qat.opt.KClique

class qat.opt.KClique(graph, K, A, B=1, **kwargs)

Specialization of the QUBO class for K-Clique.

For a right encoding, one should ensure that \(A > B * K\).

Reference

“Ising formulations of many NP problems”, A. Lucas, 2014 - Section 2.3.

import numpy as np
import networkx as nx
from qat.opt import KClique

graph = nx.Graph()
graph.add_nodes_from(np.arange(6))
graph.add_edges_from([(0,1), (0,2), (0,3), (0,4), (0,5), (1,2), (1,5)])

B = 1
K = 3
A = B*K + 1

k_clique_problem = KClique(graph, K, A, B=B)

print("To anneal the problem, the solver would need "
      + str(len(graph.nodes())) + " spins.")

To anneal the problem, the solver would need 6 spins.
Parameters

  • graph (networkx.Graph) – a networkx graph

  • K (int) – the size of the clique

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

get_best_parameters()
Returns

6-key dictionary containing

  • n_monte_carlo_updates (int) - the number of Monte Carlo updates

  • n_trotters (int) - the number of “classical replicas” or “Trotter replicas”

  • gamma_max (double) - the starting magnetic field

  • gamma_min (double) - the final magnetic field

  • temp_max (double) - the starting temperature

  • temp_min (double) - the final temperature

parse_result(result, inverse=False)

Returns the best approximated solution of the K-Clique problem from a list of samples

Parameters

result (BatchResult) – BatchResult containing a list of samples

Returns

The best partition among the samples with a K-clique as the first subset

Return type

GraphPartitioningResult

qat.opt.k_clique.produce_q_and_offset(graph, K, A, B=1)

Returns the \(Q\) matrix and the offset energy of the problem. The constant \(A\) should be bigger than \(K*B\) for a right encoding. They are also all positive.

Parameters

  • graph (networkx.Graph) – a networkx graph

  • K (int) – the size of the clique

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