Models and Variables

Variables

from qilisdk.common.variables import BinaryVariable, Bitwise, Domain, SpinVariable, Variable

x = Variable("x", domain=Domain.REAL, bounds=(1, 2), encoding=Bitwise, precision=1e-1)
s = SpinVariable("s")
b = BinaryVariable("b")

x.to_binary()

(0.1) * x(0) + (0.2) * x(1) + (0.4) * x(2) + (0.30000000000000004) * x(3) + (1.0)

x.evaluate([0, 1, 0, 0])

1.2

Building Terms from Variables

t1 = 2 * x + 3
print("t1: ", t1)
t2 = 3 * x**2 + 2 * x + 4
print("t2: ", t2)
t3 = 2 * x + b - 1
print("t3: ", t3)
t4 = t1 - t2
print("t4: ", t4)

t1:  (2) * x + (3)
t2:  (3) * (x^2) + (2) * x + (4)
t3:  (2) * x + b + (-1)
t4:  (-1.0) + (-3.0) * (x^2)

t3.evaluate({x: 1.5, b: 0})

2.0

from qilisdk.common.variables import LT

LT(2 * x - 1, 1)

(2) * x < (2.0)

Models

Building a simple model

from qilisdk.common.model import Model, ObjectiveSense

model = Model("example_model")

model.set_objective(2 * x + 3, label="obj", sense=ObjectiveSense.MINIMIZE)

print(model)

Model name: example_model
objective (obj):
         minimize :
         (2) * x + (3)

subject to the encoding constraint/s:
         x_upper_bound_constraint: x <= (2)
         x_lower_bound_constraint: x >= (1)

With Lagrange Multiplier/s:
         x_upper_bound_constraint : 100
         x_lower_bound_constraint : 100

model.set_lagrange_multiplier("x_upper_bound_constraint", 1)

print(model)

Model name: example_model
objective (obj):
         minimize :
         (2) * x + (3)

subject to the encoding constraint/s:
         x_upper_bound_constraint: x <= (2)
         x_lower_bound_constraint: x >= (1)

With Lagrange Multiplier/s:
         x_upper_bound_constraint : 1
         x_lower_bound_constraint : 100

model.add_constraint("test_constraint", LT(x, 1.5), lagrange_multiplier=10)
print(model)

Model name: example_model
objective (obj):
         minimize :
         (2) * x + (3)

subject to the constraint/s:
         test_constraint: x < (1.5)

subject to the encoding constraint/s:
         x_upper_bound_constraint: x <= (2)
         x_lower_bound_constraint: x >= (1)

With Lagrange Multiplier/s:
         x_upper_bound_constraint : 1
         x_lower_bound_constraint : 100
         test_constraint : 10

model.evaluate({x: 1.4})

{'obj': 5.8, 'test_constraint': 0.0}

model.evaluate({x: 2})

{'obj': 7.0, 'test_constraint': 10.0}

Building Knapsack model

import numpy as np

from qilisdk.common.variables import LEQ

n_items = 3

b = [BinaryVariable(f"b_{i}") for i in range(n_items)]
values = [np.random.randint(0, 10) for _ in range(n_items)]
weights = [np.random.randint(0, 10) for _ in range(n_items)]
max_weight = int(0.6 * sum(weights))

print("Knapsack Instance:")
print("-" * 10)
print()
print("Values = ", values)
print("Weights = ", weights)
print("Maximum allowed weight = ", max_weight)


knapsack = Model("knapsack")

knapsack.set_objective(sum(b[i] * values[i] for i in range(n_items)), sense=ObjectiveSense.MAXIMIZE)

knapsack.add_constraint("maximum_weight", LEQ(sum(b[i] * weights[i] for i in range(n_items)), max_weight))

print("-" * 10)
print("Knapsack Model: ")
print("-" * 10)
print(knapsack)

Knapsack Instance:
----------

Values =  [7, 6, 4]
Weights =  [1, 3, 2]
Maximum allowed weight =  3
----------
Knapsack Model:
----------
Model name: knapsack
objective (obj):
         maximize :
         (7) * b_0 + (6) * b_1 + (4) * b_2

subject to the constraint/s:
         maximum_weight: b_0 + (3) * b_1 + (2) * b_2 <= (3.0)

With Lagrange Multiplier/s:
         maximum_weight : 100

QUBO

from qilisdk.common.model import QUBO, ObjectiveSense

model = QUBO("example_qubo_model")
model.set_objective(2 * b[0] + 3, label="obj", sense=ObjectiveSense.MINIMIZE)

model.add_constraint(
    "qubo_constraint", LT(2 * b[0], 1), lagrange_multiplier=10, penalization="slack", transform_to_qubo=True
)

print(model)

Model name: example_qubo_model
objective (obj):
         minimize :
         (2) * b_0 + (3)

subject to the constraint/s:
         qubo_constraint: (4.0) * (b_0 * qubo_constraint_slack(0)) + (-1.0) * qubo_constraint_slack(0) == (-1.0)

With Lagrange Multiplier/s:
         qubo_constraint : 10

print(model.qubo_objective)

obj: (2) * b_0 + (13.0) + (40.0) * (b_0 * qubo_constraint_slack(0)) + (-10.0) * qubo_constraint_slack(0)

from qilisdk.common.model import QUBO, ObjectiveSense

model = QUBO("example_qubo_model")
model.set_objective(2 * b[0] + 3, label="obj", sense=ObjectiveSense.MINIMIZE)

model.add_constraint(
    "qubo_constraint",
    LT(2 * b[0], 1),
    lagrange_multiplier=1,
    penalization="unbalanced",
    parameters=[1, 2],
    transform_to_qubo=True,
)

print(model)

Model name: example_qubo_model
objective (obj):
         minimize :
         (2) * b_0 + (3)

subject to the constraint/s:
         qubo_constraint: (2.0) * b_0 == (-1.0)

With Lagrange Multiplier/s:
         qubo_constraint : 1

model.qubo_objective

obj: (4.0) * b_0 + (4.0)