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
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
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
objective_value
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