80 lines
4.0 KiB
Plaintext
80 lines
4.0 KiB
Plaintext
---
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title: vertex_cover
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description: API reference for qiskit.optimization.applications.ising.vertex_cover
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in_page_toc_min_heading_level: 2
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python_api_type: module
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python_api_name: qiskit.optimization.applications.ising.vertex_cover
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---
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<span id="module-qiskit.optimization.applications.ising.vertex_cover" />
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<span id="qiskit-optimization-applications-ising-vertex-cover" />
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# qiskit.optimization.applications.ising.vertex\_cover
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Convert vertex cover instances into Pauli list Deal with Gset format. See [https://web.stanford.edu/\~yyye/yyye/Gset/](https://web.stanford.edu/~yyye/yyye/Gset/)
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**Functions**
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| | |
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| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | ---------------------------------------------------------------------------------- |
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| [`check_full_edge_coverage`](#qiskit.optimization.applications.ising.vertex_cover.check_full_edge_coverage "qiskit.optimization.applications.ising.vertex_cover.check_full_edge_coverage")(x, w) | **param x**binary string as numpy array. |
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| [`get_graph_solution`](#qiskit.optimization.applications.ising.vertex_cover.get_graph_solution "qiskit.optimization.applications.ising.vertex_cover.get_graph_solution")(x) | Get graph solution from binary string. |
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| [`get_operator`](#qiskit.optimization.applications.ising.vertex_cover.get_operator "qiskit.optimization.applications.ising.vertex_cover.get_operator")(weight\_matrix) | Generate Hamiltonian for the vertex cover :param weight\_matrix: adjacency matrix. |
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### check\_full\_edge\_coverage
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<Function id="qiskit.optimization.applications.ising.vertex_cover.check_full_edge_coverage" github="https://github.com/qiskit-community/qiskit-aqua/tree/stable/0.8/qiskit/optimization/applications/ising/vertex_cover.py" signature="check_full_edge_coverage(x, w)">
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**Parameters**
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* **x** (*numpy.ndarray*) – binary string as numpy array.
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* **w** (*numpy.ndarray*) – adjacency matrix.
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**Returns**
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value of the cut.
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**Return type**
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float
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</Function>
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### get\_graph\_solution
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<Function id="qiskit.optimization.applications.ising.vertex_cover.get_graph_solution" github="https://github.com/qiskit-community/qiskit-aqua/tree/stable/0.8/qiskit/optimization/applications/ising/vertex_cover.py" signature="get_graph_solution(x)">
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Get graph solution from binary string.
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**Parameters**
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**x** (*numpy.ndarray*) – binary string as numpy array.
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**Returns**
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graph solution as binary numpy array.
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**Return type**
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numpy.ndarray
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</Function>
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### get\_operator
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<Function id="qiskit.optimization.applications.ising.vertex_cover.get_operator" github="https://github.com/qiskit-community/qiskit-aqua/tree/stable/0.8/qiskit/optimization/applications/ising/vertex_cover.py" signature="get_operator(weight_matrix)">
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Generate Hamiltonian for the vertex cover :param weight\_matrix: adjacency matrix. :type weight\_matrix: numpy.ndarray
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**Returns**
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operator for the Hamiltonian and a constant shift for the obj function.
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**Return type**
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tuple([WeightedPauliOperator](qiskit.aqua.operators.legacy.WeightedPauliOperator "qiskit.aqua.operators.legacy.WeightedPauliOperator"), float)
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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
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Hamiltonian: H = A \* H\_A + H\_B H\_A = sum\_\{(i,j)in E}\{(1-Xi)(1-Xj)} H\_B = sum\_\{i}\{Zi}
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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
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</Function>
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