example, some dwave-networkx tool graph algorithms return only the lowest-energy sample.
The dimod package provides a SampleSet
class that contains, and enables you to manipulate, samples. It also contains
information such as timing and minor-embedding from some samplers.
Example: Sampleset#
This example creates a sampleset and then demonstrates some properties and
methods of the SampleSet class.
>>> import dimod
...
>>> bqm = dimod.generators.random.ran_r(1, 7)
>>> sampler = dimod.ExactSolver()
>>> sampleset = sampler.sample(bqm)
Print the best solution’s energy.
>>> print(sampleset.first.energy)
-9.0
Print the best solutions.
>>> print(sampleset.lowest())
0 1 2 3 4 5 6 energy num_oc.
0 +1 -1 +1 -1 +1 -1 -1 -9.0 1
1 +1 +1 +1 -1 +1 -1 -1 -9.0 1
...
7 -1 +1 -1 +1 -1 -1 +1 -9.0 1
['SPIN', 8 rows, 8 samples, 7 variables]
Convert to a third-party format (pandas).
>>> sampleset.to_pandas_dataframe()
0 1 2 3 4 5 6 energy num_occurrences
0 -1 -1 -1 -1 -1 -1 -1 3.0 1
1 1 -1 -1 -1 -1 -1 -1 7.0 1
2 1 1 -1 -1 -1 -1 -1 7.0 1
...
Example: Sampleset from NumPy#
This example creates a sampleset from NumPy arrays.
>>> import numpy as np
>>> samples = np.random.randint(0, 2, (100, 10))
>>> energies = np.random.randint(-10, 0, 100)
>>> occurrences = np.random.randint(0, 50, 100)
>>> sampleset = dimod.SampleSet.from_samples(samples,
... "BINARY",
... energies,
... num_occurrences=occurrences)
Example: Timing Information#
As a simple example, this three-variable BQM,
might be solved directly on a D-Wave quantum computer by sampling 1000
times. Here, the EmbeddingComposite
composite maps the symbolic BQM to qubits on the quantum processor,
which is called by the DWaveSampler sampler:
>>> import dimod
>>> from dwave.system import DWaveSampler, EmbeddingComposite
...
>>> s0, s1, s2 = dimod.Spins(['s0', 's1', 's2'])
>>> bqm = s1*s2 - s0*s1 - s0*s2
>>> sampler = EmbeddingComposite(DWaveSampler())
>>> sampleset = sampler.sample(bqm, num_reads=1000)
>>> print(sampleset)
s0 s1 s2 energy num_oc. chain_.
0 -1 +1 -1 -1.0 183 0.0
1 -1 -1 +1 -1.0 141 0.0
2 -1 -1 -1 -1.0 206 0.0
3 +1 -1 +1 -1.0 162 0.0
4 +1 +1 +1 -1.0 123 0.0
5 +1 +1 -1 -1.0 185 0.0
['SPIN', 6 rows, 1000 samples, 3 variables]
The returned SampleSet object, in this case, shows six solutions
of equal energy \(-1.0\). Solution \(s_0=-1, s_1=+1, s_2=-1\) on the
first line occurred in 183 of the 1000 samples.
For this submission, the sampleset also contained the following additional information:
>>> print(sampleset.info.keys())
dict_keys(['timing', 'problem_id', 'embedding_context', 'warnings'])
For example, the timing information for the problem might look something like:
>>> print(sampleset.info["timing"])
{'qpu_sampling_time': 85860.0,
'qpu_anneal_time_per_sample': 20.0,
'qpu_readout_time_per_sample': 45.32,
'qpu_access_time': 101619.97,
'qpu_access_overhead_time': 2259.03,
'qpu_programming_time': 15759.97,
'qpu_delay_time_per_sample': 20.54,
'total_post_processing_time': 2277.0,
'post_processing_overhead_time': 2277.0}