def sample_BQM(BQM):
'''
:param BQM: BQM model
:return: simplified model
'''
sampler = ExactSolver()
return sampler.sample(BQM)
def scheduling(time, location, length, mandatory):
if time: # Business hours
return (location and mandatory) # In office and mandatory participation
else: # Outside business hours
return ((not location) and length) # Teleconference for a short duration
import dwavebinarycsp
csp = dwavebinarycsp.ConstraintSatisfactionProblem(dwavebinarycsp.BINARY)
csp.add_constraint(scheduling, ['time', 'location', 'length', 'mandatory'])
bqm = dwavebinarycsp.stitch(csp)
bqm.linear
{'length': -2.0, 'location': 2.0, 'mandatory': 0.0, 'time': 2.0}
bqm.quadratic
{('location', 'length'): 2.0,
('mandatory', 'length'): 0.0,
('mandatory', 'location'): -2.0,
('time', 'length'): 0.0,
('time', 'location'): -4.0,
('time', 'mandatory'): 0.0}
from dimod.reference.samplers import ExactSolver
sampler = ExactSolver()
solution = sampler.sample(bqm)
min_energy = next(solution.data(['energy']))[0]
print(min_energy)
-2.0
for sample, energy in solution.data(['sample', 'energy']):
if energy == min_energy:
time = 'business hours' if sample['time'] else 'evenings'
location = 'office' if sample['location'] else 'home'
length = 'short' if sample['length'] else 'long'
mandatory = 'mandatory' if sample['mandatory'] else 'optional'
print("During {} at {}, you can schedule a {} meeting that is {}".format(time, location, length, mandatory))
if energy == min_energy:
time = 'business hours' if sample['time'] else 'evenings'
location = 'office' if sample['location'] else 'home'
length = 'short' if sample['length'] else 'long'
mandatory = 'mandatory' if sample['mandatory'] else 'optional'
print("During {} at {}, you can schedule a {} meeting that is {}".format(time, location, length, mandatory))
# Add constraint that each pair of nodes with a shared edge not both select one color
for neighbor in neighbors:
v, u = neighbor
for i in range(colors):
variables = [v + str(i), u + str(i)]
csp.add_constraint(not_both_1, variables)
# %%
bqm = dwavebinarycsp.stitch(csp)
print('bqm', bqm.linear)
# %%
sampler = ExactSolver()
# below would cause memory overflow. (over 20GB of mem.)
response = sampler.sample(bqm)
print(response)
# %%
# Function that plots a returned sample
def plot_map(sample):
G = nx.Graph()
G.add_nodes_from(provinces)
G.add_edges_from(neighbors)
# Translate from binary to integer color representation
color_map = {}
for province in provinces:
for i in range(colors):
if sample[province + str(i)]:
color_map[province] = i
'''
import dwavebinarycsp
import dwavebinarycsp.factories.constraint.gates as gates
csp = dwavebinarycsp.ConstraintSatisfactionProblem(dwavebinarycsp.BINARY)
csp.add_constraint(gates.and_gate(['x1', 'x2', 'y1'])) # add an AND gate
bqm = dwavebinarycsp.stitch(csp)
''' The members of the two dicts are linear and quadratic coefficients, respectively, the third term is a constant offset associated with the model, and the fourth shows the variable types in this model are binary. '''
print(bqm) # BQM of the AND gate created
print('################################################################################')
from dimod.reference.samplers import ExactSolver
sampler = ExactSolver()
response = sampler.sample(bqm)
print(response)
for datum in response.data():
print(datum)
for sample, energy in response.data(fields=['sample', 'energy'], sorted_by='energy'):
print(sample, energy)
print('################################################################################')
from dwave.system.samplers import DWaveSampler
from dwave.system.composites import EmbeddingComposite
sampler = EmbeddingComposite(DWaveSampler()) # EmbeddingComposite() composite that maps unstructured problems to the graph structure of the selected sampler, a process known as minor-embedding.
response = sampler.sample(bqm, num_reads=1000) # Because of the sampler's probabilistic nature, you typically request multiple samples for a problem; this example sets num_reads to 1000.
J = {(1,1):1,(1,2):-2,(1,3): 6,(1,4):3,(2,1):-2,(2,2):4,(2,3):-12,(2,4):-6,(3,1): 6,(3,2):-12,(3,3):36,(3,4):18,(4,1):3,(4,2):-6,(4,3):18,(4,4):9}
h = {}
model = dimod.BinaryQuadraticModel(h, J, 0.0, dimod.SPIN)
print("El modelo que vamos a resolver es")
print(model)
print()
# Podemos resolver el modelo de forma exacta
from dimod.reference.samplers import ExactSolver
sampler = ExactSolver()
solution = sampler.sample(model)
print("La solucion exacta es")
print(solution)
print()
# O con *simulated annealing* (un método heurístico de optimización para ordenadores clásicos)
sampler = dimod.SimulatedAnnealingSampler()
response = sampler.sample(model, num_reads=10)
print("La solucion con simulated annealing es")
print(response)
print()
csp.add_constraint(scheduling, ['time', 'location', 'length', 'mandatory'])
bqm = dwavebinarycsp.stitch(csp)
bqm.linear
{'length': -2.0, 'location': 2.0, 'mandatory': 0.0, 'time': 2.0}
bqm.quadratic
{
('location', 'length'): 2.0,
('mandatory', 'length'): 0.0,
('mandatory', 'location'): -2.0,
('time', 'length'): 0.0,
('time', 'location'): -4.0,
('time', 'mandatory'): 0.0
}
### Classical CPU
from dimod.reference.samplers import ExactSolver
sampler = ExactSolver()
solution = sampler.sample(bqm)
min_energy = next(solution.data(['energy']))[0]
print(min_energy)
for sample, energy in solution.data(['sample', 'energy']):
if energy == min_energy:
time = 'business hours' if sample['time'] else 'evenings'
location = 'office' if sample['location'] else 'home'
length = 'short' if sample['length'] else 'long'
mandatory = 'mandatory' if sample['mandatory'] else 'optional'
print(
"During {} at {}, you can schedule a {} meeting that is {}".format(
time, location, length, mandatory))
# Create a constraint from this function and adds it to CSP instance, csp,
# instantiated with binary variables.
import dwavebinarycsp
csp = dwavebinarycsp.ConstraintSatisfactionProblem(dwavebinarycsp.BINARY)
csp.add_constraint(scheduling, ['time', 'location', 'length', 'mandatory'])
# Display the BQM’s linear and quadratic coefficients, qi and qi,j respectively in
# ∑Niqixi+∑Ni<jqi,jxixj, which are the inputs for programming the quantum computer.
bqm = dwavebinarycsp.stitch(csp)
bqm.linear
bqm.quadratic
# Solving classically on a CPU
from dimod.reference.samplers import ExactSolver
sampler = ExactSolver()
solution = sampler.sample(bqm)
# Sets variable min_energy to the BQM’s lowest value, which is in the first record of
# the returned result
min_energy = next(solution.data(['energy']))[0]
print(min_energy)
# Print all solutions (assignments of variables) for which the BQM has its minimum value.
for sample, energy in solution.data(['sample', 'energy']):
if energy == min_energy:
time = 'business hours' if sample['time'] else 'evenings'
location = 'office' if sample['location'] else 'home'
length = 'short' if sample['length'] else 'long'
mandatory = 'mandatory' if sample['mandatory'] else 'optional'
print(
"During {} at {}, you can schedule a {} meeting that is {}".format(
['time', 'location', 'length', 'mandatory'
]) # create a constraint from this function and adds it to CSP instance
bqm = dwavebinarycsp.stitch(csp) # convert the binary CSP to a BQM
print('bqm.linear', bqm.linear)
print('bqm.quadratic', bqm.quadratic)
print(
'################################################################################'
)
# Solving Classically on a CPU
from dimod.reference.samplers import ExactSolver
sampler = ExactSolver()
solution = sampler.sample(
bqm
) # returns the BQM's value (energy) for every possible assignment of variable values.
min_energy = next(solution.data(['energy']))[0]
print(
min_energy
) # assignments of variables that do not violate any constraint-should have the lowest value of the BQM
for sample, energy in solution.data(['sample', 'energy']):
if energy == min_energy: # prints all those solutions (assignments of variables) for which the BQM has its minimum value.
time = 'business hours' if sample['time'] else 'evenings'
location = 'office' if sample['location'] else 'home'
length = 'short' if sample['length'] else 'long'
mandatory = 'mandatory' if sample['mandatory'] else 'optional'
print(
"During {} at {}, you can schedule a {} meeting that is {}".format(
# Taken from documentation "Solving Problems on a D-Wave System" # @ https://dwave-meta-doc.readthedocs.io/en/latest/overview/solving_problems.html import dwavebinarycsp import dwavebinarycsp.factories.constraint.gates as gates from dimod.reference.samplers import ExactSolver from dwave.system.samplers import DWaveSampler from dwave.system.composites import EmbeddingComposite csp = dwavebinarycsp.ConstraintSatisfactionProblem(dwavebinarycsp.BINARY) csp.add_constraint(gates.and_gate(['x1', 'x2', 'y1'])) # add an AND gate bqm = dwavebinarycsp.stitch(csp) # ExactSovler() does not use QPU but runs locally # it's good to test code locally sampler = ExactSolver() response = sampler.sample(bqm) for datum in response.data(['sample', 'energy']): print(datum.sample, datum.energy) # Now execute same code on a D-Wave QPU sampler = EmbeddingComposite(DWaveSampler()) response = sampler.sample(bqm, num_reads=1000) for datum in response.data(['sample', 'energy', 'num_occurrences']): print(datum.sample, datum.energy, "Occurrences: ", datum.num_occurrences)
def Trace(g, v1, v2):
# cs0 =dwavebinarycsp.Constraint.from_func(neigbor2,L(0)+L(1), dwavebinarycsp.BINARY,name='cs0')
cs0 = dwavebinarycsp.Constraint.from_func(neigbor,
L(0) + L(1) + ['res0'],
dwavebinarycsp.BINARY,
name='cs0')
csp.add_constraint(cs0)
#cs2 = dwavebinarycsp.Constraint.from_func(neigbor, L(1) + L(3) + ['res2'], dwavebinarycsp.BINARY, name='cs2')
#cs2 = dwavebinarycsp.Constraint.from_func(neigbor2, L(1) + L(3), dwavebinarycsp.BINARY, name='cs2')
#csp.add_constraint(cs2)
cs1 = dwavebinarycsp.Constraint.from_func(neigbor,
L(1) + L(2) + ['res3'],
dwavebinarycsp.BINARY,
name='cs1')
csp.add_constraint(cs1)
r1, c1 = v1
r2, c2 = v2
# Устанавливаем начальную и конечную вершины
"""
setIntVar2(cs0, (0, 0), 2, 0) # ряд вершины 1
setIntVar2(cs0, (0, 1), 2, 0) # колонка вершины 1
setIntVar2(cs1, (2, 0), 2, 0) # ряд вершины 2
setIntVar2(cs1, (2, 1), 2, 2) # колонка вершины 2
"""
#bqm = dwavebinarycsp.stitch(csp,min_classical_gap=2.0, max_graph_size=9)
setIntVar2(cs0, (0, 0), 2, r1) # ряд вершины 1
setIntVar2(cs0, (0, 1), 2, c1) # колонка вершины 1
setIntVar2(cs1, (2, 0), 2, r2) # ряд вершины 2
setIntVar2(cs1, (2, 1), 2, c2) # колонка вершины 2
bqm = dwavebinarycsp.stitch(csp, min_classical_gap=2.0, max_graph_size=8)
#print(" Do stitch()")
# print (bqm)
# Проверка на локальной машине
from dimod.reference.samplers import ExactSolver
sampler = ExactSolver()
solution = sampler.sample(bqm)
"""
#Проверка на реальной машине
from dwave.system.samplers import DWaveSampler
from dwave.system.composites import EmbeddingComposite
# Set up a D-Wave system as the sampler
sampler = EmbeddingComposite(DWaveSampler())
#sampler = EmbeddingComposite(DWaveSampler(endpoint='https://URL_to_my_D-Wave_system/', token='ABC-123456789012345678901234567890', solver='My_D-Wave_Solver'))
solution = sampler.sample(bqm, num_reads=100)
"""
print(solution)
min_energy = next(solution.data(['energy']))[0]
print(min_energy)
res_sample = next(solution.data(['sample']))[0]
print(res_sample)
r1 = [res_sample[(1, 0, 0)],
res_sample[(1, 0, 1)]] # Собираем биты ряда узла 1
res0 = res_sample['res0']
if (not res0):
return []
# r1.append(res_sample[(1,0,0)])
# r1.append(res_sample[(1,0,1)])
nr = BinToInt(r1) # номер ряда числом
k = [res_sample[(1, 1, 0)],
res_sample[(1, 1, 1)]] # Собираем биты колонки узла 1
nk = BinToInt(k) # номер колонки числом
return [v1, (nr, nk), v2]
length = len(nodes)
A = 7
B = 1
diagonal = createDig(nodes, length, -2 * A)
matrix = fillMatrixC1(nodes, length, 2 * A)
matrix.update(fillMatrixC2(nodes, length, 2 * A))
# no edge
matrix.update(fillMatrixC3('b', 'd', length, 2 * A))
# weigth the edges that exists
matrix.update(fillMatrixC3('a', 'b', length, 3 * B))
matrix.update(fillMatrixC3('b', 'c', length, 4 * B))
matrix.update(fillMatrixC3('c', 'd', length, 5 * B))
matrix.update(fillMatrixC3('a', 'c', length, 6 * B))
matrix.update(fillMatrixC3('a', 'd', length, 7 * B))
printMatrix(diagonal, matrix, nodes, length)
# qubo matrix
qubo = dimod.BinaryQuadraticModel(diagonal, matrix, 2 * length, 'BINARY')
print(qubo)
sampler = ExactSolver()
response = sampler.sample(qubo)
print("\nQUBO")
print(response.lowest())
Ex = preprocessing.normalize([E])
for i in range(6):
E[i] = Ex[0][i] / 10 * 3
A = [179.5, 408.5, 18.79, 119.26, 1777.02, 241.05]
Ax = preprocessing.normalize([A])
A = Ax[0]
B = 2
Number_of_data = 6
theta_1 = 0.33
theta_2 = 0.33
theta_3 = 0.33
gamma = theta_3 * B**2
for i in range(Number_of_data):
hi_dict['Z{}'.format(i + 1)] = 0.5 * (theta_2 * Cov_Ri_Rj[i][i] +
theta_3 * A[i]**2 - theta_1 * E[i] -
2 * B * theta_3 * A[i])
for j in range(i + 1, Number_of_data):
J_i_j['Z{}'.format(i + 1),
'Z{}'.format(j + 1)] = 0.25 * (theta_2 * Cov_Ri_Rj[i][j] +
theta_3 * A[i] * A[j])
BQM = dimod.BinaryQuadraticModel(hi_dict, J_i_j, gamma, 'BINARY')
sampler = ExactSolver()
sampled = sampler.sample(BQM)
print(sampled)
def factor(P, use_saved_embedding=False):
####################################################################################################
# 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(solver_features=dict(online=True, name='DW_2000Q.*'))
sampler = ExactSolver()
# _, 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, **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