def spin_coherent(j, theta, phi, type='ket'):
r"""Generate the coherent spin state :math:`\lvert \theta, \phi\rangle`.
Parameters
----------
j : float
The spin of the state.
theta : float
Angle from z axis.
phi : float
Angle from x axis.
type : string {'ket', 'bra', 'dm'}
Type of state to generate.
Returns
-------
state : qobj
Qobj quantum object for spin coherent state
"""
Sp = jmat(j, '+')
Sm = jmat(j, '-')
psi = (0.5 * theta * np.exp(1j * phi) * Sm -
0.5 * theta * np.exp(-1j * phi) * Sp).expm() * spin_state(j, j)
if type == 'ket':
return psi
elif type == 'bra':
return psi.dag()
elif type == 'dm':
return ket2dm(psi)
else:
raise ValueError("invalid value keyword argument 'type'")
def rand_super(dim=5):
H = rand_herm(dim)
return propagator(
H, np.random.rand(),
[create(dim),
destroy(dim),
jmat(float(dim - 1) / 2.0, 'z')])
def rand_super(N=5, dims=None):
"""
Returns a randomly drawn superoperator acting on operators acting on
N dimensions.
Parameters
----------
N : int
Square root of the dimension of the superoperator to be returned.
dims : list
Dimensions of quantum object. Used for specifying
tensor structure. Default is dims=[[[N],[N]], [[N],[N]]].
"""
if dims is not None:
# TODO: check!
pass
else:
dims = [[[N], [N]], [[N], [N]]]
H = rand_herm(N)
S = propagator(
H, np.random.rand(),
[create(N), destroy(N),
jmat(float(N - 1) / 2.0, 'z')])
S.dims = dims
return S
def stochastic_noise_Yue(rho, t, normalization, hbar, gamma):
temp = jmat(1)
sum = 0
for i in range(0, 3):
j = temp[i].full()
sum += commutator(j, commutator(j, rho))
return -gamma / 2 * sum
def test_SuperChoiSuper(self):
"""
Superoperator: Converting superoperator to Choi matrix and back.
"""
h_5 = rand_herm(5)
superoperator = propagator(h_5, scipy.rand(),
[create(5), destroy(5), jmat(2, 'z')])
choi_matrix = super_to_choi(superoperator)
test_supe = choi_to_super(choi_matrix)
assert_((test_supe - superoperator).norm() < 1e-12)
def test_ChoiKrausChoi(self):
"""
Superoperator: Converting superoperator to Choi matrix and back.
"""
h_5 = rand_herm(5)
superoperator = propagator(h_5, scipy.rand(),
[create(5), destroy(5), jmat(2, 'z')])
choi_matrix = super_to_choi(superoperator)
kraus_ops = choi_to_kraus(choi_matrix)
test_choi = kraus_to_choi(kraus_ops)
assert_((test_choi - choi_matrix).norm() < 1e-12)
def test_SuperChoiSuper(self):
"""
Superoperator: Converting superoperator to Choi matrix and back.
"""
h_5 = rand_herm(5)
superoperator = propagator(
h_5, scipy.rand(),
[create(5), destroy(5), jmat(2, 'z')])
choi_matrix = super_to_choi(superoperator)
test_supe = choi_to_super(choi_matrix)
assert_((test_supe - superoperator).norm() < 1e-12)
def test_ChoiKrausChoi(self):
"""
Superoperator: Converting superoperator to Choi matrix and back.
"""
h_5 = rand_herm(5)
superoperator = propagator(
h_5, scipy.rand(),
[create(5), destroy(5), jmat(2, 'z')])
choi_matrix = super_to_choi(superoperator)
kraus_ops = choi_to_kraus(choi_matrix)
test_choi = kraus_to_choi(kraus_ops)
assert_((test_choi - choi_matrix).norm() < 1e-12)
def spin_coherent(j, theta, phi, type='ket'):
"""Generates the spin state |j, m>, i.e. the eigenstate
of the spin-j Sz operator with eigenvalue m.
Parameters
----------
j : float
The spin of the state.
theta : float
Angle from z axis.
phi : float
Angle from x axis.
type : string {'ket', 'bra', 'dm'}
Type of state to generate.
Returns
-------
state : qobj
Qobj quantum object for spin coherent state
"""
Sp = jmat(j, '+')
Sm = jmat(j, '-')
psi = (0.5 * theta * np.exp(1j * phi) * Sm -
0.5 * theta * np.exp(-1j * phi) * Sp).expm() * spin_state(j, j)
if type == 'ket':
return psi
elif type == 'bra':
return psi.dag()
elif type == 'dm':
return ket2dm(psi)
else:
raise ValueError("invalid value keyword argument 'type'")
def _init_operators(self):
# lc resonator creation operator
self.Aplus = tensor(create(self.nmax), qeye(self.fock_space_size))
# annihilation operators
self.Aminus = tensor(destroy(self.nmax), qeye(self.fock_space_size))
self.sigmax = operators.jmat((self.fock_space_size - 1) / 2, 'x') * 2
self.sigmaz = operators.jmat((self.fock_space_size - 1) / 2, 'z') * 2
self.sigmap = operators.jmat((self.fock_space_size - 1) / 2, '+')
self.sigmam = operators.jmat((self.fock_space_size - 1) / 2, '-')
# pauli sigma matrix at x direction
self.SigmaX = tensor(qeye(self.nmax), self.sigmax)
# pauli sigma matrix at z direction
self.SigmaZ = tensor(qeye(self.nmax), self.sigmaz)
# creation operator
self.SigmaP = tensor(qeye(self.nmax), self.sigmap)
# annihilation operator
self.SigmaN = tensor(qeye(self.nmax), self.sigmam)
# particle number operator
self.SigmaPopulation = tensor(qeye(self.nmax),
self.sigmap * self.sigmam)
self.Qeye = self.SigmaN = tensor(qeye(self.nmax),
qeye(self.fock_space_size))
def rand_super(N=5, dims=None):
"""
Returns a randomly drawn superoperator acting on operators acting on
N dimensions.
Parameters
----------
N : int
Square root of the dimension of the superoperator to be returned.
dims : list
Dimensions of quantum object. Used for specifying
tensor structure. Default is dims=[[[N],[N]], [[N],[N]]].
"""
if dims is not None:
# TODO: check!
pass
else:
dims = [[[N], [N]], [[N], [N]]]
H = rand_herm(N)
S = propagator(H, np.random.rand(), [create(N), destroy(N), jmat(float(N - 1) / 2.0, "z")])
S.dims = dims
return S
def rand_super(self):
h_5 = rand_herm(5)
return propagator(
h_5, scipy.rand(),
[create(5), destroy(5), jmat(2, 'z')])
def _rotation_matrix(theta, phi, j):
"""Private function to calculate the rotation operator for the SU2 kernel.
"""
return la.expm(1j * phi * jmat(j, 'z').full()) @ \
la.expm(1j * theta * jmat(j, 'y').full())
def _rotation_matrix(theta, phi, j):
"""Private function to calculate the rotation operator for the SU2 kernel.
"""
return la.expm(1j * phi * jmat(j, 'z').full()) @ \
la.expm(1j * theta * jmat(j, 'y').full())
def rand_super():
h_5 = rand_herm(5)
return propagator(h_5, scipy.rand(), [
create(5), destroy(5), jmat(2, 'z')
])
def rand_super(dim=5):
H = rand_herm(dim)
return propagator(H, np.random.rand(), [
create(dim), destroy(dim), jmat(float(dim - 1) / 2.0, 'z')
])
