qiskit.optimization.applications.ising.graph_partition

Convert graph partitioning instances into Pauli list Deal with Gset format. See https://web.stanford.edu/~yyye/yyye/Gset/

Functions

get_graph_solution(x)	Get graph solution from binary string.
get_operator(weight_matrix)	Generate Hamiltonian for the graph partitioning
objective_value(x, w)	Compute the value of a cut.

get_graph_solution(x)

Get graph solution from binary string.

Parameters

x (numpy.ndarray) – binary string as numpy array.

Returns

graph solution as binary numpy array.

Return type

numpy.ndarray

get_operator(weight_matrix)

Generate Hamiltonian for the graph partitioning

Notes

Goals:

1 separate the vertices into two set of the same size 2 make sure the number of edges between the two set is minimized.

Hamiltonian:

H = H_A + H_B H_A = sum_{(i,j)in E}{(1-ZiZj)/2} H_B = (sum_{i}{Zi})^2 = sum_{i}{Zi^2}+sum_{i!=j}{ZiZj} H_A is for achieving goal 2 and H_B is for achieving goal 1.

Parameters

weight_matrix (numpy.ndarray) – adjacency matrix.

Returns

operator for the Hamiltonian float: a constant shift for the obj function.

Return type

WeightedPauliOperator

objective_value(x, w)

Compute the value of a cut.

Parameters

• x (numpy.ndarray) – binary string as numpy array.

• w (numpy.ndarray) – adjacency matrix.

Returns

value of the cut.

Return type

float