Max Cut

Given an undirected graph with vertex set \(V\) and edge set \(E\), the problem consists in partitioning the graph into two subgraphs connected by the maximum number of edges. Annealing the problem with the MaxCut class (or MaxCutGenerator class) needs \(\#V\) spins (one spin per vertex of the graph).

Solving this problem using the simulated annealing method requires the SimulatedAnnealing QPU.

import networkx as nx
import numpy as np
from qat.opt import MaxCut
from qat.qpus import SimulatedAnnealing
from qat.simulated_annealing import integer_to_spins
from qat.core import Variable

# Specify the graph
graph = nx.full_rary_tree(2, 30)
max_cut_problem = MaxCut(graph)


# Extract parameters for SA
problem_parameters_dict = max_cut_problem.get_best_parameters()
n_steps = problem_parameters_dict["n_steps"]
temp_max = problem_parameters_dict["temp_max"]
temp_min = problem_parameters_dict["temp_min"]

# Create a temperature schedule and a QPU
tmax = 1.0
t = Variable("t", float)
temp_t = temp_min * (t / tmax) + temp_max * (1 - t / tmax)
sa_qpu = SimulatedAnnealing(temp_t=temp_t, n_steps=n_steps)

# Create a job and send it to the QPU
problem_job = max_cut_problem.to_job('sqa', tmax=tmax)
problem_result = sa_qpu.submit(problem_job)

# Extract and print solution configuration
state = problem_result.raw_data[0].state.int  # raw_data is a list of Samples - one per computation
solution_configuration = integer_to_spins(state, len(graph.nodes()))
print("Solution configuration: \n" + str(solution_configuration) + "\n")
indices_spin_1 = np.where(solution_configuration == 1)[0]
print("The nodes in the first subgraph:\n" + str(indices_spin_1) + "\n")
indices_spin_minus_1 = np.where(solution_configuration == -1)[0]
print("The nodes in the second subgraph:\n" + str(indices_spin_minus_1))
Solution configuration: 
[-1.  1.  1. -1. -1. -1. -1.  1.  1.  1.  1.  1.  1.  1.  1. -1. -1. -1.
 -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]

The nodes in the first subgraph:
[ 1  2  7  8  9 10 11 12 13 14]

The nodes in the second subgraph:
[ 0  3  4  5  6 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29]
<stdin>:26: UserWarning: If SQAQPU is used, gamma_t will be needed.

This example is also detailed in this notebook on solving Max Cut problems with SA.