# Binary Quadratic Models#

The binary quadratic model (BQM) class encodes Ising and quadratic unconstrained binary optimization (QUBO) models used by samplers such as the D-Wave system.

The BQM equation,

can represent both.

The Ising model is an objective function of \(N\) variables \(s=[s_1,...,s_N]\) corresponding to physical Ising spins, where \(h_i\) are the biases and \(J_{i,j}\) the couplings (interactions) between spins.

The QUBO model is an objective function of \(N\) binary variables represented as an upper-diagonal matrix \(Q\), where diagonal terms are the linear coefficients and the nonzero off-diagonal terms the quadratic coefficients.

The `dimod.BinaryQuadraticModel`

class can contain both these models and its methods provide
convenient utilities for working with, and interworking between, the two representations
of a problem.

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

Getting Started with the D-Wave System

Introduces key concepts such as objective functions, Ising models, QUBOs, and graphs, explains how these models are used to represent problems, and provides some simple examples.

D-Wave Problem-Solving Handbook

Provides a variety of techniques for, and examples of, reformulating problems as BQMs.

Solving Problems on a D-Wave System

Describes and demonstrates the use of BQM in the context of Ocean software.