UMDA

class qiskit.algorithms.optimizers.UMDA(maxiter=100, size_gen=20, alpha=0.5, callback=None)

Bases: Optimizer

Continuous Univariate Marginal Distribution Algorithm (UMDA).

UMDA [1] is a specific type of Estimation of Distribution Algorithm (EDA) where new individuals are sampled from univariate normal distributions and are updated in each iteration of the algorithm by the best individuals found in the previous iteration.

EDAs are stochastic search algorithms and belong to the family of the evolutionary algorithms. The main difference is that EDAs have a probabilistic model which is updated in each iteration from the best individuals of previous generations (elite selection). Depending on the complexity of the probabilistic model, EDAs can be classified in different ways. In this case, UMDA is a univariate EDA as the embedded probabilistic model is univariate.

UMDA has been compared to some of the already implemented algorithms in Qiskit library to optimize the parameters of variational algorithms such as QAOA or VQE and competitive results have been obtained [1]. UMDA seems to provide very good solutions for those circuits in which the number of layers is not big.

The optimization process can be personalized depending on the parameters chosen in the initialization. The main parameter is the population size. The bigger it is, the final result will be better. However, this increases the complexity of the algorithm and the runtime will be much heavier. In the work [1] different experiments have been performed where population size has been set to 20 - 30.

Example

This short example runs UMDA to optimize the parameters of a variational algorithm. Here we will use the same operator as used in the algorithms introduction, which was originally computed by Qiskit Nature for an H2 molecule. The minimum energy of the H2 Hamiltonian can be found quite easily so we are able to set maxiters to a small value.

from qiskit.opflow import X, Z, I
from qiskit import Aer
from qiskit.algorithms.optimizers import UMDA
from qiskit.algorithms import QAOA
from qiskit.utils import QuantumInstance
 
 
H2_op = (-1.052373245772859 * I ^ I) +             (0.39793742484318045 * I ^ Z) +             (-0.39793742484318045 * Z ^ I) +             (-0.01128010425623538 * Z ^ Z) +             (0.18093119978423156 * X ^ X)
 
p = 2  # Toy example: 2 layers with 2 parameters in each layer: 4 variables
 
opt = UMDA(maxiter=100, size_gen=20)
 
backend = Aer.get_backend('statevector_simulator')
vqe = QAOA(opt,
           quantum_instance=QuantumInstance(backend=backend),
           reps=p)
 
result = vqe.compute_minimum_eigenvalue(operator=H2_op)

If it is desired to modify the percentage of individuals considered to update the probabilistic model, then this code can be used. Here for example we set the 60% instead of the 50% predefined.

opt = UMDA(maxiter=100, size_gen=20, alpha = 0.6)
 
backend = Aer.get_backend('statevector_simulator')
vqe = QAOA(opt,
           quantum_instance=QuantumInstance(backend=backend),
           reps=p)
 
result = vqe.compute_minimum_eigenvalue(operator=qubit_op)

References

[1]: Vicente P. Soloviev, Pedro Larrañaga and Concha Bielza (2022, July). Quantum Parametric Circuit Optimization with Estimation of Distribution Algorithms. In 2022 The Genetic and Evolutionary Computation Conference (GECCO). DOI: https://doi.org/10.1145/3520304.3533963

[2]: Vicente P. Soloviev. Python package EDAspy. https://github.com/VicentePerezSoloviev/EDAspy.

Parameters

• maxiter (int) – Maximum number of iterations.
• size_gen (int) – Population size of each generation.
• alpha (float) – Percentage (0, 1] of the population to be selected as elite selection.
• callback (Callable[[int, np.array, float], None] | None) – A callback function passed information in each iteration step. The information is, in this order: the number of function evaluations, the parameters, the best function value in this iteration.

Attributes

ELITE_FACTOR

STD_BOUND

alpha

bounds_support_level

gradient_support_level

initial_point_support_level

is_bounds_ignored

is_bounds_required

is_bounds_supported

is_gradient_ignored

is_gradient_required

is_gradient_supported

is_initial_point_ignored

is_initial_point_required

is_initial_point_supported

maxiter

setting

settings

size_gen

Methods

get_support_level

gradient_num_diff

minimize

print_options

set_max_evals_grouped

set_options

wrap_function