def test_unembed_response_with_discard_matrix_typical(self):
h = {'a': .1, 'b': 0, 'c': 0}
J = {('a', 'b'): 1, ('b', 'c'): 1.3, ('a', 'c'): -1}
bqm = dimod.BinaryQuadraticModel.from_ising(h, J, offset=1.3)
embedding = {'a': {0}, 'b': {1}, 'c': {2, 3}}
embedded_bqm = dimod.embed_bqm(bqm,
embedding,
nx.cycle_graph(4),
chain_strength=1)
embedded_response = dimod.ExactSolver().sample(embedded_bqm)
chain_break_method = dimod.embedding.discard
response = dimod.unembed_response(
embedded_response,
embedding,
bqm,
chain_break_method=dimod.embedding.discard)
self.assertEqual(len(embedded_response) / 2,
len(response)) # half chains should be broken
for sample, energy in response.data(['sample', 'energy']):
self.assertEqual(bqm.energy(sample), energy)
def test_embed_bqm_BINARY(self):
Q = {
('a', 'a'): 0,
('a', 'b'): -1,
('b', 'b'): 0,
('c', 'c'): 0,
('b', 'c'): -1
}
bqm = dimod.BinaryQuadraticModel.from_qubo(Q)
embedding = {'a': {0}, 'b': {1}, 'c': {2, 3}}
embedded_bqm = dimod.embed_bqm(bqm,
embedding,
nx.cycle_graph(4),
chain_strength=1)
# check that the energy has been preserved
for config in itertools.product((0, 1), repeat=3):
sample = dict(zip(('a', 'b', 'c'), config))
target_sample = {
u: sample[v]
for v, chain in embedding.items() for u in chain
} # no chains broken
self.assertAlmostEqual(bqm.energy(sample),
embedded_bqm.energy(target_sample))
def test_embed_bqm_empty(self):
bqm = dimod.BinaryQuadraticModel.empty(dimod.SPIN)
embedded_bqm = dimod.embed_bqm(bqm, {}, {})
self.assertIsInstance(embedded_bqm, dimod.BinaryQuadraticModel)
self.assertFalse(embedded_bqm) # should be empty
def sample(self, bqm, chain_strength=1.0, chain_break_fraction=True, **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. Note that the energy penalty of chain breaks is 2 * `chain_strength`.
chain_break_fraction (bool, optional, default=True):
If True, a ‘chain_break_fraction’ field is added to the unembedded response which report
what fraction of the chains were broken before unembedding.
**parameters:
Parameters for the sampling method, specified by the child sampler.
Returns:
:class:`dimod.Response`
Examples:
This example uses :class:`.FixedEmbeddingComposite` to instantiate a composed sampler
that submits an unstructured Ising problem to a D-Wave solver, selected by the user's
default
:std:doc:`D-Wave Cloud Client configuration file <cloud-client:reference/intro>`,
while minor-embedding the problem's variables to physical qubits on the solver.
>>> 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]})
>>> resp = sampler.sample_ising({'a': .5, 'c': 0}, {('a', 'c'): -1})
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 = dimod.embed_bqm(bqm, embedding, target_adjacency, chain_strength=chain_strength)
if 'initial_state' in parameters:
parameters['initial_state'] = _embed_state(embedding, parameters['initial_state'])
response = child.sample(bqm_embedded, **parameters)
return dimod.unembed_response(response, embedding, source_bqm=bqm,
chain_break_fraction=chain_break_fraction)
def test_embed_bqm_identity(self):
bqm = dimod.BinaryQuadraticModel({'a': -1}, {(0, 1): .5, (1, 'a'): -1.}, 1.0, dimod.BINARY)
embedding = {v: {v} for v in bqm.linear} # identity embedding
target_adj = bqm.to_networkx_graph() # identity target graph
embedded_bqm = dimod.embed_bqm(bqm, embedding, target_adj)
self.assertEqual(bqm, embedded_bqm)
def test_embedding_with_extra_chains(self):
embedding = {0: [0, 1], 1: [2], 2: [3]}
G = nx.cycle_graph(4)
bqm = dimod.BinaryQuadraticModel.from_qubo({(0, 0): 1})
target_bqm = dimod.embed_bqm(bqm, embedding, G)
for v in itertools.chain(*embedding.values()):
self.assertIn(v, target_bqm)
def test_embed_bqm_subclass_propagation(self):
class MyBQM(dimod.BinaryQuadraticModel):
pass
bqm = MyBQM.empty(dimod.BINARY)
embedded_bqm = dimod.embed_bqm(bqm, {}, {})
self.assertIsInstance(embedded_bqm, dimod.BinaryQuadraticModel)
self.assertIsInstance(embedded_bqm, MyBQM)
self.assertFalse(embedded_bqm) # should be empty
def test_energies_functional(self):
h = {'a': .1, 'b': 0, 'c': 0}
J = {('a', 'b'): 1, ('b', 'c'): 1.3, ('a', 'c'): -1}
bqm = dimod.BinaryQuadraticModel.from_ising(h, J, offset=1.3)
embedding = {'a': {0}, 'b': {1}, 'c': {2, 3}}
embedded_bqm = dimod.embed_bqm(bqm, embedding, nx.cycle_graph(4), chain_strength=1)
embedded_response = dimod.ExactSolver().sample(embedded_bqm)
response = dimod.unembed_response(embedded_response, embedding, bqm)
for sample, energy in response.data(['sample', 'energy']):
self.assertEqual(bqm.energy(sample), energy)
def sample(self, bqm, chain_strength=1.0, **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. Note that the energy penalty of chain breaks is 2 * `chain_strength`.
**parameters:
Parameters for the sampling method, specified by the child sampler.
Returns:
:class:`dimod.Response`
Examples:
This example uses :class:`.FixedEmbeddingComposite` to instantiate a composed sampler
that submits an unstructured Ising problem to a D-Wave solver, selected by the user's
default D-Wave Cloud Client configuration_ file, while minor-embedding the problem's
variables to physical qubits on the solver.
>>> 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]})
>>> resp = sampler.sample_ising({'a': .5, 'c': 0}, {('a', 'c'): -1})
"""
# 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 = dimod.embed_bqm(bqm,
embedding,
target_adjacency,
chain_strength=chain_strength)
response = child.sample(bqm_embedded, **parameters)
return dimod.unembed_response(response, embedding, source_bqm=bqm)
def test_embed_bqm_NAE3SAT_to_square(self):
h = {'a': 0, 'b': 0, 'c': 0}
J = {('a', 'b'): 1, ('b', 'c'): 1, ('a', 'c'): 1}
bqm = dimod.BinaryQuadraticModel.from_ising(h, J)
embedding = {'a': {0}, 'b': {1}, 'c': {2, 3}}
embedded_bqm = dimod.embed_bqm(bqm,
embedding,
nx.cycle_graph(4),
chain_strength=1)
self.assertEqual(
embedded_bqm,
dimod.BinaryQuadraticModel(
{
0: 0,
1: 0,
2: 0,
3: 0
},
{
(0, 1): 1,
(1, 2): 1,
(2, 3): -1,
(0, 3): 1
},
1.0, # offset the energy from satisfying chains
dimod.SPIN))
# check that the energy has been preserved
for config in itertools.product((-1, 1), repeat=3):
sample = dict(zip(('a', 'b', 'c'), config))
target_sample = {
u: sample[v]
for v, chain in embedding.items() for u in chain
} # no chains broken
self.assertAlmostEqual(bqm.energy(sample),
embedded_bqm.energy(target_sample))
def sample(self, bqm, chain_strength=1.0, **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. Note that the energy penalty of chain breaks is 2 * `chain_strength`.
**parameters:
Parameters for the sampling method, specified by the child sampler.
Returns:
:class:`dimod.Response`
Examples:
This example uses :class:`.EmbeddingComposite` to instantiate a composed sampler
that submits an unstructured Ising problem to a D-Wave solver, selected by the user's
default D-Wave Cloud Client configuration_ file, while minor-embedding the problem's
variables to physical qubits on the solver.
>>> from dwave.system.samplers import DWaveSampler
>>> from dwave.system.composites import EmbeddingComposite
>>> import dimod
>>> sampler = EmbeddingComposite(DWaveSampler())
>>> h = {1: 1, 2: 2, 3: 3, 4: 4}
>>> J = {(1, 2): 12, (1, 3): 13, (1, 4): 14,
... (2, 3): 23, (2, 4): 24,
... (3, 4): 34}
>>> bqm = dimod.BinaryQuadraticModel.from_ising(h, J)
>>> response = sampler.sample(bqm)
>>> for sample in response.samples(): # doctest: +SKIP
... print(sample)
...
{1: -1, 2: 1, 3: 1, 4: -1}
"""
# 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 = child.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
embedding = minorminer.find_embedding(source_edgelist, target_edgelist)
if bqm and not embedding:
raise ValueError("no embedding found")
bqm_embedded = dimod.embed_bqm(bqm,
embedding,
target_adjacency,
chain_strength=chain_strength)
response = child.sample(bqm_embedded, **parameters)
return dimod.unembed_response(response, embedding, source_bqm=bqm)
def factor(P, use_saved_embedding=True):
####################################################################################################
# get circuit
####################################################################################################
construction_start_time = time.time()
validate_input(P, range(2 ** 6))
# get constraint satisfaction problem
csp = dbc.factories.multiplication_circuit(3)
# get binary quadratic model
bqm = dbc.stitch(csp, min_classical_gap=.1)
# we know that multiplication_circuit() has created these variables
p_vars = ['p0', 'p1', 'p2', 'p3', 'p4', 'p5']
# convert P from decimal to binary
fixed_variables = dict(zip(reversed(p_vars), "{:06b}".format(P)))
fixed_variables = {var: int(x) for(var, x) in fixed_variables.items()}
# fix product qubits
for var, value in fixed_variables.items():
bqm.fix_variable(var, value)
log.debug('bqm construction time: %s', time.time() - construction_start_time)
####################################################################################################
# run problem
####################################################################################################
sample_time = time.time()
# get QPU sampler
sampler = DWaveSampler()
_, target_edgelist, target_adjacency = sampler.structure
if use_saved_embedding:
# load a pre-calculated embedding
from factoring.embedding import embeddings
embedding = embeddings[sampler.solver.id]
else:
# get the embedding
embedding = minorminer.find_embedding(bqm.quadratic, target_edgelist)
if bqm and not embedding:
raise ValueError("no embedding found")
# apply the embedding to the given problem to map it to the sampler
bqm_embedded = dimod.embed_bqm(bqm, embedding, target_adjacency, 3.0)
# draw samples from the QPU
kwargs = {}
if 'num_reads' in sampler.parameters:
kwargs['num_reads'] = 50
if 'answer_mode' in sampler.parameters:
kwargs['answer_mode'] = 'histogram'
response = sampler.sample(bqm_embedded, **kwargs)
# convert back to the original problem space
response = dimod.unembed_response(response, embedding, source_bqm=bqm)
sampler.client.close()
log.debug('embedding and sampling time: %s', time.time() - sample_time)
####################################################################################################
# output results
####################################################################################################
output = {
"results": [],
# {
# "a": Number,
# "b": Number,
# "valid": Boolean,
# "numOfOccurrences": Number,
# "percentageOfOccurrences": Number
# }
"timing": {
"actual": {
"qpuProcessTime": None # microseconds
}
},
"numberOfReads": None
}
# we know that multiplication_circuit() has created these variables
a_vars = ['a0', 'a1', 'a2']
b_vars = ['b0', 'b1', 'b2']
# histogram answer_mode should return counts for unique solutions
if 'num_occurrences' not in response.data_vectors:
response.data_vectors['num_occurrences'] = [1] * len(response)
# should equal num_reads
total = sum(response.data_vectors['num_occurrences'])
results_dict = OrderedDict()
for sample, num_occurrences in response.data(['sample', 'num_occurrences']):
# convert A and B from binary to decimal
a = b = 0
for lbl in reversed(a_vars):
a = (a << 1) | sample[lbl]
for lbl in reversed(b_vars):
b = (b << 1) | sample[lbl]
# aggregate results by unique A and B values (ignoring internal circuit variables)
if (a, b, P) in results_dict:
results_dict[(a, b, P)]["numOfOccurrences"] += num_occurrences
results_dict[(a, b, P)]["percentageOfOccurrences"] = 100 * \
results_dict[(a, b, P)]["numOfOccurrences"] / total
else:
results_dict[(a, b, P)] = {"a": a,
"b": b,
"valid": a * b == P,
"numOfOccurrences": num_occurrences,
"percentageOfOccurrences": 100 * num_occurrences / total}
output['results'] = list(results_dict.values())
output['numberOfReads'] = total
if 'timing' in response.info:
output['timing']['actual']['qpuProcessTime'] = response.info['timing']['qpu_access_time']
return output
def sample(self, bqm, **kwargs):
"""Sample from the provided binary quadratic model
Args:
bqm (:obj:`dimod.BinaryQuadraticModel`):
Binary quadratic model to be sampled from.
**kwargs:
Optional keyword arguments for the sampling method, specified per solver.
Returns:
:class:`dimod.Response`
Examples:
This example uses :class:`.TilingComposite` to instantiate a composed sampler
that submits a simple Ising problem of just two variables that map to qubits 0 and 1
on the D-Wave solver selected by the user's default D-Wave Cloud Client
configuration_ file. (The simplicity of this example obviates the need for an embedding
composite.) Because the problem fits in a single Chimera_ unit cell, it is tiled
across the solver's entire Chimera graph, resulting in multiple samples.
>>> from dwave.system.samplers import DWaveSampler
>>> from dwave.system.composites import EmbeddingComposite
>>> samplertile = TilingComposite(DWaveSampler(), 1, 1, 4)
>>> response = sampler_tile.sample_ising({0: -1, 1: 1}, {})
>>> for sample in response.samples(): # doctest: +SKIP
... print(sample)
...
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
>>> # Snipped above response for brevity
.. _configuration: http://dwave-cloud-client.readthedocs.io/en/latest/#module-dwave.cloud.config
.. _Chimera: http://dwave-system.readthedocs.io/en/latest/reference/intro.html#chimera
"""
# apply the embeddings to the given problem to tile it across the child sampler
embedded_bqm = dimod.BinaryQuadraticModel.empty(bqm.vartype)
__, __, target_adjacency = self.child.structure
for embedding in self.embeddings:
embedded_bqm.update(dimod.embed_bqm(bqm, embedding, target_adjacency))
# solve the problem on the child system
response = self.child.sample(embedded_bqm, **kwargs)
data_vectors = response.data_vectors.copy()
source_response = None
for embedding in self.embeddings:
# filter for problem variables
embedding = {v: chain for v, chain in embedding.items() if v in bqm.linear}
tile_response = dimod.unembed_response(response, embedding, source_bqm=bqm)
if source_response is None:
source_response = tile_response
source_response.info.update(response.info) # overwrite the info
else:
source_response.update(tile_response)
return source_response
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.Response`: A `dimod` :obj:`~dimod.Response` 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:reference/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 = dimod.embed_bqm(bqm,
embedding,
target_adjacency,
chain_strength=chain_strength)
if 'initial_state' in parameters:
parameters['initial_state'] = _embed_state(
embedding, parameters['initial_state'])
response = child.sample(bqm_embedded, **parameters)
return dimod.unembed_response(
response,
embedding,
source_bqm=bqm,
chain_break_fraction=chain_break_fraction)
def sample(self,
bqm,
chain_strength=1.0,
chain_break_fraction=True,
**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. Note that the energy penalty of chain breaks is 2 * `chain_strength`.
chain_break_fraction (bool, optional, default=True):
If True, a ‘chain_break_fraction’ field is added to the unembedded response which report
what fraction of the chains were broken before unembedding.
**parameters:
Parameters for the sampling method, specified by the child sampler.
Returns:
:class:`dimod.Response`
Examples:
This example uses :class:`.EmbeddingComposite` to instantiate a composed sampler
that submits an unstructured Ising problem to a D-Wave solver, selected by the user's
default
:std:doc:`D-Wave Cloud Client configuration file <cloud-client:reference/intro>`,
while minor-embedding the problem's variables to physical qubits on the solver.
>>> from dwave.system.samplers import DWaveSampler
>>> from dwave.system.composites import EmbeddingComposite
>>> import dimod
>>> sampler = EmbeddingComposite(DWaveSampler())
>>> h = {1: 1, 2: 2, 3: 3, 4: 4}
>>> J = {(1, 2): 12, (1, 3): 13, (1, 4): 14,
... (2, 3): 23, (2, 4): 24,
... (3, 4): 34}
>>> bqm = dimod.BinaryQuadraticModel.from_ising(h, J)
>>> response = sampler.sample(bqm)
>>> for sample in response.samples(): # doctest: +SKIP
... print(sample)
...
{1: -1, 2: 1, 3: 1, 4: -1}
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_edgelist, target_adjacency = child.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
embedding = minorminer.find_embedding(source_edgelist, target_edgelist)
if bqm and not embedding:
raise ValueError("no embedding found")
bqm_embedded = dimod.embed_bqm(bqm,
embedding,
target_adjacency,
chain_strength=chain_strength)
if 'initial_state' in parameters:
parameters['initial_state'] = _embed_state(
embedding, parameters['initial_state'])
response = child.sample(bqm_embedded, **parameters)
return dimod.unembed_response(
response,
embedding,
source_bqm=bqm,
chain_break_fraction=chain_break_fraction)
def sample(self, bqm, **kwargs):
"""Sample from the provided binary quadratic model
Args:
bqm (:obj:`dimod.BinaryQuadraticModel`):
Binary quadratic model to be sampled from.
**kwargs:
Optional keyword arguments for the sampling method, specified per solver.
Returns:
:class:`dimod.Response`
Examples:
This example uses :class:`.TilingComposite` to instantiate a composed sampler
that submits a simple Ising problem of just two variables that map to qubits 0 and 1
on the D-Wave solver selected by the user's default
:std:doc:`D-Wave Cloud Client configuration file <cloud-client:reference/intro>`.
(The simplicity of this example obviates the need for an embedding
composite.) Because the problem fits in a single
:std:doc:`Chimera <system:reference/intro>` unit cell, it is tiled
across the solver's entire Chimera graph, resulting in multiple samples.
>>> from dwave.system.samplers import DWaveSampler
>>> from dwave.system.composites import EmbeddingComposite, TilingComposite
>>> sampler = TilingComposite(DWaveSampler(), 1, 1, 4)
>>> response = sampler.sample_ising({0: -1, 1: 1}, {})
>>> for sample in response.samples(): # doctest: +SKIP
... print(sample)
...
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
{0: 1, 1: -1}
>>> # Snipped above response for brevity
See `Ocean Glossary <https://docs.ocean.dwavesys.com/en/latest/glossary.html>`_
for explanations of technical terms in descriptions of Ocean tools.
"""
# apply the embeddings to the given problem to tile it across the child sampler
embedded_bqm = dimod.BinaryQuadraticModel.empty(bqm.vartype)
__, __, target_adjacency = self.child.structure
for embedding in self.embeddings:
embedded_bqm.update(
dimod.embed_bqm(bqm, embedding, target_adjacency))
# solve the problem on the child system
tiled_response = self.child.sample(embedded_bqm, **kwargs)
responses = []
for embedding in self.embeddings:
embedding = {
v: chain
for v, chain in embedding.items() if v in bqm.linear
}
responses.append(
dimod.unembed_response(tiled_response, embedding, bqm))
# stack the records
record = np.rec.array(np.hstack((resp.record for resp in responses)))
vartypes = set(resp.vartype for resp in responses)
if len(vartypes) > 1:
raise RuntimeError("inconsistent vartypes returned")
vartype = vartypes.pop()
info = {}
for resp in responses:
info.update(resp.info)
labels = responses[0].variable_labels
return dimod.Response(record, labels, info, vartype)
def sample(self, bqm, **kwargs):
"""Sample from the specified binary quadratic model.
Args:
bqm (:obj:`dimod.BinaryQuadraticModel`):
Binary quadratic model to be sampled from.
**kwargs:
Optional keyword arguments for the sampling method, specified per solver.
Returns:
:class:`dimod.Response`: A `dimod` :obj:`~dimod.Response` object.
Examples:
This example submits a simple Ising problem of just two variables on a
D-Wave system selected by the user's default
:std:doc:`D-Wave Cloud Client configuration file <cloud-client:reference/intro>`.
Because the problem fits in a single :term:`Chimera` unit cell, it is tiled
across the solver's entire Chimera graph, resulting in multiple samples
(the exact number depends on the working Chimera graph of the D-Wave system).
>>> from dwave.system.samplers import DWaveSampler
>>> from dwave.system.composites import EmbeddingComposite
>>> from dwave.system.composites import EmbeddingComposite, TilingComposite
...
>>> sampler = EmbeddingComposite(TilingComposite(DWaveSampler(), 1, 1, 4))
>>> response = sampler.sample_ising({},{('a', 'b'): 1})
>>> len(response) # doctest: +SKIP
246
See `Ocean Glossary <https://docs.ocean.dwavesys.com/en/latest/glossary.html>`_
for explanations of technical terms in descriptions of Ocean tools.
"""
# apply the embeddings to the given problem to tile it across the child sampler
embedded_bqm = dimod.BinaryQuadraticModel.empty(bqm.vartype)
__, __, target_adjacency = self.child.structure
for embedding in self.embeddings:
embedded_bqm.update(
dimod.embed_bqm(bqm, embedding, target_adjacency))
# solve the problem on the child system
tiled_response = self.child.sample(embedded_bqm, **kwargs)
responses = []
for embedding in self.embeddings:
embedding = {
v: chain
for v, chain in embedding.items() if v in bqm.linear
}
responses.append(
dimod.unembed_response(tiled_response, embedding, bqm))
# stack the records
record = np.rec.array(np.hstack((resp.record for resp in responses)))
vartypes = set(resp.vartype for resp in responses)
if len(vartypes) > 1:
raise RuntimeError("inconsistent vartypes returned")
vartype = vartypes.pop()
info = {}
for resp in responses:
info.update(resp.info)
labels = responses[0].variable_labels
return dimod.Response(record, labels, info, vartype)
def sample(self, bqm, apply_flux_bias_offsets=True, **kwargs):
"""Sample from the given Ising model.
Args:
h (list/dict):
Linear biases of the Ising model. If a list, the list's indices
are used as variable labels.
J (dict of (int, int):float):
Quadratic biases of the Ising model.
apply_flux_bias_offsets (bool, optional):
If True, use the calculated flux_bias offsets (if available).
**kwargs:
Optional keyword arguments for the sampling method, specified per solver.
Examples:
This example uses :class:`.VirtualGraphComposite` to instantiate a composed sampler
that submits an Ising problem to a D-Wave solver selected by the user's
default D-Wave Cloud Client configuration_ file. The problem represents a logical
NOT gate using penalty function :math:`P = xy`, where variable x is the gate's input
and y the output. This simple two-variable problem is manually
minor-embedded to a single Chimera_ unit cell: each variable is represented by a
chain of half the cell's qubits, x as qubits 0, 1, 4, 5, and y as qubits 2, 3, 6, 7.
The chain strength is set to half the maximum allowed found from querying the solver's extended
J range. In this example, the ten returned samples all represent valid states of
the NOT gate.
>>> from dwave.system.samplers import DWaveSampler
>>> from dwave.system.composites import VirtualGraphComposite
>>> embedding = {'x': {0, 4, 1, 5}, 'y': {2, 6, 3, 7}}
>>> DWaveSampler().properties['extended_j_range'] # doctest: +SKIP
[-2.0, 1.0]
>>> sampler = VirtualGraphComposite(DWaveSampler(), embedding, chain_strength=1) # doctest: +SKIP
>>> h = {}
>>> J = {('x', 'y'): 1}
>>> response = sampler.sample_ising(h, J, num_reads=10) # doctest: +SKIP
>>> for sample in response.samples(): # doctest: +SKIP
... print(sample)
...
{'y': -1, 'x': 1}
{'y': 1, 'x': -1}
{'y': -1, 'x': 1}
{'y': -1, 'x': 1}
{'y': -1, 'x': 1}
{'y': 1, 'x': -1}
{'y': 1, 'x': -1}
{'y': 1, 'x': -1}
{'y': -1, 'x': 1}
{'y': 1, 'x': -1}
.. _configuration: http://dwave-cloud-client.readthedocs.io/en/latest/#module-dwave.cloud.config
.. _Chimera: http://dwave-system.readthedocs.io/en/latest/reference/intro.html#chimera
"""
# apply the embedding to the given problem to map it to the child sampler
__, __, target_adjacency = self.child.structure
embedding = self.embedding
embedded_bqm = dimod.embed_bqm(bqm, self.embedding, target_adjacency, self.chain_strength)
# solve the problem on the child system
child = self.child
if apply_flux_bias_offsets and self.flux_biases is not None:
# If self.flux_biases is in the old format (list of lists) convert it to the new format (flat list).
if isinstance(self.flux_biases[0], list):
flux_bias_dict = dict(self.flux_biases)
kwargs[FLUX_BIAS_KWARG] = [flux_bias_dict.get(v, 0.) for v in range(child.properties['num_qubits'])]
else:
kwargs[FLUX_BIAS_KWARG] = self.flux_biases
assert len(kwargs[FLUX_BIAS_KWARG]) == child.properties['num_qubits'], \
"{} must have length {}, the solver's num_qubits."\
.format(FLUX_BIAS_KWARG, child.properties['num_qubits'])
# Embed arguments providing initial states for reverse annealing, if applicable.
kwargs = _embed_initial_state_kwargs(kwargs, self.embedding, self.child.structure[0])
response = child.sample(embedded_bqm, **kwargs)
return dimod.unembed_response(response, embedding, source_bqm=bqm)
_, target_edgelist, target_adjacency = sampler.structure
# Mapping between the graph of our problem—the multiplication circuit's graph with nodes labeled "a0", "b0" etc.—to the D-Wave QPU's numerically indexed qubits, is known as *minor-embedding*. A problem can be minor embedded onto the QPU in a variety of ways and this affects solution quality and performance. Ocean software provides tools suited for different types of problems; for example, [dwave-system](https://docs.ocean.dwavesys.com/projects/system/en/latest/) *EmbeddingComposite()* has a heuristic for automatic embedding.
# This example uses a pre-calculated minor-embedding (see [below](#Further-Information) for details).
# In[ ]:
import dimod
from helpers.embedding import embeddings
# Set a pre-calculated minor-embeding
embedding = embeddings[sampler.solver.id]
bqm_embedded = dimod.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) # False
print("First five nodes in QPU graph: ", sampler.structure.nodelist[:5]) # [0, 1, 2, 3, 4]
# When the 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. Because the sampled solution is probabilistic, returned solutions may differ between runs. Typically, when submitting a problem to the system, we ask for many samples, not just one. This way, we see multiple “best” answers and reduce the probability of settling on a suboptimal answer.
# In the code below, *num_reads* should provide enough samples to make it likely a valid answer is among them.
# In[ ]:
# Return num_reads solutions (responses are in the D-Wave's graph of indexed qubits)
kwargs = {}
def test_embed_bqm_only_offset(self):
bqm = dimod.BinaryQuadraticModel({}, {}, 1.0, dimod.SPIN)
embedded_bqm = dimod.embed_bqm(bqm, {}, {})
self.assertEqual(bqm, embedded_bqm)