def test_tempo_parameters_bad_input():
with pytest.raises(AssertionError):
tempo.TempoParameters("x", 42, 1.0e-5, "rough", "bla", {})
with pytest.raises(AssertionError):
tempo.TempoParameters(0.1, "x", 1.0e-5, "rough", "bla", {})
with pytest.raises(AssertionError):
tempo.TempoParameters(0.1, 42, "x", "rough", "bla", {})
def test_tempo_bad_input():
start_time = -0.3
end_time = 0.84
system = tempo.System(0.5 * tempo.operators.sigma("x"))
correlation_function = lambda t: (np.cos(6.0*t)+1j*np.sin(6.0*t)) \
* np.exp(-12.0*t)
correlations = tempo.CustomCorrelations(correlation_function,
max_correlation_time=0.5)
bath = tempo.Bath(0.5 * tempo.operators.sigma("z"), correlations)
initial_state = tempo.operators.spin_dm("z+")
tempo_param_A = tempo.TempoParameters(0.1, 5, 1.0e-5, name="rough-A")
with pytest.raises(AssertionError):
tempo_sys_A = tempo.Tempo(system=system,
bath=bath,
parameters=tempo_param_A,
initial_state="bla",
start_time=start_time)
with pytest.raises(AssertionError):
tempo_sys_A = tempo.Tempo(system=system,
bath=bath,
parameters=tempo_param_A,
initial_state=initial_state,
start_time="bla")
tempo_sys_A = tempo.Tempo(system=system,
bath=bath,
parameters=tempo_param_A,
initial_state=initial_state,
start_time=start_time)
with pytest.raises(AssertionError):
tempo_sys_A.compute(end_time="bla", progress_type="bar")
def test_tempo():
start_time = -0.3
end_time1 = 0.4
end_time2 = 0.6
end_time3 = 0.84
system = tempo.System(0.5 * tempo.operators.sigma("x"))
correlation_function = lambda t: (np.cos(6.0*t)+1j*np.sin(6.0*t)) \
* np.exp(-12.0*t)
correlations = tempo.CustomCorrelations(correlation_function,
max_correlation_time=0.5)
bath = tempo.Bath(0.5 * tempo.operators.sigma("z"), correlations)
initial_state = tempo.operators.spin_dm("z+")
tempo_param_A = tempo.TempoParameters(0.1, 5, 1.0e-5, name="rough-A")
tempo_sys_A = tempo.Tempo(system=system,
bath=bath,
parameters=tempo_param_A,
initial_state=initial_state,
start_time=start_time)
assert tempo_sys_A.dimension == 2
tempo_sys_A.compute(end_time=end_time1, progress_type="bar")
tempo_sys_A.compute(end_time=end_time2, progress_type="silent")
tempo_sys_A.compute(end_time=end_time3, progress_type="simple")
dyn_A = tempo_sys_A.get_dynamics()
assert len(dyn_A.times) == 13
def test_plot_correlations_with_parameters():
correlation_function = lambda t: (np.cos(t) + 1j * np.sin(6.0 * t)
) * np.exp(-2.0 * t)
correlations = tempo.CustomCorrelations(correlation_function,
max_correlation_time=10.0)
param = tempo.TempoParameters(dt=0.1, dkmax=50, epsrel=3.9e-8)
tempo.helpers.plot_correlations_with_parameters(correlations, param)
def generate_pt(temp):
start_time = 0.0
end_time = 10.0
correlations = tempo.PowerLawSD(alpha=alpha,
zeta=3,
cutoff=omega_cutoff,
cutoff_type='gaussian',
temperature=temp)
bath = tempo.Bath(0.5 * tempo.operators.sigma("z"), correlations)
dt = 0.1 # 0.01
dkmax = 20 # 200
epsrel = 1.0e-6 # 1.0e-7
tempo_parameters = tempo.TempoParameters(dt=dt, dkmax=dkmax, epsrel=epsrel)
pt_tempo_parameters = tempo.PtTempoParameters(dt=dt,
dkmax=dkmax,
epsrel=epsrel)
pt = tempo.pt_tempo_compute(bath=bath,
start_time=start_time,
end_time=end_time,
parameters=pt_tempo_parameters,
progress_type='bar')
pt.export("details_pt_tempo_{}K.processTensor".format(temp),
overwrite=True)
def test_tensor_network_tempo_backend_C(backend):
tempo_params_C = tempo.TempoParameters(dt=0.05, dkmax=10, epsrel=10**(-7))
tempo_C = tempo.Tempo(system_C,
bath_C,
tempo_params_C,
initial_state_C,
start_time=0.0,
backend=backend)
tempo_C.compute(end_time=1.0)
dyn_C = tempo_C.get_dynamics()
assert dyn_C.times[-1] == 1.0
np.testing.assert_almost_equal(dyn_C.states[-1], rho_C, decimal=4)
def test_tensor_network_tempo_backend_non_diag(backend):
Omega = 1.0
omega_cutoff = 5.0
alpha = 0.3
sx = tempo.operators.sigma("x")
sy = tempo.operators.sigma("y")
sz = tempo.operators.sigma("z")
bases = [{"sys_op":sx, "coupling_op":sz, \
"init_state":tempo.operators.spin_dm("y+")},
{"sys_op":sy, "coupling_op":sx, \
"init_state":tempo.operators.spin_dm("z+")},
{"sys_op":sz, "coupling_op":sy, \
"init_state":tempo.operators.spin_dm("x+")}]
results = []
for i, base in enumerate(bases):
system = tempo.System(0.5 * base["sys_op"])
correlations = tempo.PowerLawSD(alpha=alpha,
zeta=1,
cutoff=omega_cutoff,
cutoff_type='exponential',
max_correlation_time=8.0)
bath = tempo.Bath(0.5 * base["coupling_op"], correlations)
tempo_parameters = tempo.TempoParameters(dt=0.1,
dkmax=30,
epsrel=10**(-5))
dynamics = tempo.tempo_compute(system=system,
bath=bath,
initial_state=base["init_state"],
start_time=0.0,
end_time=1.0,
parameters=tempo_parameters,
backend=backend)
_, s_x = dynamics.expectations(0.5 * tempo.operators.sigma("x"),
real=True)
_, s_y = dynamics.expectations(0.5 * tempo.operators.sigma("y"),
real=True)
_, s_z = dynamics.expectations(0.5 * tempo.operators.sigma("z"),
real=True)
if i == 0:
results.append(np.array([s_x, s_y, s_z]))
elif i == 1:
results.append(np.array([s_y, s_z, s_x]))
elif i == 2:
results.append(np.array([s_z, s_x, s_y]))
assert np.allclose(results[0], results[1], atol=tempo_parameters.epsrel)
assert np.allclose(results[0], results[2], atol=tempo_parameters.epsrel)
def test_tensor_network_tempo_backend_E(backend, backend_config):
tempo_params_E = tempo.TempoParameters(dt=0.4,
dkmax=5,
epsrel=1.0e-6)
tempo_E = tempo.Tempo(system_E,
bath_E,
tempo_params_E,
initial_state_E,
start_time=t_start_E,
backend=backend,
backend_config=backend_config)
tempo_E.compute(end_time=t_end_E)
dyn_E = tempo_E.get_dynamics()
np.testing.assert_almost_equal(dyn_E.states[-1], rho_E, decimal=4)
def test_tempo_parameters():
tempo_param = tempo.TempoParameters(0.1, None, 1.0e-5, "rough", "bla", {})
str(tempo_param)
assert tempo_param.dt == 0.1
assert tempo_param.dkmax == None
assert tempo_param.epsrel == 1.0e-5
tempo_param.dt = 0.05
tempo_param.dkmax = 42
tempo_param.epsrel = 1.0e-6
assert tempo_param.dt == 0.05
assert tempo_param.dkmax == 42
assert tempo_param.epsrel == 1.0e-6
del tempo_param.dkmax
assert tempo_param.dkmax == None
def test_tensor_network_tempo_backend_A(backend, backend_config):
tempo_params_A = tempo.TempoParameters(dt=0.05,
dkmax=None,
epsrel=10**(-7))
tempo_A = tempo.Tempo(system_A,
bath_A,
tempo_params_A,
initial_state_A,
start_time=0.0,
backend=backend,
backend_config=backend_config)
tempo_A.compute(end_time=1.0)
dyn_A = tempo_A.get_dynamics()
np.testing.assert_almost_equal(dyn_A.states[-1], rho_A, decimal=4)
def test_tempo_dynamics_reference():
system = tempo.System(0.5 * tempo.operators.sigma("x"))
correlations = tempo.PowerLawSD(alpha=0.1,
zeta=1,
cutoff=1.0,
cutoff_type='exponential',
max_correlation_time=0.5)
bath = tempo.Bath(0.5 * tempo.operators.sigma("z"), correlations)
tempo_parameters = tempo.TempoParameters(dt=0.1, dkmax=10, epsrel=10**(-4))
tempo_A = tempo.Tempo(system=system,
bath=bath,
parameters=tempo_parameters,
initial_state=tempo.operators.spin_dm("up"),
start_time=0.0)
dynamics_1 = tempo_A.compute(end_time=0.2)
t_1, sz_1 = dynamics_1.expectations(tempo.operators.sigma("z"))
tempo_A.compute(end_time=0.4)
dynamics_2 = tempo_A.get_dynamics()
t_2, sz_2 = dynamics_2.expectations(tempo.operators.sigma("z"))
assert dynamics_1 == dynamics_2
assert len(t_2) > len(t_1)
system = tempo.TimeDependentSystem(hamiltonian_t)
correlations = tempo.PowerLawSD(alpha=alpha,
zeta=3,
cutoff=omega_cutoff,
cutoff_type='gaussian',
max_correlation_time=5.0,
temperature=temperature)
bath = tempo.Bath(tempo.operators.sigma("z") / 2.0, correlations)
# ### B.4: TEMPO computation
# With all physical objects defined, we are now ready to compute the dynamics of the quantum dot using TEMPO (using quite rough convergence parameters):
# In[7]:
tempo_parameters = tempo.TempoParameters(dt=0.05, dkmax=40, epsrel=10**(-5))
tempo_sys = tempo.Tempo(system=system,
bath=bath,
initial_state=initial_state,
start_time=-2.0,
parameters=tempo_parameters)
dynamics = tempo_sys.compute(end_time=3.0)
# and extract the expectation values $\langle\sigma_{xy}\rangle = \sqrt{\langle\sigma_x\rangle^2 + \langle\sigma_y\rangle^2}$ for plotting:
# In[8]:
t, s_x = dynamics.expectations(tempo.operators.sigma("x"), real=True)
t, s_y = dynamics.expectations(tempo.operators.sigma("y"), real=True)
s_xy = np.sqrt(s_x**2 + s_y**2)
# As a first example let's try to reconstruct one of the lines in figure 2a of [Strathearn2018] ([Nat. Comm. 9, 3322 (2018)](https://doi.org/10.1038/s41467-018-05617-3) / [arXiv:1711.09641v3](https://arxiv.org/abs/1711.09641)). In this example we compute the time evolution of a spin which is strongly coupled to an ohmic bath (spin-boson model). Before we go through this step by step below, let's have a brief look at the script that will do the job - just to have an idea where we are going:
# In[3]:
Omega = 1.0
omega_cutoff = 5.0
alpha = 0.3
system = tempo.System(0.5 * Omega * tempo.operators.sigma("x"))
correlations = tempo.PowerLawSD(alpha=alpha,
zeta=1,
cutoff=omega_cutoff,
cutoff_type='exponential',
max_correlation_time=8.0)
bath = tempo.Bath(0.5 * tempo.operators.sigma("z"), correlations)
tempo_parameters = tempo.TempoParameters(dt=0.1, dkmax=30, epsrel=10**(-4))
dynamics = tempo.tempo_compute(system=system,
bath=bath,
initial_state=tempo.operators.spin_dm("up"),
start_time=0.0,
end_time=15.0,
parameters=tempo_parameters)
t, s_z = dynamics.expectations(0.5 * tempo.operators.sigma("z"), real=True)
plt.plot(t, s_z, label=r'$\alpha=0.3$')
plt.xlabel(r'$t\,\Omega$')
plt.ylabel(r'$<S_z>$')
plt.legend()
# ### A.1: The Model and its Parameters