For use cases when the Hamiltonian of the system is time-dependent, Qadence provides a special parameter TimeParameter("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.
Noiseless time-dependent Hamiltonian evolution
from qadence import X, Y, HamEvo, TimeParameter, FeatureParameter, run
from pyqtorch.utils import SolverType
import torch
# Simulation parameters
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 = FeatureParameter("omega")
# Arbitrarily compose a time-dependent generator
td_generator = omega_param * (t * X(0) + t**2 * Y(1))
# Create parameterized HamEvo block
hamevo = HamEvo(td_generator, t)
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.
By default, the code above will initialize an internal parameter FeatureParameter("duration") in the HamEvo. Alternatively,
the duration argument can be used to rename this parameter, or to pass a fixed value directly. If no fixed value is passed,
it must then be set in the values dictionary at runtime.
Future improvements
Currently it is only possible to pass a single value for the duration, and the only result obtained will be the one corresponding to the state at end of the integration. In the future we will change the interface to allow directly passing some array of save values to obtain expectation values or statevectors at intermediate steps during the evolution.
values = {"omega": torch.tensor(10.0), "duration": torch.tensor(1.0)}
config = {"ode_solver": ode_solver, "n_steps_hevo": n_steps_hevo}
out_state = run(hamevo, values = values, configuration = config)
print(out_state)
Note that Qadence makes no assumption on units. 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.
Noisy time-dependent Hamiltonian evolution
To perform noisy time-dependent Hamiltonian evolution, one needs to pass a list of noise operators to the noise_operators argument in HamEvo. They correspond to the jump operators used within the time-dependent Schrodinger equation solver method SolverType.DP5_ME:
from qadence import X, Y, HamEvo, TimeParameter, FeatureParameter, run
from pyqtorch.utils import SolverType
import torch
# Simulation parameters
ode_solver = SolverType.DP5_ME # time-dependent Schrodinger equation solver method
n_steps_hevo = 500 # integration time steps used by solver
# Define block parameters
t = TimeParameter("t")
omega_param = FeatureParameter("omega")
# Arbitrarily compose a time-dependent generator
td_generator = omega_param * (t * X(0) + t**2 * Y(1))
# Create parameterized HamEvo block
noise_operators = [X(i) for i in td_generator.qubit_support]
hamevo = HamEvo(td_generator, t, noise_operators = noise_operators)
values = {"omega": torch.tensor(10.0), "duration": torch.tensor(1.0)}
config = {"ode_solver": ode_solver, "n_steps_hevo": n_steps_hevo}
out_state = run(hamevo, values = values, configuration = config)
print(out_state)
Noise operators definition
Note it is not possible to define noise_operators with parametric operators. If you want to do so, we recommend obtaining the tensors via run and set noise_operators using MatrixBlock. Also, noise_operators should have the same or a subset of the qubit support of the HamEvo instance.