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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.