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Source code for qiskit.finance.applications.ising.portfolio

# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 2021.
#
# 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 portfolio optimization instances into Pauli list
"""

import numpy as np
from sklearn.datasets import make_spd_matrix
from qiskit.quantum_info import Pauli

from qiskit.aqua import aqua_globals
from qiskit.aqua.operators import WeightedPauliOperator


[docs]def random_model(n, seed=None): """Generate random model (mu, sigma) for portfolio optimization problem. Args: n (int): number of assets. seed (int or None): random seed - if None, will not initialize. Returns: numpy.narray: expected return vector numpy.ndarray: covariance matrix """ if seed: aqua_globals.random_seed = seed # draw random return values between [0, 1] m_u = aqua_globals.random.uniform(size=n, low=0, high=1) # construct positive semi-definite covariance matrix sigma = make_spd_matrix(n) return m_u, sigma
[docs]def get_operator(mu, sigma, q, budget, penalty): # pylint: disable=invalid-name """ get qubit op """ # pylint: disable=invalid-name # get problem dimension n = len(mu) e = np.ones(n) E = np.matmul(np.asmatrix(e).T, np.asmatrix(e)) # map problem to Ising model offset = -1 * np.dot(mu, e) / 2 + penalty * budget ** 2 - \ budget * n * penalty + n ** 2 * penalty / 4 + q / 4 * np.dot(e, np.dot(sigma, e)) mu_z = mu / 2 + budget * penalty * e - n * penalty / 2 * e - q / 2 * np.dot(sigma, e) sigma_z = penalty / 4 * E + q / 4 * sigma # construct operator pauli_list = [] for i in range(n): i_ = i # i_ = n - i - 1 if np.abs(mu_z[i_]) > 1e-6: xp = np.zeros(n, dtype=bool) zp = np.zeros(n, dtype=bool) zp[i_] = True pauli_list.append([mu_z[i_], Pauli(zp, xp)]) for j in range(i): j_ = j # j_ = n-j-1 if np.abs(sigma_z[i_, j_]) > 1e-6: xp = np.zeros(n, dtype=bool) zp = np.zeros(n, dtype=bool) zp[i_] = True zp[j_] = True pauli_list.append([2 * sigma_z[i_, j_], Pauli(zp, xp)]) offset += sigma_z[i_, i_] return WeightedPauliOperator(paulis=pauli_list), offset
[docs]def portfolio_value(x, mu, sigma, q, budget, penalty): # pylint: disable=invalid-name """ returns portfolio value """ return q * np.dot(x, np.dot(sigma, x)) - np.dot(mu, x) + penalty * pow(sum(x) - budget, 2)
[docs]def portfolio_expected_value(x, mu): # pylint: disable=invalid-name """ returns portfolio expected value """ return np.dot(mu, x)
[docs]def portfolio_variance(x, sigma): """ returns portfolio variance """ return np.dot(x, np.dot(sigma, x))

© Copyright 2020, Qiskit Development Team. Last updated on 2021/03/04.

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