minorminer is a library of tools for finding graph minor embeddings, developed to embed Ising problems onto quantum annealers (QA). While this library can be used to find minors in arbitrary graphs, it is particularly geared towards state-of-the-art QA: problem graphs of a few to a few hundred variables, and hardware graphs of a few thousand qubits.

minorminer has both a Python and C++ API, and includes implementations of multiple embedding algorithms to best fit different problems.

Minor-Embedding and QPU Topology

For an introduction to minor-embedding, see Minor-Embedding.

For an introduction to the topologies of D-Wave hardware graphs, see QPU Topology. Leap users also have access to the Exploring Pegasus Jupyter Notebook that explains the architecture of D-Wave’s quantum computer, Advantage, in further detail.

Minor-embedding can be done manually, though typically for very small problems only. For a walkthrough of the manual minor-embedding process, see the Constraints Example: Minor-Embedding.

Minor-Embedding in Ocean

Minor-embedding can also be automated through Ocean. minorminer is used by several Ocean embedding composites for this purpose. For details on automated (and manual) minor-embedding through Ocean, see how the EmbeddingComposite and FixedEmbeddingComposite are used in this Boolean AND Gate example.

Once an embedding has been found, D-Wave’s Problem Inspector tool can be used to evaluate its quality. See Using the Problem Inspector for more information.