BQM Usage Examples

Working with Binary Quadratic Models in Dynex SDK

BQM Usage Examples

Learn how to create and manipulate Binary Quadratic Models for quantum computing.

Creating BQMs

From Scratch

import dimod

# Method 1: Direct construction
bqm = dimod.BinaryQuadraticModel(
    linear={0: 1.0, 1: -1.0, 2: 0.5},
    quadratic={(0, 1): 0.5, (1, 2): -0.3},
    offset=0.0,
    vartype='BINARY'
)

From QUBO Matrix

import numpy as np

# Create QUBO matrix
Q = np.array([
    [1.0, 0.5, 0.0],
    [0.0, -1.0, -0.3],
    [0.0, 0.0, 0.5]
])

# Convert to BQM
bqm = dimod.BinaryQuadraticModel.from_qubo(Q)

BQM Operations

Scaling for QPU

import dynex

# Scale BQM coefficients for QPU compatibility
scaled_bqm, scale_factor = dynex.scale_bqm_to_range(bqm, max_abs_coeff=9.0)

print(f"Original max coefficient: {max(abs(c) for c in bqm.linear.values())}")
print(f"Scaled max coefficient: {max(abs(c) for c in scaled_bqm.linear.values())}")
print(f"Scale factor: {scale_factor}")

BQM Analysis

# Analyze BQM properties
print(f"Number of variables: {len(bqm.variables)}")
print(f"Number of interactions: {len(bqm.quadratic)}")
print(f"Variable types: {bqm.vartype}")
print(f"Energy range: [{bqm.lower_bound}, {bqm.upper_bound}]")

Sampling Different BQM Types

SPIN vs BINARY

# BINARY variables (0, 1)
binary_bqm = dimod.BinaryQuadraticModel(
    {0: 1, 1: -1}, {(0, 1): 2}, 0.0, 'BINARY'
)

# SPIN variables (-1, +1)  
spin_bqm = dimod.BinaryQuadraticModel(
    {0: 1, 1: -1}, {(0, 1): 2}, 0.0, 'SPIN'
)

# Sample both
for name, bqm in [("BINARY", binary_bqm), ("SPIN", spin_bqm)]:
    model = dynex.BQM(bqm)
    sampler = dynex.DynexSampler(model)
    sampleset = sampler.sample(num_reads=10)
    
    print(f"{name} result: {sampleset.first.sample}")

Real-World Example: Max-Cut Problem

import networkx as nx

# Create a graph
G = nx.Graph()
G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (0, 2)])

# Formulate as QUBO
Q = {}
for u, v in G.edges():
    Q[(u, u)] = Q.get((u, u), 0) + 1
    Q[(v, v)] = Q.get((v, v), 0) + 1  
    Q[(u, v)] = Q.get((u, v), 0) - 2

# Convert to BQM and solve
bqm = dimod.BinaryQuadraticModel.from_qubo(Q)
model = dynex.BQM(bqm)
sampler = dynex.DynexSampler(model)
sampleset = sampler.sample(num_reads=100)

# Interpret results
solution = sampleset.first.sample
partition_0 = [node for node, val in solution.items() if val == 0]
partition_1 = [node for node, val in solution.items() if val == 1]

print(f"Partition 0: {partition_0}")
print(f"Partition 1: {partition_1}")
print(f"Cut size: {-sampleset.first.energy}")

Next Steps

• Explore Machine Learning with QRBMs
• Learn about Optimization Problems
• Check API Reference