dimod¶
dimod is a shared API for binary quadratic samplers. It provides a binary quadratic model (BQM) class that contains Ising and quadratic unconstrained binary optimization (QUBO) models used by samplers such as the D-Wave system. It also provides utilities for constructing new samplers and composed samplers and for minor-embedding. Its reference examples include several samplers and composed samplers.
Example Usage¶
The QUBO form, \(\text{E}(a_i, b_{i,j}; q_i) = -q_1 -q_2 + 2q_1 q_2\), is related to the Ising form, \(\text{E}(h_i, j_{i,j}; s_i) = \frac{1}{2}(s_1s_2-1)\), via the simple manipulation \(s_i=2q_i-1\).
This example constructs a simple QUBO and converts it to Ising format.
>>> import dimod
>>> bqm = dimod.BinaryQuadraticModel({0: -1, 1: -1}, {(0, 1): 2}, 0.0, dimod.BINARY) # QUBO
>>> bqm_ising = bqm.change_vartype(dimod.SPIN, inplace=False) # Ising
This example uses one of dimod’s test samplers, ExactSampler, a solver that calculates the energies of all possible samples.
>>> import dimod
>>> h = {0: 0.0, 1: 0.0}
>>> J = {(0, 1): -1.0}
>>> bqm = dimod.BinaryQuadraticModel.from_ising(h, J)
>>> response = dimod.ExactSolver().sample(bqm)
>>> for sample, energy in response.data(['sample', 'energy']): print(sample, energy)
{0: -1, 1: -1} -1.0
{0: 1, 1: 1} -1.0
{0: 1, 1: -1} 1.0
{0: -1, 1: 1} 1.0