dwave.embedding.chimera.find_biclique_embedding#

find_biclique_embedding(a, b, m=None, n=None, t=None, target_edges=None, target_graph=None)[source]#

Find an embedding for a biclique in a Chimera graph.

Given a biclique (a bipartite graph where every vertex in a set in connected to all vertices in the other set) and a target Chimera graph size or edges, attempts to find an embedding.

Parameters:

  • a (int/iterable) – Left shore of the biclique to embed. If a is an integer, generates an embedding for a biclique with the left shore of size a labelled [0,a-1]. If a is an iterable of nodes, generates an embedding for a biclique with the left shore of size len(a) labelled for the given nodes.

  • b (int/iterable) – Right shore of the biclique to embed.If b is an integer, generates an embedding for a biclique with the right shore of size b labelled [0,b-1]. If b is an iterable of nodes, generates an embedding for a biclique with the right shore of size len(b) labelled for the given nodes.

  • m (int, optional, default=None) – Number of rows in the Chimera lattice.

  • n (int, optional, default=m) – Number of columns in the Chimera lattice.

  • t (int, optional, default 4) – Size of the shore within each Chimera tile.

  • target_edges (iterable[edge]) – A list of edges in the target Chimera graph. Nodes are labelled as returned by chimera_graph().

  • target_graph (networkx.Graph) – A Chimera graph constructed by chimera_graph().

Returns:

A 2-tuple containing:

dict: An embedding mapping the left shore of the biclique to the Chimera lattice.

dict: An embedding mapping the right shore of the biclique to the Chimera lattice.

Return type:

tuple

Note

Either target_edges or target_graph must be None. If both are None, a graph with perfect yield is assumed from the parameters m, n, t. If target_edges is not None, at least m must not be None.

Examples

This example finds an embedding for an alphanumerically labeled biclique in a single Chimera unit cell.

>>> from dwave.embedding.chimera import find_biclique_embedding
...
>>> left, right = find_biclique_embedding(['a', 'b', 'c'], ['d', 'e'], 1, 1)
>>> print(left, right)  
{'a': [4], 'b': [5], 'c': [6]} {'d': [0], 'e': [1]}