# dwave.embedding.embed_qubo¶

Embed a QUBO onto a target graph.

Parameters
• source_Q (dict[(variable, variable), bias]) – Coefficients of a quadratic unconstrained binary optimization (QUBO) model.

• 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 target-graph variable and Nt is its set of neighbours.

• chain_strength (float/mapping/callable, optional) – Sets the coupling strength between qubits representing variables that form a chain. Mappings should specify the required chain strength for each variable. Callables should accept the BQM and embedding and return a float or mapping. By default, chain_strength is calculated with uniform_torque_compensation().

Returns

Quadratic biases of the target QUBO.

Return type

dict[(variable, variable), bias]

Examples

This example embeds a triangular QUBO representing a $$K_3$$ clique into a square target graph by mapping variable c in the source to nodes 2 and 3 in the target.

>>> import networkx as nx
...
>>> target = nx.cycle_graph(4)
>>> # QUBO
>>> Q = {('a', 'b'): 1, ('b', 'c'): 1, ('a', 'c'): 1}
>>> # Variable c is a chain
>>> embedding = {'a': {0}, 'b': {1}, 'c': {2, 3}}
>>> # Embed and show the resulting biases
>>> tQ = dwave.embedding.embed_qubo(Q, embedding, target)
>>> tQ
{(0, 1): 1.0,
(0, 3): 1.0,
(1, 2): 1.0,
(2, 3): -4.0,
(0, 0): 0.0,
(1, 1): 0.0,
(2, 2): 2.0,
(3, 3): 2.0}