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