def test_kraus_to_ptm_qubit(self):
p_damp = 0.5
damp_kraus_mat = np.array(
[[[1, 0], [0, np.sqrt(1 - p_damp)]],
[[0, np.sqrt(p_damp)], [0, 0]]])
gm_qubit_basis = (bases.gell_mann(2),)
gm_two_qubit_basis = gm_qubit_basis + gm_qubit_basis
damp_op = Operation.from_kraus(damp_kraus_mat, 2)
damp_ptm = damp_op.set_bases(bases_in=gm_qubit_basis,
bases_out=gm_qubit_basis).ptm
expected_mat = np.array([[1, 0, 0, 0],
[0, np.sqrt(1-p_damp), 0, 0],
[0, 0, np.sqrt(1-p_damp), 0],
[p_damp, 0, 0, 1-p_damp]])
assert np.allclose(damp_ptm, expected_mat)
with pytest.raises(ValueError, match=r'.* should be a list, .*'):
damp_op.set_bases(bases.gell_mann(2), bases.gell_mann(2))
cz_kraus_mat = np.diag([1, 1, 1, -1])
cz = Operation.from_kraus(cz_kraus_mat, 2).set_bases(gm_two_qubit_basis,
gm_two_qubit_basis)
assert cz.ptm.shape == (4, 4, 4, 4)
cz_ptm = cz.ptm.reshape((16, 16))
assert np.all(cz_ptm.round(3) <= 1)
assert np.all(cz_ptm.round(3) >= -1)
assert np.isclose(np.sum(cz_ptm[0, :]), 1)
assert np.isclose(np.sum(cz_ptm[:, 0]), 1)
def test_kraus_to_ptm_qubit(self):
p_damp = 0.5
damp_kraus_mat = np.array([[[1, 0], [0, np.sqrt(1 - p_damp)]],
[[0, np.sqrt(p_damp)], [0, 0]]])
gm_qubit_basis = (bases.gell_mann(2), )
gm_two_qubit_basis = gm_qubit_basis * 2
damp_op = Operation.from_kraus(damp_kraus_mat, gm_qubit_basis)
damp_ptm = damp_op.ptm(gm_qubit_basis)
expected_mat = np.array([[1, 0, 0, 0], [0,
np.sqrt(1 - p_damp), 0, 0],
[0, 0, np.sqrt(1 - p_damp), 0],
[p_damp, 0, 0, 1 - p_damp]])
assert np.allclose(damp_ptm, expected_mat)
with pytest.raises(ValueError, match=r'.* must be list-like, .*'):
damp_op.set_bases(bases.gell_mann(2), bases.gell_mann(2))
cz_kraus_mat = np.diag([1, 1, 1, -1])
cz = Operation.from_kraus(cz_kraus_mat, gm_two_qubit_basis)
cz_ptm = cz.ptm(gm_two_qubit_basis)
assert cz_ptm.shape == (4, 4, 4, 4)
cz_ptm = cz_ptm.reshape((16, 16))
assert np.all(cz_ptm.round(3) <= 1)
assert np.all(cz_ptm.round(3) >= -1)
assert np.isclose(np.sum(cz_ptm[0, :]), 1)
assert np.isclose(np.sum(cz_ptm[:, 0]), 1)
def test_lindblad_singlequbit(self):
ham = random_hermitian_matrix(2, seed=56)
lindblad_ops = np.array([
[[0, 0.1], [0, 0]],
[[0, 0], [0, 0.33]],
])
t1 = 10
t2 = 25
b1 = (bases.general(2), )
b2 = (bases.gell_mann(2), )
op1 = Operation.from_lindblad_form(t1,
b1,
b2,
hamiltonian=ham,
lindblad_ops=lindblad_ops)
op2 = Operation.from_lindblad_form(t2,
b2,
b1,
hamiltonian=ham,
lindblad_ops=lindblad_ops)
op = Operation.from_lindblad_form(t1 + t2,
b1,
hamiltonian=ham,
lindblad_ops=lindblad_ops)
dm = random_hermitian_matrix(2, seed=3)
state1 = PauliVector.from_dm(dm, b1)
state2 = PauliVector.from_dm(dm, b1)
op1(state1, 0)
op2(state1, 0)
op(state2, 0)
assert np.allclose(state1.to_pv(), state2.to_pv())
def test_convert_ptm_basis(self):
p_damp = 0.5
damp_kraus_mat = np.array([[[1, 0], [0, np.sqrt(1 - p_damp)]],
[[0, np.sqrt(p_damp)], [0, 0]]])
gell_mann_basis = (bases.gell_mann(2), )
general_basis = (bases.general(2), )
op1 = Operation.from_kraus(damp_kraus_mat, gell_mann_basis)
op2 = op1.set_bases(general_basis, general_basis) \
.set_bases(gell_mann_basis, gell_mann_basis)
assert np.allclose(op1.ptm(gell_mann_basis), op2.ptm(gell_mann_basis))
assert op1.bases_in == op2.bases_in
assert op1.bases_out == op2.bases_out
def phase_damping(total_rate=None, *, x_deph_rate=None,
y_deph_rate=None, z_deph_rate=None):
if total_rate is not None:
kraus = np.array([[[1, 0], [0, np.sqrt(1 - total_rate)]],
[[0, 0], [0, np.sqrt(total_rate)]]])
return Operation.from_kraus(kraus, 2)
else:
if None in (x_deph_rate, y_deph_rate, z_deph_rate):
raise ValueError(
"Either the total_rate or the dephasing rates along each of "
"the three axis must be provided")
ptm = np.diag(
[1, 1 - x_deph_rate, 1 - y_deph_rate, 1 - z_deph_rate])
return Operation.from_ptm(ptm, (bases.gell_mann(2),))
def test_kraus_to_ptm_qutrits(self):
cz_kraus_mat = np.diag([1, 1, 1, 1, -1, 1, -1, 1, 1])
qutrit_basis = (bases.gell_mann(3),)
system_bases = qutrit_basis * 2
cz = Operation.from_kraus(cz_kraus_mat, 3).set_bases(system_bases,
system_bases)
assert cz.ptm.shape == (9, 9, 9, 9)
cz_ptm_flat = cz.ptm.reshape((81, 81))
assert np.all(cz_ptm_flat.round(3) <= 1) and np.all(
cz.ptm.round(3) >= -1)
assert np.isclose(np.sum(cz_ptm_flat[0, :]), 1)
assert np.isclose(np.sum(cz_ptm_flat[:, 0]), 1)
def test_kraus_to_ptm_qutrits(self):
cz_kraus_mat = np.diag([1, 1, 1, 1, -1, 1, -1, 1, 1])
qutrit_basis = (bases.gell_mann(3), )
system_bases = qutrit_basis * 2
cz = Operation.from_kraus(cz_kraus_mat, system_bases)
cz_ptm = cz.ptm(system_bases)
assert cz_ptm.shape == (9, 9, 9, 9)
cz_ptm_flat = cz_ptm.reshape((81, 81))
assert np.all(cz_ptm_flat.round(3) <= 1) and np.all(
cz_ptm.round(3) >= -1)
assert np.isclose(np.sum(cz_ptm_flat[0, :]), 1)
assert np.isclose(np.sum(cz_ptm_flat[:, 0]), 1)
def test_convert_ptm_basis(self):
p_damp = 0.5
damp_kraus_mat = np.array(
[[[1, 0], [0, np.sqrt(1-p_damp)]],
[[0, np.sqrt(p_damp)], [0, 0]]])
gell_mann_basis = (bases.gell_mann(2),)
general_basis = (bases.general(2),)
damp_op_kraus = Operation.from_kraus(damp_kraus_mat, 2)
op1 = damp_op_kraus.set_bases(gell_mann_basis, gell_mann_basis)
op2 = damp_op_kraus.set_bases(general_basis, general_basis) \
.set_bases(gell_mann_basis, gell_mann_basis)
assert np.allclose(op1.ptm, op2.ptm)
assert op1.bases_in == op2.bases_in
assert op1.bases_out == op2.bases_out
def amp_damping(total_rate=None, *, exc_rate=None, damp_rate=None):
if total_rate is not None:
kraus = np.array([[[1, 0], [0, np.sqrt(1 - total_rate)]],
[[0, np.sqrt(total_rate)], [0, 0]]])
return Operation.from_kraus(kraus, 2)
else:
if None in (exc_rate, damp_rate):
raise ValueError(
"Either the total_rate or both the exc_rate and damp_rate "
"must be provided")
comb_rate = exc_rate + damp_rate
ptm = np.array([[1, 0, 0, 0], [0, np.sqrt((1 - comb_rate)), 0, 0],
[0, 0, np.sqrt((1 - comb_rate)), 0],
[2 * damp_rate - comb_rate, 0, 0, 1 - comb_rate]])
return Operation.from_ptm(ptm, (bases.gell_mann(2), ))
def phase_damping(total_rate=None,
*,
x_deph_rate=None,
y_deph_rate=None,
z_deph_rate=None):
if total_rate is not None:
kraus = np.array([[[1, 0], [0, np.sqrt(1 - total_rate)]],
[[0, 0], [0, np.sqrt(total_rate)]]])
return Operation.from_kraus(kraus, 2)
else:
if None in (x_deph_rate, y_deph_rate, z_deph_rate):
raise ValueError(
"Either the total_rate or the dephasing rates along each of "
"the three axis must be provided")
ptm = np.diag([1, 1 - x_deph_rate, 1 - y_deph_rate, 1 - z_deph_rate])
return Operation.from_ptm(ptm, (bases.gell_mann(2), ))
def amp_damping(total_rate=None, *, exc_rate=None, damp_rate=None):
if total_rate is not None:
kraus = np.array([[[1, 0], [0, np.sqrt(1 - total_rate)]],
[[0, np.sqrt(total_rate)], [0, 0]]])
return Operation.from_kraus(kraus, 2)
else:
if None in (exc_rate, damp_rate):
raise ValueError(
"Either the total_rate or both the exc_rate and damp_rate "
"must be provided")
comb_rate = exc_rate + damp_rate
ptm = np.array([
[1, 0, 0, 0],
[0, np.sqrt((1 - comb_rate)), 0, 0],
[0, 0, np.sqrt((1 - comb_rate)), 0],
[2*damp_rate - comb_rate, 0, 0, 1 - comb_rate]])
return Operation.from_ptm(ptm, (bases.gell_mann(2),))
import numpy as np
from functools import lru_cache
from quantumsim import bases, Operation
_PAULI = dict(zip(['I', 'X', 'Y', 'Z'], bases.gell_mann(2).vectors))
@lru_cache(maxsize=64)
def rotate_euler(phi, theta, lamda):
"""A perfect single qubit rotation described by three Euler angles.
Unitary operation, that corresponds to this rotation, is:
.. math::
U = R_Z(\\phi) \\cdot R_X(\\theta) \\cdot R_Z(\\lambda)
Parameters
----------
phi, theta, lamda: float
Euler rotation angles in radians.
Returns
-------
Operation
An operation, that corresponds to the rotation.
"""
exp_phi, exp_lambda = np.exp(1j * phi), np.exp(1j * lamda)
sin_theta, cos_theta = np.sin(theta / 2), np.cos(theta / 2)
matrix = np.array([
[cos_theta, -1j * exp_lambda * sin_theta],
import numpy as np
from functools import lru_cache
from scipy.linalg import expm
from quantumsim import bases, Operation
_PAULI = dict(zip(['I', 'X', 'Y', 'Z'], bases.gell_mann(2).vectors))
@lru_cache(maxsize=64)
def rotate_euler(phi, theta, lamda):
"""A perfect single qubit rotation described by three Euler angles.
Unitary operation, that corresponds to this rotation, is:
.. math::
U = R_Z(\\phi) \\cdot R_X(\\theta) \\cdot R_Z(\\lambda)
Parameters
----------
phi, theta, lamda: float
Euler rotation angles in radians.
Returns
-------
Operation
An operation, that corresponds to the rotation.
"""
exp_phi, exp_lambda = np.exp(1j * phi), np.exp(1j * lamda)
sin_theta, cos_theta = np.sin(theta / 2), np.cos(theta / 2)
matrix = np.array([
