# Graph Partitioning Generator

The GraphPartitioningGenerator can be used to generate batches to solve the Graph Partitioning problem on an input graph. Some examples using different types of job generation and QPUs on some simple graphs are shown below:

## QAOA job generation

import networkx as nx
from qat.generators import GraphPartitioningGenerator
from qat.plugins import ScipyMinimizePlugin
from qat.qpus import get_default_qpu

graph = nx.full_rary_tree(3, 6)

scipy_args = dict(method="COBYLA", tol=1e-5, options={"maxiter": 200})
graph_partitioning_application = GraphPartitioningGenerator(job_type="qaoa") | (ScipyMinimizePlugin(**scipy_args) | get_default_qpu())
combinatorial_result = graph_partitioning_application.execute(graph, 1)

print("The nodes in the first subgraph are", combinatorial_result.subsets[0])
print("The nodes in the second subgraph are", combinatorial_result.subsets[1])

The nodes in the first subgraph are [0, 2, 3]
The nodes in the second subgraph are [1, 4, 5]
<stdin>:10: FutureWarning: adjacency_matrix will return a scipy.sparse array instead of a matrix in Networkx 3.0.


The parsed combinatorial result can also be displayed with networkx using the display() method:

combinatorial_result.display()


## Annealing job generation

import networkx as nx
from qat.generators import GraphPartitioningGenerator
from qat.qpus import SimulatedAnnealing
from qat.core import Variable
from qat.opt.sqa_best_parameters import sqa_best_parameters_dicts

graph = nx.full_rary_tree(2, 30)

# Create a temperature function
t = Variable("t", float)
temp_max = sqa_best_parameters_dicts["GraphPartitioning"]["temp_max"]
temp_min = sqa_best_parameters_dicts["GraphPartitioning"]["temp_min"]
temp_t = temp_min * t + temp_max * (1 - t)  # annealing requires going from a high to a very low temperature
n_steps = 5000

graph_partitioning_application = GraphPartitioningGenerator(job_type="annealing") | SimulatedAnnealing(temp_t, n_steps)
combinatorial_result = graph_partitioning_application.execute(graph, 1)

print("The nodes in the first subgraph are", combinatorial_result.subsets[0])
print("The nodes in the second subgraph are", combinatorial_result.subsets[1])

The nodes in the first subgraph are [0, 2, 3, 6, 7, 8, 13, 14, 15, 16, 17, 18, 27, 28, 29]
The nodes in the second subgraph are [1, 4, 5, 9, 10, 11, 12, 19, 20, 21, 22, 23, 24, 25, 26]
<stdin>:17: FutureWarning: adjacency_matrix will return a scipy.sparse array instead of a matrix in Networkx 3.0.


Similarly, the function display() method can be used to display the result:

combinatorial_result.display()


## Scheduling job generation

import networkx as nx
from qat.generators import GraphPartitioningGenerator

graph = nx.full_rary_tree(3, 6)

graph_partitioning_generator = GraphPartitioningGenerator(job_type="schedule")
schedule_batch = graph_partitioning_generator.generate(None, graph, 1)


Currently the analog qpus that can be used to execute the schedule are only available in the QLM. Therefore the generated schedule_batch here can be passed to a QLM for execution.

class qat.opt.generators.GraphPartitioningGenerator(job_type='qaoa')

Specialization of the CombinatorialOptimizerGenerator class for generator that solves the Graph Partitioning problem

Parameters

job_type (str) – The job type of the batches to be generated. Can be either “qaoa”, “schedule” or “annealing”

generate(specs, graph, A, B=1, **kwargs)

Generate a batch that solves the Graph Partitioning problem on a particular graph. The batch can then be sent to a computational stack of plugins and QPU to be executed. The result will be parsed into GraphPartitioningResult that contains interpretable information

Parameters
• specs (HardwareSpecs) – will be used to run the job

• graph (networkx.Graph) – a networkx graph to run the Graph Partitioning algorithm on

• A (double) – a positive constant by which the terms inside $$H_A$$ from $$H = H_A + H_B$$ are multiplied. This equation comes from the Hamiltonian representation of the problem.

• B (double, optional) – similar to $$A$$, $$B$$ is a positive factor for the $$H_B$$ terms, default is 1

Returns

A parsed result of combinatorial optimization problem

Return type

GraphPartitioningResult