Learn OCEAN-SDK with Real Code Examples

Updated Nov 25, 2025

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Code Sample Descriptions

Ocean SDK Minimal Optimization Problem

from dwave.system import DWaveSampler, EmbeddingComposite
import dimod

# BQM: minimize x0 + x1 - 2*x0*x1
bqm = dimod.BinaryQuadraticModel({'x0':1, 'x1':1}, {('x0','x1'):-2}, 0, vartype=dimod.BINARY)

sampler = EmbeddingComposite(DWaveSampler())
sampleset = sampler.sample(bqm, num_reads=10)
print(sampleset)

Defines a small BQM and samples it on a D-Wave system.

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Ocean SDK Single Variable BQM

from dwave.system import DWaveSampler, EmbeddingComposite
import dimod

bqm = dimod.BinaryQuadraticModel({'x':-1}, {}, 0, vartype=dimod.BINARY)
sampleset = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=20)
print(sampleset)

A simple one-variable binary quadratic model submitted to a sampler.

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Ocean SDK Two-Variable Minimization

import dimod
from dwave.system import DWaveSampler, EmbeddingComposite

bqm = dimod.BinaryQuadraticModel({'a':0, 'b':0}, {('a','b'):1}, 0, vartype=dimod.BINARY)
samples = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=50)
print(samples)

Minimizes a two-variable energy landscape using BQM.

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Ocean SDK Spin Model Example

import dimod
from dwave.system import DWaveSampler, EmbeddingComposite

bqm = dimod.BinaryQuadraticModel({'s0':-1, 's1':1}, {('s0','s1'):-1}, 0, vartype=dimod.SPIN)
sampleset = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=20)
print(sampleset)

Uses SPIN variables instead of BINARY.

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Ocean SDK QUBO Example

import dimod
from dwave.system import DWaveSampler, EmbeddingComposite

Q = {('x0','x0'):1, ('x1','x1'):1, ('x0','x1'):-1}
bqm = dimod.BinaryQuadraticModel.from_qubo(Q)
sampleset = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=15)
print(sampleset)

Creates a QUBO dictionary and solves it using dimod.

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Ocean SDK Constraint Example

import dimod
from dwave.system import DWaveSampler, EmbeddingComposite

bqm = dimod.BinaryQuadraticModel({'x':1, 'y':1}, {('x','y'):2}, 0, vartype=dimod.BINARY)
bqm.add_variable('z', -1)
samples = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=30)
print(samples)

Adds a soft constraint to a BQM and samples it.

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Ocean SDK Penalty Model Example

import dimod
from dwave.system import DWaveSampler, EmbeddingComposite

x, y = 'x', 'y'
bqm = dimod.BinaryQuadraticModel({x:1, y:1}, {(x,y):-2}, 0, vartype=dimod.BINARY)
samples = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=20)
print(samples)

Uses dimod to encode a penalty for x+y=1.

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Ocean SDK Random BQM

import dimod
from dwave.system import EmbeddingComposite, DWaveSampler

bqm = dimod.generators.random.randint(3)
samples = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=25)
print(samples)

Generates a random BQM with 3 variables.

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Ocean SDK Simulated Annealing

import dimod

bqm = dimod.BinaryQuadraticModel({'x':1, 'y':1}, {('x','y'):-1}, 0, vartype=dimod.BINARY)
sampleset = dimod.SimulatedAnnealingSampler().sample(bqm, num_reads=10)
print(sampleset)

Uses dimod's simulated annealing sampler for local testing.

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Ocean SDK Hybrid Solver Example

import dimod
from dwave.system import LeapHybridSampler

bqm = dimod.BinaryQuadraticModel({'a':-1, 'b':2}, {('a','b'):1}, 0, vartype=dimod.BINARY)
sampleset = LeapHybridSampler().sample(bqm)
print(sampleset)

Runs BQM on D-Wave's hybrid solver if available.

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Code Sample Descriptions

Ocean SDK Minimal Optimization Problem

from dwave.system import DWaveSampler, EmbeddingComposite
import dimod

# BQM: minimize x0 + x1 - 2*x0*x1
bqm = dimod.BinaryQuadraticModel({'x0':1, 'x1':1}, {('x0','x1'):-2}, 0, vartype=dimod.BINARY)

sampler = EmbeddingComposite(DWaveSampler())
sampleset = sampler.sample(bqm, num_reads=10)
print(sampleset)

Defines a small BQM and samples it on a D-Wave system.

Let’s Try →

Ocean SDK Single Variable BQM

from dwave.system import DWaveSampler, EmbeddingComposite
import dimod

bqm = dimod.BinaryQuadraticModel({'x':-1}, {}, 0, vartype=dimod.BINARY)
sampleset = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=20)
print(sampleset)

A simple one-variable binary quadratic model submitted to a sampler.

Let’s Try →

Ocean SDK Two-Variable Minimization

import dimod
from dwave.system import DWaveSampler, EmbeddingComposite

bqm = dimod.BinaryQuadraticModel({'a':0, 'b':0}, {('a','b'):1}, 0, vartype=dimod.BINARY)
samples = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=50)
print(samples)

Minimizes a two-variable energy landscape using BQM.

Let’s Try →

Ocean SDK Spin Model Example

import dimod
from dwave.system import DWaveSampler, EmbeddingComposite

bqm = dimod.BinaryQuadraticModel({'s0':-1, 's1':1}, {('s0','s1'):-1}, 0, vartype=dimod.SPIN)
sampleset = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=20)
print(sampleset)

Uses SPIN variables instead of BINARY.

Let’s Try →

Ocean SDK QUBO Example

import dimod
from dwave.system import DWaveSampler, EmbeddingComposite

Q = {('x0','x0'):1, ('x1','x1'):1, ('x0','x1'):-1}
bqm = dimod.BinaryQuadraticModel.from_qubo(Q)
sampleset = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=15)
print(sampleset)

Creates a QUBO dictionary and solves it using dimod.

Let’s Try →

Ocean SDK Constraint Example

import dimod
from dwave.system import DWaveSampler, EmbeddingComposite

bqm = dimod.BinaryQuadraticModel({'x':1, 'y':1}, {('x','y'):2}, 0, vartype=dimod.BINARY)
bqm.add_variable('z', -1)
samples = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=30)
print(samples)

Adds a soft constraint to a BQM and samples it.

Let’s Try →

Ocean SDK Penalty Model Example

import dimod
from dwave.system import DWaveSampler, EmbeddingComposite

x, y = 'x', 'y'
bqm = dimod.BinaryQuadraticModel({x:1, y:1}, {(x,y):-2}, 0, vartype=dimod.BINARY)
samples = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=20)
print(samples)

Uses dimod to encode a penalty for x+y=1.

Let’s Try →

Ocean SDK Random BQM

import dimod
from dwave.system import EmbeddingComposite, DWaveSampler

bqm = dimod.generators.random.randint(3)
samples = EmbeddingComposite(DWaveSampler()).sample(bqm, num_reads=25)
print(samples)

Generates a random BQM with 3 variables.

Let’s Try →

Ocean SDK Simulated Annealing

import dimod

bqm = dimod.BinaryQuadraticModel({'x':1, 'y':1}, {('x','y'):-1}, 0, vartype=dimod.BINARY)
sampleset = dimod.SimulatedAnnealingSampler().sample(bqm, num_reads=10)
print(sampleset)

Uses dimod's simulated annealing sampler for local testing.

Let’s Try →

Ocean SDK Hybrid Solver Example

import dimod
from dwave.system import LeapHybridSampler

bqm = dimod.BinaryQuadraticModel({'a':-1, 'b':2}, {('a','b'):1}, 0, vartype=dimod.BINARY)
sampleset = LeapHybridSampler().sample(bqm)
print(sampleset)

Runs BQM on D-Wave's hybrid solver if available.

Let’s Try →