dimod.embed_bqm

embed_bqm(source_bqm, embedding, target_adjacency, chain_strength=1.0)

Embed a binary quadratic model onto a target graph.

Parameters:

• source_bqm (BinaryQuadraticModel) – Binary quadratic model to embed.
• embedding (dict) – Mapping from source graph to target graph as a dict of form {s: {t, …}, …}, where s is a source-model variable and t is a target-model variable.
• target_adjacency (dict/networkx.Graph) – Adjacency of the target graph as a dict of form {t: Nt, …}, where t is a variable in the target graph and Nt is its set of neighbours.
• chain_strength (float, optional) – Magnitude of the quadratic bias (in SPIN-space) applied between variables to create chains. Note that the energy penalty of chain breaks is 2 * chain_strength.

Returns:

Target binary quadratic model.

Return type:

BinaryQuadraticModel

Examples

This example embeds a fully connected \(K_3\) graph onto a square target graph. Embedding is accomplished by an edge contraction operation on the target graph: target-nodes 2 and 3 are chained to represent source-node c.

>>> import dimod
>>> import networkx as nx
>>> # Binary quadratic model for a triangular source graph
>>> bqm = dimod.BinaryQuadraticModel.from_ising({}, {('a', 'b'): 1, ('b', 'c'): 1, ('a', 'c'): 1})
>>> # Target graph is a graph
>>> target = nx.cycle_graph(4)
>>> # Embedding from source to target graphs
>>> embedding = {'a': {0}, 'b': {1}, 'c': {2, 3}}
>>> # Embed the BQM
>>> target_bqm = dimod.embed_bqm(bqm, embedding, target)
>>> target_bqm.quadratic[(0, 1)] == bqm.quadratic[('a', 'b')]
True
>>> target_bqm.quadratic   
{(0, 1): 1.0, (0, 3): 1.0, (1, 2): 1.0, (2, 3): -1.0}

This example embeds a fully connected \(K_3\) graph onto the target graph of a dimod reference structured sampler, StructureComposite, using the dimod reference ExactSolver sampler with a square graph specified. Target-nodes 2 and 3 are chained to represent source-node c.

>>> import dimod
>>> # Binary quadratic model for a triangular source graph
>>> bqm = dimod.BinaryQuadraticModel.from_ising({}, {('a', 'b'): 1, ('b', 'c'): 1, ('a', 'c'): 1})
>>> # Structured dimod sampler with a structure defined by a square graph
>>> sampler = dimod.StructureComposite(dimod.ExactSolver(), [0, 1, 2, 3], [(0, 1), (1, 2), (2, 3), (0, 3)])
>>> # Embedding from source to target graph
>>> embedding = {'a': {0}, 'b': {1}, 'c': {2, 3}}
>>> # Embed the BQM
>>> target_bqm = dimod.embed_bqm(bqm, embedding, sampler.adjacency)
>>> # Sample
>>> response = sampler.sample(target_bqm)
>>> response.samples_matrix   
matrix([[-1, -1, -1, -1],
        [ 1, -1, -1, -1],
        [ 1,  1, -1, -1],
        [-1,  1, -1, -1],
        [-1,  1,  1, -1],
>>> # Snipped above response for brevity