# この時点でIsing形式用のJ, h, BINARY形式用のQが生成済みである。 # ISING形式の場合 #bqm = dimod.BinaryQuadraticModel.from_ising(h, J) # BINARY形式の場合 bqm = dimod.BinaryQuadraticModel.from_qubo(Q) url = "https://cloud.dwavesys.com/sapi" token = "your_token" solver_name = "DW_2000Q_5" sampler = DWaveSampler(endpoint=url, token=token, solver=solver_name) # minorminerでエンベディング embedding = minorminer.find_embedding(S, sampler.edgelist) bqm_embed = embed_bqm(bqm, embedding, sampler.adjacency) # D-Waveによるサンプリング result = sampler.sample(bqm_embed, num_reads=1000, postprocess="optimization", beta=3.0) # minimize energyによる後処理 cbm = MinimizeEnergy(bqm, embedding) unembedded, idx = cbm(result, list(embedding.values())) # アンエンベッドされた解に関して、エネルギーの再計算や重複解などの整理をする # 出力結果はdimod.SampleSetの形式 (Ocean SDKによる他のサンプリング結果と同じデータ形式) sample = dimod.SampleSet.from_samples_bqm(unembedded, bqm, num_occurrences=result.record['num_occurrences']).aggregate() # 出力のテンプレート print(sample) print(sample.record['sample'])
# Confirm that a P variable has been removed from the BQM, for example, "p0"
print("Variable p0 in BQM: ", 'p0' in bqm)
print("Variable a0 in BQM: ", 'a0' in bqm)
# Use a D-Wave system as the sampler
# sampler = DWaveSampler(solver={'qpu': True}) # Some accounts need to replace this line with the next:
sampler = DWaveSampler(solver='DW_2000Q_2_1',
token='DEV-289c9dcb0d1d85f3a9059f77fd53bc84e3935d52')
_, target_edgelist, target_adjacency = sampler.structure
# Find an embedding
embedding = minorminer.find_embedding(bqm.quadratic, target_edgelist)
if bqm and not embedding:
raise ValueError("no embedding found")
bqm_embedded = embed_bqm(bqm, embedding, target_adjacency, 3.0)
# Confirm mapping of variables from a0, b0, etc to indexed qubits
print("Variable a0 in embedded BQM: ", 'a0' in bqm_embedded)
print("First five nodes in QPU graph: ", sampler.structure.nodelist[:5])
kwargs = {}
if 'num_reads' in sampler.parameters:
kwargs['num_reads'] = 5
if 'answer_mode' in sampler.parameters:
kwargs['answer_mode'] = 'histogram'
# Request num_reads samples
kwargs['num_reads'] = 1000
response = sampler.sample(bqm_embedded, **kwargs)
def sample(self,
bqm,
chain_strength=1.0,
chain_break_method=None,
chain_break_fraction=True,
embedding_parameters=None,
return_embedding=None,
warnings=None,
**parameters):
"""Sample from the provided binary quadratic model.
Args:
bqm (:obj:`dimod.BinaryQuadraticModel`):
Binary quadratic model to be sampled from.
chain_strength (float, optional, default=1.0):
Magnitude of the quadratic bias (in SPIN-space) applied between
variables to create chains. The energy penalty of chain breaks
is 2 * `chain_strength`.
chain_break_method (function, optional):
Method used to resolve chain breaks during sample unembedding.
See :func:`~dwave.embedding.unembed_sampleset`.
chain_break_fraction (bool, optional, default=True):
Add a `chain_break_fraction` field to the unembedded response with
the fraction of chains broken before unembedding.
embedding_parameters (dict, optional):
If provided, parameters are passed to the embedding method as
keyword arguments. Overrides any `embedding_parameters` passed
to the constructor.
return_embedding (bool, optional):
If True, the embedding, chain strength, chain break method and
embedding parameters are added to :attr:`dimod.SampleSet.info`
of the returned sample set. The default behaviour is defined
by :attr:`return_embedding_default`, which itself defaults to
False.
warnings (:class:`~dwave.system.warnings.WarningAction`, optional):
Defines what warning action to take, if any. See
:mod:`~dwave.system.warnings`. The default behaviour is defined
by :attr:`warnings_default`, which itself defaults to
:class:`~dwave.system.warnings.IGNORE`
**parameters:
Parameters for the sampling method, specified by the child
sampler.
Returns:
:obj:`dimod.SampleSet`
Examples:
See the example in :class:`EmbeddingComposite`.
"""
if return_embedding is None:
return_embedding = self.return_embedding_default
# solve the problem on the child system
child = self.child
# apply the embedding to the given problem to map it to the child sampler
__, target_edgelist, target_adjacency = self.target_structure
# add self-loops to edgelist to handle singleton variables
source_edgelist = list(bqm.quadratic) + [(v, v) for v in bqm.linear]
# get the embedding
if embedding_parameters is None:
embedding_parameters = self.embedding_parameters
else:
# we want the parameters provided to the constructor, updated with
# the ones provided to the sample method. To avoid the extra copy
# we do an update, avoiding the keys that would overwrite the
# sample-level embedding parameters
embedding_parameters.update(
(key, val) for key, val in self.embedding_parameters
if key not in embedding_parameters)
embedding = self.find_embedding(source_edgelist, target_edgelist,
**embedding_parameters)
if warnings is None:
warnings = self.warnings_default
elif 'warnings' in child.parameters:
parameters.update(warnings=warnings)
warninghandler = WarningHandler(warnings)
warninghandler.chain_strength(bqm, chain_strength)
warninghandler.chain_length(embedding)
if bqm and not embedding:
raise ValueError("no embedding found")
bqm_embedded = embed_bqm(bqm,
embedding,
target_adjacency,
chain_strength=chain_strength,
smear_vartype=dimod.SPIN)
if 'initial_state' in parameters:
# if initial_state was provided in terms of the source BQM, we want
# to modify it to now provide the initial state for the target BQM.
# we do this by spreading the initial state values over the
# chains
state = parameters['initial_state']
parameters['initial_state'] = {
u: state[v]
for v, chain in embedding.items() for u in chain
}
if self.scale_aware and 'ignored_interactions' in child.parameters:
ignored = []
for chain in embedding.values():
# just use 0 as a null value because we don't actually need
# the biases, just the interactions
ignored.extend(chain_to_quadratic(chain, target_adjacency, 0))
parameters['ignored_interactions'] = ignored
response = child.sample(bqm_embedded, **parameters)
warninghandler.chain_break(response, embedding)
sampleset = unembed_sampleset(
response,
embedding,
source_bqm=bqm,
chain_break_method=chain_break_method,
chain_break_fraction=chain_break_fraction,
return_embedding=return_embedding)
if return_embedding:
sampleset.info['embedding_context'].update(
embedding_parameters=embedding_parameters,
chain_strength=chain_strength)
if chain_break_fraction and len(sampleset):
warninghandler.issue(
"all samples had broken chains",
func=lambda:
(sampleset.record.chain_break_fraction.all(), None))
if warninghandler.action is WarningAction.SAVE:
# we're done with the warning handler so we can just pass the list
# off, if later we want to pass in a handler or similar we should
# do a copy
sampleset.info.setdefault('warnings',
[]).extend(warninghandler.saved)
return sampleset
}
chainstrength = 1.01
numruns = 100
dwave_sampler = DWaveSampler()
A = dwave_sampler.edgelist
Adj = dwave_sampler.adjacency
embedding = find_embedding(Q, A)
print(embedding)
bqm = BinaryQuadraticModel.from_qubo(Q)
# Cannot use a Composite to get the broken chains, so do the embedding
# directly
bqm_embedded = embed_bqm(bqm, embedding, Adj, chain_strength=chainstrength)
response = DWaveSampler().sample(bqm_embedded, num_reads=numruns)
# We need to get the chains directly, as a list
chains = [embedding[v] for v in list(bqm)]
# Obtain the broken chains
broken = broken_chains(response, chains)
# Interpret the results in terms of the embedding. Be sure to
# tell the method to compute the chain_break_frequency.
print(
unembed_sampleset(response,
embedding,
source_bqm=bqm,
chain_break_fraction=True), broken)
def from_bqm_sampleset(bqm,
sampleset,
sampler,
embedding_context=None,
warnings=None,
params=None):
"""Construct problem data for visualization based on the BQM and sampleset
in logical space (both unembedded).
In order for the embedded problem/response to be reconstructed, an embedding
is required in either the sampleset, or as a standalone argument.
Note:
This adapter can only provide best-effort estimate of the submitted
problem and received samples. Namely, because values of logical
variables in `sampleset` are produced by a chain break resolution
method, information about individual physical qubit values is lost.
Please have in mind you will never see "broken chains" when using this
adapter.
Args:
bqm (:class:`dimod.BinaryQuadraticModel`/:class:`dimod.core.bqm.BQM`):
Problem in logical (unembedded) space, given as a BQM.
sampleset (:class:`~dimod.sampleset.SampleSet`):
Sampling response as a sampleset.
sampler (:class:`~dimod.Sampler` or :class:`~dimod.ComposedSampler`):
The :class:`~dwave.system.samplers.dwave_sampler.DWaveSampler`-
derived sampler used to produce the sampleset off the bqm.
embedding_context (dict, optional):
A map containing an embedding of logical problem onto the
solver's graph (the ``embedding`` key) and embedding parameters
used (e.g. ``chain_strength``). It is optional only if
``sampleset.info`` contains it (see `return_embedding` argument of
:meth:`~dwave.system.composites.embedding.EmbeddingComposite`).
warnings (list[dict], optional):
Optional list of warnings.
params (dict, optional):
Sampling parameters used.
"""
logger.debug("from_bqm_sampleset({!r})".format(
dict(bqm=bqm,
sampleset=sampleset,
sampler=sampler,
warnings=warnings,
embedding_context=embedding_context,
params=params)))
if not isinstance(sampler, dimod.Sampler):
raise TypeError("dimod.Sampler instance expected for 'sampler'")
# get embedding parameters
if embedding_context is None:
embedding_context = sampleset.info.get('embedding_context', {})
if embedding_context is None:
raise ValueError("embedding_context not given")
embedding = embedding_context.get('embedding')
if embedding is None:
raise ValueError("embedding not given")
chain_strength = embedding_context.get('chain_strength')
def find_solver(sampler):
if hasattr(sampler, 'solver'):
return sampler.solver
for child in getattr(sampler, 'children', []):
try:
return find_solver(child)
except:
pass
raise TypeError("'sampler' doesn't use DWaveSampler")
solver = find_solver(sampler)
if not isinstance(solver, StructuredSolver):
raise TypeError("only structured solvers are supported")
topology = _get_solver_topology(solver)
if topology['type'] not in SUPPORTED_SOLVER_TOPOLOGY_TYPES:
raise TypeError("unsupported solver topology type")
solver_id = solver.id
problem_type = "ising" if sampleset.vartype is dimod.SPIN else "qubo"
# bqm vartype must match sampleset vartype
if bqm.vartype is not sampleset.vartype:
bqm = bqm.change_vartype(sampleset.vartype, inplace=False)
# if `embedding` is `dwave.embedding.transforms.EmbeddedStructure`, we don't
# need `target_adjacency`
emb_params = dict(embedding=embedding)
if not hasattr(embedding, 'embed_bqm'):
# proxy for detecting dict vs. EmbeddedStructure, without actually
# importing EmbeddedStructure (did not exist in dwave-system<0.9.10)
target_adjacency = edgelist_to_adjacency(solver.edges)
emb_params.update(target_adjacency=target_adjacency)
# get embedded bqm
bqm_embedded = embed_bqm(bqm,
chain_strength=chain_strength,
smear_vartype=dimod.SPIN,
**emb_params)
# best effort reconstruction of (unembedded/qmi) response/solutions
# NOTE: we **can not** reconstruct physical qubit values from logical variables
# (sampleset we have access to has variable values after chain breaks resolved!)
active_variables = sorted(list(bqm_embedded.variables))
active_variables_set = set(active_variables)
logical_variables = list(sampleset.variables)
var_to_idx = {var: idx for idx, var in enumerate(logical_variables)}
unembedding = {q: var_to_idx[v] for v, qs in embedding.items() for q in qs}
# sanity check
assert set(unembedding) == active_variables_set
def expand_sample(sample):
return [int(sample[unembedding[q]]) for q in active_variables]
solutions = [expand_sample(sample) for sample in sampleset.record.sample]
# adjust energies to values returned by SAPI (offset embedding)
energies = list(map(float, sampleset.record.energy - bqm_embedded.offset))
num_occurrences = list(map(int, sampleset.record.num_occurrences))
num_variables = solver.num_qubits
timing = sampleset.info.get('timing')
linear, quadratic, offset = bqm_embedded.to_ising()
problem_data = {
"format":
"qp", # SAPI non-conforming (nulls vs nans)
"lin": [
uniform_get(linear, v, 0 if v in active_variables_set else None)
for v in solver._encoding_qubits
],
"quad": [
quadratic.get((q1, q2), 0) + quadratic.get((q2, q1), 0)
for (q1, q2) in solver._encoding_couplers
if q1 in active_variables_set and q2 in active_variables_set
],
"embedding":
embedding
}
# try to get problem id. if not available, auto-generate one
problem_id = sampleset.info.get('problem_id')
if problem_id is None:
problem_id = "local-%s" % uuid.uuid4()
# try to reconstruct sampling params
if params is None:
params = {'num_reads': int(sum(num_occurrences))}
# expand with defaults
params = _expand_params(solver, params, timing)
# try to get warnings from sampleset.info
if warnings is None:
warnings = sampleset.info.get('warnings')
# construct problem stats
problem_stats = _problem_stats(response=None,
sampleset=sampleset,
embedding_context=embedding_context)
data = {
"ready":
True,
"details": {
"id": problem_id,
"type": problem_type,
"solver": solver.id,
"label": sampleset.info.get('problem_label'),
},
"data":
_problem_dict(solver_id, problem_type, problem_data, params,
problem_stats),
"answer":
_answer_dict(solutions, active_variables, energies, num_occurrences,
timing, num_variables),
"unembedded_answer":
_unembedded_answer_dict(sampleset),
"warnings":
_warnings(warnings),
"rel":
dict(solver=solver),
}
logger.trace("from_bqm_sampleset returned %r", data)
return data
def from_bqm_response(bqm,
embedding_context,
response,
warnings=None,
params=None,
sampleset=None):
"""Construct problem data for visualization based on the unembedded BQM,
the embedding used when submitting, and the low-level sampling response.
Args:
bqm (:class:`dimod.BinaryQuadraticModel`/:class:`dimod.core.bqm.BQM`):
Problem in logical (unembedded) space, given as a BQM.
embedding_context (dict):
A map containing an embedding of logical problem onto the
solver's graph (the ``embedding`` key) and embedding parameters
used (e.g. ``chain_strength``, ``chain_break_method``, etc).
response (:class:`dwave.cloud.computation.Future`):
Sampling response, as returned by the low-level sampling interface
in the Cloud Client (e.g. :meth:`dwave.cloud.solver.sample_ising`
for Ising problems).
warnings (list[dict], optional):
Optional list of warnings.
params (dict, optional):
Sampling parameters used.
sampleset (:class:`dimod.SampleSet`, optional):
Optional unembedded sampleset.
"""
logger.debug("from_bqm_response({!r})".format(
dict(bqm=bqm,
response=response,
response_energies=response['energies'],
embedding_context=embedding_context,
warnings=warnings,
params=params,
sampleset=sampleset)))
solver = response.solver
if not isinstance(response.solver, StructuredSolver):
raise TypeError("only structured solvers are supported")
topology = _get_solver_topology(solver)
if topology['type'] not in SUPPORTED_SOLVER_TOPOLOGY_TYPES:
raise TypeError("unsupported solver topology type")
solver_id = solver.id
problem_type = response.problem_type
active_variables = response['active_variables']
active = set(active_variables)
solutions = list(map(itemsgetter(*active_variables),
response['solutions']))
energies = response['energies']
num_occurrences = response.num_occurrences
num_variables = solver.num_qubits
timing = response.timing
# bqm vartype must match response vartype
if problem_type == "ising":
bqm = bqm.change_vartype(dimod.SPIN, inplace=False)
else:
bqm = bqm.change_vartype(dimod.BINARY, inplace=False)
# get embedding parameters
if 'embedding' not in embedding_context:
raise ValueError("embedding not given")
embedding = embedding_context.get('embedding')
chain_strength = embedding_context.get('chain_strength')
chain_break_method = embedding_context.get('chain_break_method')
# if `embedding` is `dwave.embedding.transforms.EmbeddedStructure`, we don't
# need `target_adjacency`
emb_params = dict(embedding=embedding)
if not hasattr(embedding, 'embed_bqm'):
# proxy for detecting dict vs. EmbeddedStructure, without actually
# importing EmbeddedStructure (did not exist in dwave-system<0.9.10)
target_adjacency = edgelist_to_adjacency(solver.edges)
emb_params.update(target_adjacency=target_adjacency)
# get embedded bqm
bqm_embedded = embed_bqm(bqm,
chain_strength=chain_strength,
smear_vartype=dimod.SPIN,
**emb_params)
linear, quadratic, offset = bqm_embedded.to_ising()
problem_data = {
"format":
"qp", # SAPI non-conforming (nulls vs nans)
"lin": [
uniform_get(linear, v, 0 if v in active else None)
for v in solver._encoding_qubits
],
"quad": [
quadratic.get((q1, q2), 0) + quadratic.get((q2, q1), 0)
for (q1, q2) in solver._encoding_couplers
if q1 in active and q2 in active
],
"embedding":
embedding
}
# try to reconstruct sampling params
if params is None:
params = {'num_reads': int(sum(num_occurrences))}
# expand with defaults
params = _expand_params(solver, params, timing)
# TODO: if warnings are missing, calculate them here (since we have the
# low-level response)
# construct problem stats
problem_stats = _problem_stats(response=response,
sampleset=sampleset,
embedding_context=embedding_context)
data = {
"ready":
True,
"details":
_details_dict(response),
"data":
_problem_dict(solver_id, problem_type, problem_data, params,
problem_stats),
"answer":
_answer_dict(solutions, active_variables, energies, num_occurrences,
timing, num_variables),
"warnings":
_warnings(warnings),
"rel":
dict(solver=solver),
}
if sampleset is not None:
data["unembedded_answer"] = _unembedded_answer_dict(sampleset)
logger.trace("from_bqm_response returned %r", data)
return data
def sample(self,
bqm,
chain_strength=1.0,
chain_break_fraction=True,
**parameters):
"""Sample from the provided binary quadratic model.
Also set parameters for handling a chain, the set of vertices in a target graph that
represents a source-graph vertex; when a D-Wave system is the sampler, it is a set
of qubits that together represent a variable of the binary quadratic model being
minor-embedded.
Args:
bqm (:obj:`dimod.BinaryQuadraticModel`):
Binary quadratic model to be sampled from.
chain_strength (float, optional, default=1.0):
Magnitude of the quadratic bias (in SPIN-space) applied between variables to create
chains. The energy penalty of chain breaks is 2 * `chain_strength`.
chain_break_fraction (bool, optional, default=True):
If True, the unembedded response contains a ‘chain_break_fraction’ field
that reports the fraction of chains broken before unembedding.
**parameters:
Parameters for the sampling method, specified by the child sampler.
Returns:
:class:`dimod.SampleSet`: A `dimod` :obj:`~dimod.SampleSet` object.
Examples:
This example submits an triangle-structured problem to a D-Wave solver, selected
by the user's default
:std:doc:`D-Wave Cloud Client configuration file <cloud-client:intro>`,
using a specified minor-embedding of the problem’s variables to physical qubits.
>>> from dwave.system.samplers import DWaveSampler
>>> from dwave.system.composites import FixedEmbeddingComposite
>>> import dimod
...
>>> sampler = FixedEmbeddingComposite(DWaveSampler(), {'a': [0, 4], 'b': [1, 5], 'c': [2, 6]})
>>> response = sampler.sample_ising({}, {'ab': 0.5, 'bc': 0.5, 'ca': 0.5}, chain_strength=2)
>>> response.first # doctest: +SKIP
Sample(sample={'a': 1, 'b': -1, 'c': 1}, energy=-0.5, num_occurrences=1, chain_break_fraction=0.0)
See `Ocean Glossary <https://docs.ocean.dwavesys.com/en/latest/glossary.html>`_
for explanations of technical terms in descriptions of Ocean tools.
"""
# solve the problem on the child system
child = self.child
# apply the embedding to the given problem to map it to the child sampler
__, __, target_adjacency = child.structure
# get the embedding
embedding = self.embedding
bqm_embedded = embed_bqm(bqm,
embedding,
target_adjacency,
chain_strength=chain_strength,
smear_vartype=dimod.SPIN)
if 'initial_state' in parameters:
parameters['initial_state'] = _embed_state(
embedding, parameters['initial_state'])
response = child.sample(bqm_embedded, **parameters)
return unembed_sampleset(response,
embedding,
source_bqm=bqm,
chain_break_fraction=chain_break_fraction)
_, edgelist, adjacency = sampler.structure from minorminer import find_embedding embedding = find_embedding(qubo, edgelist, random_seed=0) # random_seed=0 - which ensures that the same embedding is always generated. if manual_embed: # Pick the method for fixing broken chains. from dwave.embedding.chain_breaks import majority_vote # weighted_random method = majority_vote # Submit the job via an embedded BinaryQuadraticModel. from dimod import BinaryQuadraticModel as BQM from dwave.embedding import embed_bqm, unembed_sampleset # Generate a BQM from the QUBO. q = BQM.from_qubo(qubo) # Embed the BQM onto the target structure. embedded_q = embed_bqm(q, embedding, adjacency) # chain_strength=chain_strength, smear_vartype=dimod.SPIN # Collect the sample output. response = unembed_sampleset( sampler.sample(embedded_q, num_reads=num_samples), embedding, q, chain_break_method=method, chain_break_fraction=True) else: # Use a FixedEmbeddingComposite if we don't care about chains. from dwave.system.composites import FixedEmbeddingComposite system_composite = FixedEmbeddingComposite(sampler, embedding) response = system_composite.sample_qubo(qubo, num_reads=num_samples) constant = 0 # Cycle through the results and yield them to the caller.
