05 - ADMM Optimizer

# This code is from the tutorial at:
# https://qiskit-community.github.io/qiskit-optimization/tutorials/05_admm_optimizer.html

Initialization

import matplotlib.pyplot as plt

from docplex.mp.model import Model

from qiskit_algorithms import QAOA, NumPyMinimumEigensolver
from qiskit_algorithms.optimizers import COBYLA

# Switch to Quantum Rings's Sampler
#from qiskit.primitives import Sampler
from quantumrings.toolkit.qiskit import QrSamplerV1 as Sampler

from qiskit_optimization.algorithms import CobylaOptimizer, MinimumEigenOptimizer
from qiskit_optimization.algorithms.admm_optimizer import ADMMParameters, ADMMOptimizer
from qiskit_optimization.translators import from_docplex_mp

# If CPLEX is installed, you can uncomment this line to import the CplexOptimizer.
# CPLEX can be used in this tutorial to solve the convex continuous problem,
# but also as a reference to solve the QUBO, or even the full problem.
#
# from qiskit.optimization.algorithms import CplexOptimizer

# define COBYLA optimizer to handle convex continuous problems.
cobyla = CobylaOptimizer()

# define QAOA via the minimum eigen optimizer
qaoa = MinimumEigenOptimizer(QAOA(sampler=Sampler(), optimizer=COBYLA()))

# exact QUBO solver as classical benchmark
exact = MinimumEigenOptimizer(NumPyMinimumEigensolver())  # to solve QUBOs

# in case CPLEX is installed it can also be used for the convex problems, the QUBO,
# or as a benchmark for the full problem.
#
# cplex = CplexOptimizer()

Example

# construct model using docplex
mdl = Model("ex6")

v = mdl.binary_var(name="v")
w = mdl.binary_var(name="w")
t = mdl.binary_var(name="t")
u = mdl.continuous_var(name="u")

mdl.minimize(v + w + t + 5 * (u - 2) ** 2)
mdl.add_constraint(v + 2 * w + t + u <= 3, "cons1")
mdl.add_constraint(v + w + t >= 1, "cons2")
mdl.add_constraint(v + w == 1, "cons3")

# load quadratic program from docplex model
qp = from_docplex_mp(mdl)
print(qp.prettyprint())

Problem name: ex6

Minimize
  5*u^2 + t - 20*u + v + w + 20

Subject to
  Linear constraints (3)
    t + u + v + 2*w <= 3  'cons1'
    t + v + w >= 1  'cons2'
    v + w == 1  'cons3'

  Continuous variables (1)
    0 <= u

  Binary variables (3)
    v w t

Classical Solution

admm_params = ADMMParameters(
    rho_initial=1001, beta=1000, factor_c=900, maxiter=100, three_block=True, tol=1.0e-6
)

Calling 3-ADMM-H algorithm

# define QUBO optimizer
qubo_optimizer = exact
# qubo_optimizer = cplex  # uncomment to use CPLEX instead

# define classical optimizer
convex_optimizer = cobyla
# convex_optimizer = cplex  # uncomment to use CPLEX instead

# initialize ADMM with classical QUBO and convex optimizer
admm = ADMMOptimizer(
    params=admm_params, qubo_optimizer=qubo_optimizer, continuous_optimizer=convex_optimizer
)

# run ADMM to solve problem
result = admm.solve(qp)

Classical Solver Result

print(result.prettyprint())

objective function value: 1.0
variable values: v=1.0, w=0.0, t=0.0, u=2.0
status: SUCCESS

plt.plot(result.state.residuals)
plt.xlabel("Iterations")
plt.ylabel("Residuals")
plt.show()

Quantum Solution

# define QUBO optimizer
qubo_optimizer = qaoa

# define classical optimizer
convex_optimizer = cobyla
# convex_optimizer = cplex  # uncomment to use CPLEX instead

# initialize ADMM with quantum QUBO optimizer and classical convex optimizer
admm_q = ADMMOptimizer(
    params=admm_params, qubo_optimizer=qubo_optimizer, continuous_optimizer=convex_optimizer
)

# run ADMM to solve problem
result_q = admm_q.solve(qp)

Quantum Solver Results

print(result.prettyprint())

objective function value: 1.0
variable values: v=1.0, w=0.0, t=0.0, u=2.0
status: SUCCESS

plt.clf()
plt.plot(result_q.state.residuals)
plt.xlabel("Iterations")
plt.ylabel("Residuals")
plt.show()