Time-dependent generators

For use cases when the Hamiltonian of the system is time-dependent, Qadence provides a special parameter TimePrameter("t") that denotes the explicit time dependence. Using this time parameter one can define a parameterized block acting as the generator passed to HamEvo that encapsulates the required time dependence function.

from qadence import X, Y, HamEvo, TimeParameter, Parameter, run
from pyqtorch.utils import SolverType
import torch

# simulation parameters
duration = 1.0  # duration of time-dependent block simulation
ode_solver = SolverType.DP5_SE  # time-dependent Schrodinger equation solver method
n_steps_hevo = 500  # integration time steps used by solver

# define block parameters
t = TimeParameter("t")
omega_param = Parameter("omega")

# create time-dependent generator
generator_td = omega_param * (t * X(0) + t**2 * Y(1))

# create parameterized HamEvo block
hamevo = HamEvo(generator_td, t, duration=duration)

# run simulation
out_state = run(hamevo,
                values={"omega": torch.tensor(10.0)},
                configuration={"ode_solver": ode_solver,
                               "n_steps_hevo": n_steps_hevo})

print(out_state)

tensor([[-0.2785+0.0000j, -0.0541+0.0000j,  0.0000-0.9414j,  0.0000-0.1827j]])

Note that when using HamEvo with a time-dependent generator, the actual time parameter that was used to construct the generator must be passed for the second argument parameter. In time-dependent case a value for duration argument to HamEvo must be passed in order to define the duration of the simulation. The unit of passed duration value \(\tau\) must be aligned with the units of other parameters in the time-dependent generator so that the integral of generator \(\overset{\tau}{\underset{0}{\int}}\mathcal{\hat{H}}(t){\rm d}t\) is dimensionless.