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Fixesapply_channel #155

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May 28, 2023
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Fixesapply_channel #155

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36 changes: 36 additions & 0 deletions tests/test_channel_ops/test_apply_channel.py
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Original file line number Diff line number Diff line change
@@ -1,8 +1,10 @@
"""Tests for apply_channel."""
import numpy as np
import pytest

from toqito.channel_ops import apply_channel
from toqito.perms import swap_operator
from toqito.matrices import pauli


def test_apply_channel_choi():
Expand All @@ -21,6 +23,21 @@ def test_apply_channel_choi():
bool_mat = np.isclose(res, expected_res)
np.testing.assert_equal(np.all(bool_mat), True)

def test_apply_channel_choi_non_square():
"""
The swap operator is the Choi matrix of the transpose map.

The following test is a (non-ideal, but illustrative) way of computing
the transpose of a non square matrix.
"""
test_input_mat = np.array([[0, 1], [2, 3], [4, 5]])

expected_res = np.array([[0, 2, 4], [1, 3, 5]])

res = apply_channel(test_input_mat, swap_operator([2, 3]))

bool_mat = np.isclose(res, expected_res)
np.testing.assert_equal(np.all(bool_mat), True)

def test_apply_channel_kraus():
"""
Expand All @@ -45,6 +62,25 @@ def test_apply_channel_kraus():
bool_mat = np.isclose(res, expected_res)
np.testing.assert_equal(np.all(bool_mat), True)

@pytest.mark.parametrize("nested", [1, 2, 3])
def test_apply_channel_cpt_kraus(nested):
"""
Apply Kraus map of single qubit depolarizing channel.
"""
test_input_mat = np.array([[1, 0], [0, 0]])

expected_res = np.array([[0.5, 0], [0, 0.5]])

kraus = [0.5 * pauli(ind) for ind in range(4)]
if nested == 2:
kraus = [kraus]
elif nested == 3:
kraus = [[mat] for mat in kraus]

res = apply_channel(test_input_mat, kraus)

bool_mat = np.isclose(res, expected_res)
np.testing.assert_equal(np.all(bool_mat), True)

def test_apply_channel_invalid_input():
"""Invalid input for apply map."""
Expand Down
30 changes: 30 additions & 0 deletions tests/test_channel_ops/test_partial_channel.py
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Original file line number Diff line number Diff line change
@@ -1,8 +1,10 @@
"""Tests for partial_channel."""
import numpy as np
import pytest

from toqito.channel_ops import partial_channel
from toqito.channels import depolarizing
from toqito.matrices import pauli


def test_partial_channel_depolarizing_first_system():
Expand Down Expand Up @@ -122,6 +124,34 @@ def test_partial_channel_dim_list():
np.testing.assert_equal(np.all(bool_mat), True)


@pytest.mark.parametrize("nested", [1, 2, 3])
def test_partial_channel_cpt_kraus(nested):
"""
Perform the partial map using the Kraus representation of
the depolarizing channel.
"""
rho = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]])
kraus = [0.5 * pauli(ind) for ind in range(4)]
if nested == 2:
kraus = [kraus]
elif nested == 3:
kraus = [[mat] for mat in kraus]

res = partial_channel(rho, kraus)

expected_res = np.array(
[
[3.5, 0.0, 5.5, 0.0],
[0.0, 3.5, 0.0, 5.5],
[11.5, 0.0, 13.5, 0.0],
[0.0, 11.5, 0.0, 13.5],
]
)

bool_mat = np.isclose(expected_res, res)
np.testing.assert_equal(np.all(bool_mat), True)


def test_partial_channel_non_square_matrix():
"""Matrix must be square."""
with np.testing.assert_raises(ValueError):
Expand Down
6 changes: 3 additions & 3 deletions tests/test_channel_props/test_is_unital.py
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Original file line number Diff line number Diff line change
Expand Up @@ -31,9 +31,9 @@ def test_is_unital_swap_operator_choi_true():
np.testing.assert_equal(is_unital(swap_operator(3)), True)


def test_is_unital_depolarizing_choi_false():
"""Verify Choi matrix of the depolarizing map is not unital."""
np.testing.assert_equal(is_unital(depolarizing(4)), False)
def test_is_unital_depolarizing_choi_true():
"""Verify Choi matrix of the depolarizing map is unital."""
np.testing.assert_equal(is_unital(depolarizing(4)), True)


if __name__ == "__main__":
Expand Down
6 changes: 3 additions & 3 deletions tests/test_channels/test_dephasing.py
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Original file line number Diff line number Diff line change
Expand Up @@ -20,10 +20,10 @@ def test_dephasing_completely_dephasing():
def test_dephasing_partially_dephasing():
"""The partially dephasing channel for `p = 0.5`."""
test_input_mat = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]])
param_p = 0.5

expected_res = np.array([[17.5, 0, 0, 0], [0, 20, 0, 0], [0, 0, 22.5, 0], [0, 0, 0, 25]])

res = apply_channel(test_input_mat, dephasing(4, 0.5))
res = apply_channel(test_input_mat, dephasing(4, param_p))
expected_res = (1 - param_p) * np.diag(np.diag(test_input_mat)) + param_p * test_input_mat

bool_mat = np.isclose(expected_res, res)
np.testing.assert_equal(np.all(bool_mat), True)
Expand Down
19 changes: 6 additions & 13 deletions tests/test_channels/test_depolarizing.py
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Original file line number Diff line number Diff line change
Expand Up @@ -11,9 +11,7 @@ def test_depolarizing_complete_depolarizing():
[[1 / 2, 0, 0, 1 / 2], [0, 0, 0, 0], [0, 0, 0, 0], [1 / 2, 0, 0, 1 / 2]]
)

expected_res = (
1 / 4 * np.array([[1 / 2, 0, 0, 1 / 2], [0, 0, 0, 0], [0, 0, 0, 0], [1 / 2, 0, 0, 1 / 2]])
)
expected_res = 1 / 4 * np.identity(4)

res = apply_channel(test_input_mat, depolarizing(4))

Expand All @@ -24,17 +22,12 @@ def test_depolarizing_complete_depolarizing():
def test_depolarizing_partially_depolarizing():
"""The partially depolarizing channel for `p = 0.5`."""
test_input_mat = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]])
param_p = 0.5

expected_res = np.array(
[
[17.125, 0.25, 0.375, 0.5],
[0.625, 17.75, 0.875, 1],
[1.125, 1.25, 18.375, 1.5],
[1.625, 1.75, 1.875, 19],
]
)

res = apply_channel(test_input_mat, depolarizing(4, 0.5))
res = apply_channel(test_input_mat, depolarizing(4, param_p))
expected_res = (1 - param_p) * np.trace(test_input_mat) * np.identity(
4
) / 4 + param_p * test_input_mat

bool_mat = np.isclose(expected_res, res)
np.testing.assert_equal(np.all(bool_mat), True)
Expand Down
30 changes: 19 additions & 11 deletions toqito/channel_ops/apply_channel.py
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Original file line number Diff line number Diff line change
@@ -1,6 +1,7 @@
"""Apply channel to an operator."""
from __future__ import annotations
import numpy as np
import itertools

from toqito.matrix_ops import vec
from toqito.perms import swap
Expand Down Expand Up @@ -101,23 +102,29 @@ def apply_channel(mat: np.ndarray, phi_op: np.ndarray | list[list[np.ndarray]])
if isinstance(phi_op, list):
s_phi_op = [len(phi_op), len(phi_op[0])]

# Map is completely positive.
if s_phi_op[1] == 1 or (s_phi_op[0] == 1 and s_phi_op[1] > 2):
for i in range(s_phi_op[0]):
phi_op[i][1] = phi_op[i][0].conj().T
else:
for i in range(s_phi_op[0]):
phi_op[i][1] = phi_op[i][1].conj().T
phi_0_list = []
phi_1_list = []
for i in range(s_phi_op[0]):
phi_0_list.append(phi_op[i][0])
phi_1_list.append(phi_op[i][1])

# Map is completely positive if input is given as:
# 1. [K1, K2, .. Kr]
# 2. [[K1], [K2], .. [Kr]]
# 3. [[K1, K2, .. Kr]] and r > 2
if isinstance(phi_op[0], np.ndarray):
phi_0_list = phi_op
elif s_phi_op[1] == 1 or (s_phi_op[0] == 1 and s_phi_op[1] > 2):
phi_0_list = list(itertools.chain(*phi_op))
else:
# Input is given as: [[A1, B1], [A2, B2], .. [Ar, Br]]
phi_0_list = [k_mat[0] for k_mat in phi_op]
phi_1_list = [k_mat[1].conj().T for k_mat in phi_op]

if not phi_1_list:
phi_1_list = [k_mat.conj().T for k_mat in phi_0_list]

k_1 = np.concatenate(phi_0_list, axis=1)
k_2 = np.concatenate(phi_1_list, axis=0)

a_mat = np.kron(np.identity(len(phi_op)), mat)
a_mat = np.kron(np.identity(len(phi_0_list)), mat)
return k_1 @ a_mat @ k_2

# The superoperator was given as a Choi matrix:
Expand All @@ -134,6 +141,7 @@ def apply_channel(mat: np.ndarray, phi_op: np.ndarray | list[list[np.ndarray]])
True,
).T,
(int(phi_size[0] * np.prod(mat_size)), int(phi_size[1])),
order="F"
)
return a_mat @ b_mat
raise ValueError(
Expand Down
41 changes: 25 additions & 16 deletions toqito/channel_ops/partial_channel.py
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Original file line number Diff line number Diff line change
@@ -1,6 +1,7 @@
"""Apply channel a subsystem of an operator."""
from __future__ import annotations
import numpy as np
import itertools

from toqito.channel_ops import apply_channel
from toqito.states import max_entangled
Expand Down Expand Up @@ -93,11 +94,19 @@ def partial_channel(
if isinstance(phi_map, list):
# Compute the Kraus operators on the full system.
s_phi_1, s_phi_2 = len(phi_map), len(phi_map[0])

# Map is completely positive.
if s_phi_2 == 1 or s_phi_1 == 1 and s_phi_2 > 2:
phi_list = []
# Map is completely positive if input is given as:
# 1. [K1, K2, .. Kr]
# 2. [[K1], [K2], .. [Kr]]
# 3. [[K1, K2, .. Kr]] and r > 2
if isinstance(phi_map[0], np.ndarray):
phi_list = phi_map
elif s_phi_2 == 1 or s_phi_1 == 1 and s_phi_2 > 2:
phi_list = list(itertools.chain(*phi_map))

if phi_list:
phi = []
for m in phi_map:
for m in phi_list:
phi.append(
np.kron(
np.kron(np.identity(prod_dim_r1), m),
Expand Down Expand Up @@ -134,27 +143,27 @@ def partial_channel(
dim = np.array(
[
[
prod_dim_r2,
prod_dim_r2,
int(dim[0, sys - 1]),
int(dim_phi[0] / dim[0, sys - 1]),
prod_dim_r1,
prod_dim_r1,
int(dim[0, sys - 1]),
int(dim_phi[0] / dim[0, sys - 1]),
prod_dim_r2,
prod_dim_r2,
],
[
prod_dim_c2,
prod_dim_c2,
int(dim[1, sys - 1]),
int(dim_phi[1] / dim[1, sys - 1]),
prod_dim_c1,
prod_dim_c1,
int(dim[1, sys - 1]),
int(dim_phi[1] / dim[1, sys - 1]),
prod_dim_c2,
prod_dim_c2,
],
]
)
psi_r1 = max_entangled(prod_dim_r2, False, False)
psi_c1 = max_entangled(prod_dim_c2, False, False)
psi_r2 = max_entangled(prod_dim_r1, False, False)
psi_c2 = max_entangled(prod_dim_c1, False, False)
psi_r1 = max_entangled(prod_dim_r1, False, False)
psi_c1 = max_entangled(prod_dim_c1, False, False)
psi_r2 = max_entangled(prod_dim_r2, False, False)
psi_c2 = max_entangled(prod_dim_c2, False, False)

phi_map = permute_systems(
np.kron(np.kron(psi_r1 * psi_c1.conj().T, phi_map), psi_r2 * psi_c2.conj().T),
Expand Down
8 changes: 4 additions & 4 deletions toqito/channels/dephasing.py
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Original file line number Diff line number Diff line change
Expand Up @@ -66,10 +66,10 @@ def dephasing(dim: int, param_p: float = 0) -> np.ndarray:
>>> [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]
>>> )
>>> apply_channel(test_input_mat, dephasing(4, 0.5))
[[17.5 0. 0. 0. ]
[ 0. 20. 0. 0. ]
[ 0. 0. 22.5 0. ]
[ 0. 0. 0. 25. ]]
[[ 1. 1. 1.5 2. ]
[ 2.5 6. 3.5 4. ]
[ 4.5 5. 11. 6. ]
[ 6.5 7. 7.5 16. ]]

References
==========
Expand Down
24 changes: 12 additions & 12 deletions toqito/channels/depolarizing.py
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Expand Up @@ -42,10 +42,10 @@ def depolarizing(dim: int, param_p: float = 0) -> np.ndarray:

.. math::
\Phi(\rho) = \frac{1}{4} \begin{pmatrix}
\frac{1}{2} & 0 & 0 & \frac{1}{2} \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
\frac{1}{2} & 0 & 0 & \frac{1}{2}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{pmatrix}.

This can be observed in :code:`toqito` as follows.
Expand All @@ -57,10 +57,10 @@ def depolarizing(dim: int, param_p: float = 0) -> np.ndarray:
>>> [[1 / 2, 0, 0, 1 / 2], [0, 0, 0, 0], [0, 0, 0, 0], [1 / 2, 0, 0, 1 / 2]]
>>> )
>>> apply_channel(test_input_mat, depolarizing(4))
[[0.125 0. 0. 0.125]
[0. 0. 0. 0. ]
[0. 0. 0. 0. ]
[0.125 0. 0. 0.125]]
[[0.25 0. 0. 0. ]
[0. 0.25 0. 0. ]
[0. 0. 0.25 0. ]
[0. 0. 0. 0.25]]

>>> from toqito.channel_ops import apply_channel
>>> from toqito.channels import depolarizing
Expand All @@ -69,10 +69,10 @@ def depolarizing(dim: int, param_p: float = 0) -> np.ndarray:
>>> [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]
>>> )
>>> apply_channel(test_input_mat, depolarizing(4, 0.5))
[[17.125 0.25 0.375 0.5 ]
[ 0.625 17.75 0.875 1. ]
[ 1.125 1.25 18.375 1.5 ]
[ 1.625 1.75 1.875 19. ]]
[[ 4.75 1. 1.5 2. ]
[ 2.5 7.25 3.5 4. ]
[ 4.5 5. 9.75 6. ]
[ 6.5 7. 7.5 12.25]]


References
Expand Down