# Discrete Quadratic Models¶

The discrete quadratic model (DQM) is a polynomial over discrete variables with
terms all of degree two or less. Suppose that there are \(N\) discrete
variables \(\bf{d}_i\), each with \(n_i\) cases. Conceptually, the
cases may represent any collection of discrete values, such as ```
{red, green,
blue, yellow}
```

or `{3.2, 67}`

. Using a binary variable \(x_{i,u}\) to
indicate whether discrete variable \(\bf{d}_i\) is set to case \(u\),
the objective function can be expressed by the equation:

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 documentationDescribes the DQM class and its methods.

`LeapHybridDQMSampler`

class documentationDescribes Leap’s DQM solver API.