# -*- coding: utf-8 -*-
# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 2020.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""
Convert max-cut instances into Pauli list
Deal with Gset format. See https://web.stanford.edu/~yyye/yyye/Gset/
Design the max-cut object `w` as a two-dimensional np.array
e.g., w[i, j] = x means that the weight of a edge between i and j is x
Note that the weights are symmetric, i.e., w[j, i] = x always holds.
"""
import logging
import numpy as np
from qiskit.quantum_info import Pauli
from qiskit.aqua.operators import WeightedPauliOperator
logger = logging.getLogger(__name__)
[docs]def get_operator(weight_matrix):
"""Generate Hamiltonian for the max-cut problem of a graph.
Args:
weight_matrix (numpy.ndarray) : adjacency matrix.
Returns:
WeightedPauliOperator: operator for the Hamiltonian
float: a constant shift for the obj function.
"""
num_nodes = weight_matrix.shape[0]
pauli_list = []
shift = 0
for i in range(num_nodes):
for j in range(i):
if weight_matrix[i, j] != 0:
x_p = np.zeros(num_nodes, dtype=np.bool)
z_p = np.zeros(num_nodes, dtype=np.bool)
z_p[i] = True
z_p[j] = True
pauli_list.append([0.5 * weight_matrix[i, j], Pauli(z_p, x_p)])
shift -= 0.5 * weight_matrix[i, j]
return WeightedPauliOperator(paulis=pauli_list), shift
[docs]def max_cut_value(x, w):
"""Compute the value of a cut.
Args:
x (numpy.ndarray): binary string as numpy array.
w (numpy.ndarray): adjacency matrix.
Returns:
float: value of the cut.
"""
# pylint: disable=invalid-name
X = np.outer(x, (1 - x))
return np.sum(w * X)
[docs]def get_graph_solution(x):
"""Get graph solution from binary string.
Args:
x (numpy.ndarray) : binary string as numpy array.
Returns:
numpy.ndarray: graph solution as binary numpy array.
"""
return 1 - x