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qiskit/test/python/quantum_info/states/test_measures.py

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# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 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.
"""Quick program to test the quantum information states modules."""
import unittest
import numpy as np
from qiskit import QiskitError
from qiskit.quantum_info.states import DensityMatrix, Statevector
from qiskit.quantum_info import state_fidelity
from qiskit.quantum_info import purity
from qiskit.quantum_info import entropy
from qiskit.quantum_info import concurrence
from qiskit.quantum_info import entanglement_of_formation
from qiskit.quantum_info import mutual_information
from qiskit.quantum_info.states import shannon_entropy
from qiskit.quantum_info import negativity
from test import QiskitTestCase # pylint: disable=wrong-import-order
class TestStateMeasures(QiskitTestCase):
"""Tests state measure functions"""
def test_state_fidelity_statevector(self):
"""Test state_fidelity function for statevector inputs"""
psi1 = [0.70710678118654746, 0, 0, 0.70710678118654746]
psi2 = [0.0, 0.70710678118654746, 0.70710678118654746, 0.0]
self.assertAlmostEqual(state_fidelity(psi1, psi1), 1.0, places=7, msg="vector-vector input")
self.assertAlmostEqual(state_fidelity(psi2, psi2), 1.0, places=7, msg="vector-vector input")
self.assertAlmostEqual(state_fidelity(psi1, psi2), 0.0, places=7, msg="vector-vector input")
psi1 = Statevector([0.70710678118654746, 0, 0, 0.70710678118654746])
psi2 = Statevector([0.0, 0.70710678118654746, 0.70710678118654746, 0.0])
self.assertAlmostEqual(state_fidelity(psi1, psi1), 1.0, places=7, msg="vector-vector input")
self.assertAlmostEqual(state_fidelity(psi2, psi2), 1.0, places=7, msg="vector-vector input")
self.assertAlmostEqual(state_fidelity(psi1, psi2), 0.0, places=7, msg="vector-vector input")
psi1 = Statevector([1, 0, 0, 1]) # invalid state
psi2 = Statevector([1, 0, 0, 0])
self.assertRaises(QiskitError, state_fidelity, psi1, psi2)
self.assertRaises(QiskitError, state_fidelity, psi1, psi2, validate=True)
self.assertEqual(state_fidelity(psi1, psi2, validate=False), 1)
def test_state_fidelity_density_matrix(self):
"""Test state_fidelity function for density matrix inputs"""
rho1 = [[0.5, 0, 0, 0.5], [0, 0, 0, 0], [0, 0, 0, 0], [0.5, 0, 0, 0.5]]
mix = [[0.25, 0, 0, 0], [0, 0.25, 0, 0], [0, 0, 0.25, 0], [0, 0, 0, 0.25]]
self.assertAlmostEqual(state_fidelity(rho1, rho1), 1.0, places=7, msg="matrix-matrix input")
self.assertAlmostEqual(state_fidelity(mix, mix), 1.0, places=7, msg="matrix-matrix input")
self.assertAlmostEqual(state_fidelity(rho1, mix), 0.25, places=7, msg="matrix-matrix input")
rho1 = DensityMatrix(rho1)
mix = DensityMatrix(mix)
self.assertAlmostEqual(state_fidelity(rho1, rho1), 1.0, places=7, msg="matrix-matrix input")
self.assertAlmostEqual(state_fidelity(mix, mix), 1.0, places=7, msg="matrix-matrix input")
self.assertAlmostEqual(state_fidelity(rho1, mix), 0.25, places=7, msg="matrix-matrix input")
rho1 = DensityMatrix([1, 0, 0, 0])
mix = DensityMatrix(np.diag([1, 0, 0, 1]))
self.assertRaises(QiskitError, state_fidelity, rho1, mix)
self.assertRaises(QiskitError, state_fidelity, rho1, mix, validate=True)
self.assertEqual(state_fidelity(rho1, mix, validate=False), 1)
def test_state_fidelity_mixed(self):
"""Test state_fidelity function for statevector and density matrix inputs"""
psi1 = Statevector([0.70710678118654746, 0, 0, 0.70710678118654746])
rho1 = DensityMatrix([[0.5, 0, 0, 0.5], [0, 0, 0, 0], [0, 0, 0, 0], [0.5, 0, 0, 0.5]])
mix = DensityMatrix([[0.25, 0, 0, 0], [0, 0.25, 0, 0], [0, 0, 0.25, 0], [0, 0, 0, 0.25]])
self.assertAlmostEqual(state_fidelity(psi1, rho1), 1.0, places=7, msg="vector-matrix input")
self.assertAlmostEqual(state_fidelity(psi1, mix), 0.25, places=7, msg="vector-matrix input")
self.assertAlmostEqual(state_fidelity(rho1, psi1), 1.0, places=7, msg="matrix-vector input")
def test_purity_statevector(self):
"""Test purity function on statevector inputs"""
psi = Statevector([1, 0, 0, 0])
self.assertEqual(purity(psi), 1)
self.assertEqual(purity(psi, validate=True), 1)
self.assertEqual(purity(psi, validate=False), 1)
psi = [0.70710678118654746, 0.70710678118654746]
self.assertAlmostEqual(purity(psi), 1)
self.assertAlmostEqual(purity(psi, validate=True), 1)
self.assertAlmostEqual(purity(psi, validate=False), 1)
psi = np.array([0.5, 0.5j, -0.5j, -0.5])
self.assertAlmostEqual(purity(psi), 1)
self.assertAlmostEqual(purity(psi, validate=True), 1)
self.assertAlmostEqual(purity(psi, validate=False), 1)
psi = Statevector([1, 0, 0, 1])
self.assertRaises(QiskitError, purity, psi)
self.assertRaises(QiskitError, purity, psi, validate=True)
self.assertEqual(purity(psi, validate=False), 4)
def test_purity_density_matrix(self):
"""Test purity function on density matrix inputs"""
rho = DensityMatrix(np.diag([1, 0, 0, 0]))
self.assertEqual(purity(rho), 1)
self.assertEqual(purity(rho, validate=True), 1)
self.assertEqual(purity(rho, validate=False), 1)
rho = np.diag([0.25, 0.25, 0.25, 0.25])
self.assertEqual(purity(rho), 0.25)
self.assertEqual(purity(rho, validate=True), 0.25)
self.assertEqual(purity(rho, validate=False), 0.25)
rho = [[0.5, 0, 0, 0.5], [0, 0, 0, 0], [0, 0, 0, 0], [0.5, 0, 0, 0.5]]
self.assertEqual(purity(rho), 1)
self.assertEqual(purity(rho, validate=True), 1)
self.assertEqual(purity(rho, validate=False), 1)
rho = np.diag([1, 0, 0, 1])
self.assertRaises(QiskitError, purity, rho)
self.assertRaises(QiskitError, purity, rho, validate=True)
self.assertEqual(purity(rho, validate=False), 2)
def test_purity_equivalence(self):
"""Test purity is same for equivalent inputs"""
for alpha, beta in [
(0, 0),
(0, 0.25),
(0.25, 0),
(0.33, 0.33),
(0.5, 0.5),
(0.75, 0.25),
(0, 0.75),
]:
psi = Statevector([alpha, beta, 0, 1j * np.sqrt(1 - alpha**2 - beta**2)])
rho = DensityMatrix(psi)
self.assertAlmostEqual(purity(psi), purity(rho))
def test_entropy_statevector(self):
"""Test entropy function on statevector inputs"""
test_psis = [
[1, 0],
[0, 1, 0, 0],
[0.5, 0.5, 0.5, 0.5],
[0.5, 0.5j, -0.5j, 0.5],
[0.70710678118654746, 0, 0, -0.70710678118654746j],
[0.70710678118654746] + (14 * [0]) + [0.70710678118654746j],
]
for psi_ls in test_psis:
self.assertEqual(entropy(psi_ls), 0)
self.assertEqual(entropy(np.array(psi_ls)), 0)
def test_entropy_density_matrix(self):
"""Test entropy function on density matrix inputs"""
# Density matrix input
rhos = [DensityMatrix(np.diag([0.5] + (n * [0]) + [0.5])) for n in range(1, 5)]
for rho in rhos:
self.assertAlmostEqual(entropy(rho), 1)
self.assertAlmostEqual(entropy(rho, base=2), 1)
self.assertAlmostEqual(entropy(rho, base=np.e), -1 * np.log(0.5))
# Array input
for prob in [0.001, 0.3, 0.7, 0.999]:
rho = np.diag([prob, 1 - prob])
self.assertAlmostEqual(entropy(rho), shannon_entropy([prob, 1 - prob]))
self.assertAlmostEqual(
entropy(rho, base=np.e), shannon_entropy([prob, 1 - prob], base=np.e)
)
self.assertAlmostEqual(entropy(rho, base=2), shannon_entropy([prob, 1 - prob], base=2))
# List input
rho = [[0.5, 0], [0, 0.5]]
self.assertAlmostEqual(entropy(rho), 1)
def test_entropy_equivalence(self):
"""Test entropy is same for equivalent inputs"""
for alpha, beta in [
(0, 0),
(0, 0.25),
(0.25, 0),
(0.33, 0.33),
(0.5, 0.5),
(0.75, 0.25),
(0, 0.75),
]:
psi = Statevector([alpha, beta, 0, 1j * np.sqrt(1 - alpha**2 - beta**2)])
rho = DensityMatrix(psi)
self.assertAlmostEqual(entropy(psi), entropy(rho))
def test_concurrence_statevector(self):
"""Test concurrence function on statevector inputs"""
# Statevector input
psi = Statevector([0.70710678118654746, 0, 0, -0.70710678118654746j])
self.assertAlmostEqual(concurrence(psi), 1)
# List input
psi = [1, 0, 0, 0]
self.assertAlmostEqual(concurrence(psi), 0)
# Array input
psi = np.array([0.5, 0.5, 0.5, 0.5])
self.assertAlmostEqual(concurrence(psi), 0)
# Larger than 2 qubit input
psi_ls = [0.70710678118654746] + (14 * [0]) + [0.70710678118654746j]
psi = Statevector(psi_ls, dims=(2, 8))
self.assertAlmostEqual(concurrence(psi), 1)
psi = Statevector(psi_ls, dims=(4, 4))
self.assertAlmostEqual(concurrence(psi), 1)
psi = Statevector(psi_ls, dims=(8, 2))
self.assertAlmostEqual(concurrence(psi), 1)
def test_concurrence_density_matrix(self):
"""Test concurrence function on density matrix inputs"""
# Density matrix input
rho1 = DensityMatrix([[0.5, 0, 0, 0.5], [0, 0, 0, 0], [0, 0, 0, 0], [0.5, 0, 0, 0.5]])
rho2 = DensityMatrix([[0, 0, 0, 0], [0, 0.5, -0.5j, 0], [0, 0.5j, 0.5, 0], [0, 0, 0, 0]])
self.assertAlmostEqual(concurrence(rho1), 1)
self.assertAlmostEqual(concurrence(rho2), 1)
self.assertAlmostEqual(concurrence(0.5 * rho1 + 0.5 * rho2), 0)
self.assertAlmostEqual(concurrence(0.75 * rho1 + 0.25 * rho2), 0.5)
# List input
rho = [[0.5, 0.5, 0, 0], [0.5, 0.5, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
self.assertEqual(concurrence(rho), 0)
# Array input
rho = np.diag([0.25, 0.25, 0.25, 0.25])
self.assertEqual(concurrence(rho), 0)
def test_concurrence_equivalence(self):
"""Test concurrence is same for equivalent inputs"""
for alpha, beta in [
(0, 0),
(0, 0.25),
(0.25, 0),
(0.33, 0.33),
(0.5, 0.5),
(0.75, 0.25),
(0, 0.75),
]:
psi = Statevector([alpha, beta, 0, 1j * np.sqrt(1 - alpha**2 - beta**2)])
rho = DensityMatrix(psi)
self.assertAlmostEqual(concurrence(psi), concurrence(rho))
def test_entanglement_of_formation_statevector(self):
"""Test entanglement of formation function on statevector inputs"""
# Statevector input
psi = Statevector([0.70710678118654746, 0, 0, -0.70710678118654746j])
self.assertAlmostEqual(entanglement_of_formation(psi), 1)
# List input
psi = [1, 0, 0, 0]
self.assertAlmostEqual(entanglement_of_formation(psi), 0)
# Array input
psi = np.array([0.5, 0.5, 0.5, 0.5])
self.assertAlmostEqual(entanglement_of_formation(psi), 0)
# Larger than 2 qubit input
psi_ls = [0.70710678118654746] + (14 * [0]) + [0.70710678118654746j]
psi = Statevector(psi_ls, dims=(2, 8))
self.assertAlmostEqual(entanglement_of_formation(psi), 1)
psi = Statevector(psi_ls, dims=(4, 4))
self.assertAlmostEqual(entanglement_of_formation(psi), 1)
psi = Statevector(psi_ls, dims=(8, 2))
self.assertAlmostEqual(entanglement_of_formation(psi), 1)
def test_entanglement_of_formation_density_matrix(self):
"""Test entanglement of formation function on density matrix inputs"""
# Density matrix input
rho1 = DensityMatrix([[0.5, 0, 0, 0.5], [0, 0, 0, 0], [0, 0, 0, 0], [0.5, 0, 0, 0.5]])
rho2 = DensityMatrix([[0, 0, 0, 0], [0, 0.5, -0.5j, 0], [0, 0.5j, 0.5, 0], [0, 0, 0, 0]])
self.assertAlmostEqual(entanglement_of_formation(rho1), 1)
self.assertAlmostEqual(entanglement_of_formation(rho2), 1)
self.assertAlmostEqual(entanglement_of_formation(0.5 * rho1 + 0.5 * rho2), 0)
self.assertAlmostEqual(
entanglement_of_formation(0.75 * rho1 + 0.25 * rho2), 0.35457890266527003
)
# List input
rho = [[0.5, 0.5, 0, 0], [0.5, 0.5, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
self.assertEqual(entanglement_of_formation(rho), 0)
# Array input
rho = np.diag([0.25, 0.25, 0.25, 0.25])
self.assertEqual(entanglement_of_formation(rho), 0)
def test_entanglement_of_formation_equivalence(self):
"""Test entanglement of formation is same for equivalent inputs"""
for alpha, beta in [
(0, 0),
(0, 0.25),
(0.25, 0),
(0.33, 0.33),
(0.5, 0.5),
(0.75, 0.25),
(0, 0.75),
]:
psi = Statevector([alpha, beta, 0, 1j * np.sqrt(1 - alpha**2 - beta**2)])
rho = DensityMatrix(psi)
self.assertAlmostEqual(entanglement_of_formation(psi), entanglement_of_formation(rho))
def test_mutual_information_statevector(self):
"""Test mutual_information function on statevector inputs"""
# Statevector input
psi = Statevector([0.70710678118654746, 0, 0, -0.70710678118654746j])
self.assertAlmostEqual(mutual_information(psi), 2)
# List input
psi = [1, 0, 0, 0]
self.assertAlmostEqual(mutual_information(psi), 0)
# Array input
psi = np.array([0.5, 0.5, 0.5, 0.5])
self.assertAlmostEqual(mutual_information(psi), 0)
# Larger than 2 qubit input
psi_ls = [0.70710678118654746] + (14 * [0]) + [0.70710678118654746j]
psi = Statevector(psi_ls, dims=(2, 8))
self.assertAlmostEqual(mutual_information(psi), 2)
psi = Statevector(psi_ls, dims=(4, 4))
self.assertAlmostEqual(mutual_information(psi), 2)
psi = Statevector(psi_ls, dims=(8, 2))
self.assertAlmostEqual(mutual_information(psi), 2)
def test_mutual_information_density_matrix(self):
"""Test mutual_information function on density matrix inputs"""
# Density matrix input
rho1 = DensityMatrix([[0.5, 0, 0, 0.5], [0, 0, 0, 0], [0, 0, 0, 0], [0.5, 0, 0, 0.5]])
rho2 = DensityMatrix([[0, 0, 0, 0], [0, 0.5, -0.5j, 0], [0, 0.5j, 0.5, 0], [0, 0, 0, 0]])
self.assertAlmostEqual(mutual_information(rho1), 2)
self.assertAlmostEqual(mutual_information(rho2), 2)
# List input
rho = [[0.5, 0.5, 0, 0], [0.5, 0.5, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
self.assertEqual(mutual_information(rho), 0)
# Array input
rho = np.diag([0.25, 0.25, 0.25, 0.25])
self.assertEqual(mutual_information(rho), 0)
def test_mutual_information_equivalence(self):
"""Test mutual_information is same for equivalent inputs"""
for alpha, beta in [
(0, 0),
(0, 0.25),
(0.25, 0),
(0.33, 0.33),
(0.5, 0.5),
(0.75, 0.25),
(0, 0.75),
]:
psi = Statevector([alpha, beta, 0, 1j * np.sqrt(1 - alpha**2 - beta**2)])
rho = DensityMatrix(psi)
self.assertAlmostEqual(mutual_information(psi), mutual_information(rho))
def test_negativity_statevector(self):
"""Test negativity function on statevector inputs"""
# Constructing separable quantum statevector
state = Statevector([1 / np.sqrt(2), 1 / np.sqrt(2), 0, 0])
negv = negativity(state, [0])
self.assertAlmostEqual(negv, 0, places=7)
# Constructing entangled quantum statevector
state = Statevector([0, 1 / np.sqrt(2), -1 / np.sqrt(2), 0])
negv = negativity(state, [1])
self.assertAlmostEqual(negv, 0.5, places=7)
def test_negativity_density_matrix(self):
"""Test negativity function on density matrix inputs"""
# Constructing separable quantum state
rho = DensityMatrix.from_label("10+")
negv = negativity(rho, [0, 1])
self.assertAlmostEqual(negv, 0, places=7)
negv = negativity(rho, [0, 2])
self.assertAlmostEqual(negv, 0, places=7)
# Constructing entangled quantum state
rho = DensityMatrix([[0, 0, 0, 0], [0, 0.5, -0.5, 0], [0, -0.5, 0.5, 0], [0, 0, 0, 0]])
negv = negativity(rho, [0])
self.assertAlmostEqual(negv, 0.5, places=7)
negv = negativity(rho, [1])
self.assertAlmostEqual(negv, 0.5, places=7)
if __name__ == "__main__":
unittest.main()
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