GoemansWilliamsonOptimizer¶

class GoemansWilliamsonOptimizer(num_cuts, sort_cuts=True, unique_cuts=True, seed=0)[source]¶

Bases: qiskit_optimization.algorithms.optimization_algorithm.OptimizationAlgorithm

Goemans-Williamson algorithm to approximate the max-cut of a problem. The quadratic program for max-cut is given by:

max sum_{i,j<i} w[i,j]*x[i]*(1-x[j])

Therefore the quadratic term encodes the negative of the adjacency matrix of the graph.

Parameters

num_cuts (int) – Number of cuts to generate.
sort_cuts (bool) – True if sort cuts by their values.
unique_cuts (bool) – The solve method returns only unique cuts, thus there may be less cuts than num_cuts.
seed (int) – A seed value for the random number generator.

Raises

MissingOptionalLibraryError – CVXPY is not installed.

Methods

`get_compatibility_msg`(problem)	Checks whether a given problem can be solved with the optimizer implementing this method.
`max_cut_value`(x, adj_matrix)	Compute the value of a cut from an adjacency matrix and a list of binary values.
`solve`(problem)	Returns a list of cuts generated according to the Goemans-Williamson algorithm.