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
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Get graph solution from binary string. |
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Generate Hamiltonian for the vertex cover :param weight_matrix: adjacency matrix. |
- check_full_edge_coverage(x, w)[source]¶
- 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(x)[source]¶
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)[source]¶
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