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Pasqal Documentation

Noiseless time-dependent Hamiltonian evolution

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.

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.

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

Note that Qadence makes no assumption on units. The unit of passed duration value τ\tau must be aligned with the units of other parameters in the time-dependent generator so that the integral of generator ∫0τH^(t)dt\overset{\tau}{\underset{0}{\int}}\mathcal{\hat{H}}(t){\rm d}t is dimensionless.

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)
DensityMatrix([[[0.2734+0.0000j, 0.0297+0.0000j, 0.0000-0.0227j, 0.0000-0.0025j], [0.0297+0.0000j, 0.1698+0.0000j, 0.0000-0.0025j, 0.0000-0.0141j], [0.0000+0.0227j, 0.0000+0.0025j, 0.3435+0.0000j, 0.0373+0.0000j], [0.0000+0.0025j, 0.0000+0.0141j, 0.0373+0.0000j, 0.2133+0.0000j]]])