def build_knapsack_cqm(costs, weights, max_weight):
"""Construct a CQM for the knapsack problem.
Args:
costs (array-like):
Array of costs for the items.
weights (array-like):
Array of weights for the items.
max_weight (int):
Maximum allowable weight for the knapsack.
Returns:
Constrained quadratic model instance that represents the knapsack problem.
"""
num_items = len(costs)
print("\nBuilding a CQM for {} items.".format(str(num_items)))
cqm = ConstrainedQuadraticModel()
obj = BinaryQuadraticModel(vartype='BINARY')
constraint = QuadraticModel()
for i in range(num_items):
# Objective is to maximize the total costs
obj.add_variable(i)
obj.set_linear(i, -costs[i])
# Constraint is to keep the sum of items' weights under or equal capacity
constraint.add_variable('BINARY', i)
constraint.set_linear(i, weights[i])
cqm.set_objective(obj)
cqm.add_constraint(constraint, sense="<=", rhs=max_weight, label='capacity')
return cqm
def anti_crossing_loops(num_variables):
"""Anti crossing problems with two loops. These instances are copies of the
instance studied in [DJA]_.
Args:
num_variables (int):
Number of variables used to generate the problem. Must be an even number
greater than 8.
Returns:
:obj:`.BinaryQuadraticModel`.
.. [DJA] Dickson, N., Johnson, M., Amin, M. et al. Thermally assisted
quantum annealing of a 16-qubit problem. Nat Commun 4, 1903 (2013).
https://doi.org/10.1038/ncomms2920
"""
bqm = BinaryQuadraticModel({}, {}, 0, 'SPIN')
if num_variables % 2 != 0 or num_variables < 8:
raise ValueError('num_variables must be an even number > 8')
hf = int(num_variables / 4)
for n in range(hf):
if n % 2 == 1:
bqm.set_quadratic(n, n + hf, -1)
bqm.set_quadratic(n, (n + 1) % hf, -1)
bqm.set_quadratic(n + hf, (n + 1) % hf + hf, -1)
bqm.set_quadratic(n, n + 2 * hf, -1)
bqm.set_quadratic(n + hf, n + 3 * hf, -1)
bqm.add_variable(n, 1)
bqm.add_variable(n + hf, 1)
bqm.add_variable(n + 2 * hf, -1)
bqm.add_variable(n + 3 * hf, -1)
bqm.set_linear(0, 0)
bqm.set_linear(hf, 0)
return bqm
def anti_crossing_clique(num_variables):
"""Anti crossing problems with a single clique.
Given the number of variables, the code will generate a clique of size
num_variables/2, each variable ferromagnetically interacting with a partner
variable with opposite bias. A single variable in the cluster will have
no bias applied.
Args:
num_variables (int):
Number of variables used to generate the problem. Must be an even number
greater than 6.
Returns:
:obj:`.BinaryQuadraticModel`.
"""
if num_variables % 2 != 0 or num_variables < 6:
raise ValueError('num_variables must be an even number > 6')
bqm = BinaryQuadraticModel({}, {}, 0, 'SPIN')
hf = int(num_variables / 2)
for n in range(hf):
for m in range(n + 1, hf):
bqm.add_interaction(n, m, -1)
bqm.add_interaction(n, n + hf, -1)
bqm.add_variable(n, 1)
bqm.add_variable(n + hf, -1)
bqm.set_linear(1, 0)
return bqm
