qiskit.optimization.applications.ising.vertex_cover
Convert vertex cover instances into Pauli list Deal with Gset format. See https://web.stanford.edu/~yyye/yyye/Gset/
Functions
check_full_edge_coverage(x, w) | param xbinary string as numpy array. |
get_graph_solution(x) | Get graph solution from binary string. |
get_operator(weight_matrix) | Generate Hamiltonian for the vertex cover :param weight_matrix: adjacency matrix. |
check_full_edge_coverage
check_full_edge_coverage(x, w)
Parameters
- x (numpy.ndarray) – binary string as numpy array.
- w (numpy.ndarray) – adjacency matrix.
Returns
value of the cut.
Return type
float
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 vertex cover :param weight_matrix: adjacency matrix. :type weight_matrix: numpy.ndarray
Returns
operator for the Hamiltonian and a constant shift for the obj function.
Return type
tuple(WeightedPauliOperator, float)
Goals: 1 color some vertices as red such that every edge is connected to some red vertex 2 minimize the vertices to be colored as red
Hamiltonian: H = A * H_A + H_B H_A = sum_{(i,j)in E}{(1-Xi)(1-Xj)} H_B = sum_{i}{Zi}
H_A is to achieve goal 1 while H_b is to achieve goal 2. H_A is hard constraint so we place a huge penality on it. A=5. Note Xi = (Zi+1)/2