class RecursiveMinimumEigenOptimizer(min_eigen_optimizer, min_num_vars=1, min_num_vars_optimizer=None, penalty=None)[source]

A meta-algorithm that applies a recursive optimization.

The recursive minimum eigen optimizer applies a recursive optimization on top of MinimumEigenOptimizer. The algorithm is introduced in [1].


Outline of how to use this class:

from qiskit.aqua.algorithms import QAOA
from qiskit.optimization.problems import QuadraticProgram
from qiskit.optimization.algorithms import RecursiveMinimumEigenOptimizer
problem = QuadraticProgram()
# specify problem here
# specify minimum eigen solver to be used, e.g., QAOA
qaoa = QAOA(...)
optimizer = RecursiveMinimumEigenOptimizer(qaoa)
result = optimizer.solve(problem)


[1]: Bravyi et al. (2019), Obstacles to State Preparation and Variational Optimization

from Symmetry Protection.

Initializes the recursive minimum eigen optimizer.

This initializer takes a MinimumEigenOptimizer, the parameters to specify until when to to apply the iterative scheme, and the optimizer to be applied once the threshold number of variables is reached.

  • min_eigen_optimizer (MinimumEigenOptimizer) – The eigen optimizer to use in every iteration.

  • min_num_vars (int) – The minimum number of variables to apply the recursive scheme. If this threshold is reached, the min_num_vars_optimizer is used.

  • min_num_vars_optimizer (Optional[OptimizationAlgorithm]) – This optimizer is used after the recursive scheme for the problem with the remaining variables.

  • penalty (Optional[float]) – The factor that is used to scale the penalty terms corresponding to linear equality constraints.

TODO: add flag to store full history.


QiskitOptimizationError – In case of invalid parameters (num_min_vars < 1).



Checks whether a given problem can be solved with this optimizer.


Checks whether a given problem can be solved with the optimizer implementing this method.


Tries to solve the given problem using the recursive optimizer.