Discrete Quadratic Models

The discrete quadratic model (DQM) is a polynomial over discrete variables with terms all of degree two or less, represented by equation,

\[E(\bf{v}) = \sum_{i=1} a_i v_i + \sum_{i<j} b_{i,j} v_i v_j + c \qquad\qquad v_i \in\{A, B, C, ...\}\]

where \(\{A, B, C, ...\}\) are some set of discrete values such {red, green, blue, yellow} or {3.2, 67}.

The dimod.DiscreteQuadraticModel class can contain this model and its methods provide convenient utilities for working with representations of a problem.

These models and their use in solving problems on the D-Wave system are described in the following documentation:

• Example Map Coloring: Hybrid DQM Sampler

  Shows an example of using Leap’s hybrid DQM solver, hybrid_binary_quadratic_model_version<x>, to solve a map coloring problem.

• dimod.DiscreteQuadraticModel class documentation

  Describes the DQM class and its methods.

• LeapHybridDQMSampler class documentation

  Describes Leap’s DQM solver API.