"""
This module provides solvers for the unitary Schrodinger equation.
"""
__all__ = ['sesolve', 'SESolver']
import numpy as np
from time import time
from .. import Qobj, QobjEvo
from .solver_base import Solver
[docs]def sesolve(H, psi0, tlist, e_ops=None, args=None, options=None):
"""
Schrodinger equation evolution of a state vector or unitary matrix
for a given Hamiltonian.
Evolve the state vector (`psi0`) using a given
Hamiltonian (`H`), by integrating the set of ordinary differential
equations that define the system. Alternatively evolve a unitary matrix in
solving the Schrodinger operator equation.
The output is either the state vector or unitary matrix at arbitrary points
in time (`tlist`), or the expectation values of the supplied operators
(`e_ops`). If e_ops is a callback function, it is invoked for each
time in `tlist` with time and the state as arguments, and the function
does not use any return values. e_ops cannot be used in conjunction
with solving the Schrodinger operator equation
**Time-dependent operators**
For time-dependent problems, `H` and `c_ops` can be a :class:`QobjEvo` or
object that can be interpreted as :class:`QobjEvo` such as a list of
(Qobj, Coefficient) pairs or a function.
Parameters
----------
H : :class:`Qobj`, :class:`QobjEvo`, :class:`QobjEvo` compatible format.
System Hamiltonian as a Qobj or QobjEvo for time-dependent
Hamiltonians. List of [:class:`Qobj`, :class:`Coefficient`] or callable
that can be made into :class:`QobjEvo` are also accepted.
psi0 : :class:`qutip.qobj`
initial state vector (ket)
or initial unitary operator `psi0 = U`
tlist : *list* / *array*
list of times for :math:`t`.
e_ops : :class:`qutip.qobj`, callable, or list.
Single operator or list of operators for which to evaluate
expectation values or callable or list of callable.
Callable signature must be, `f(t: float, state: Qobj)`.
See :func:`expect` for more detail of operator expectation.
args : None / *dictionary*
dictionary of parameters for time-dependent Hamiltonians
options : None / dict
Dictionary of options for the solver.
- store_final_state : bool
Whether or not to store the final state of the evolution in the
result class.
- store_states : bool, None
Whether or not to store the state vectors or density matrices.
On `None` the states will be saved if no expectation operators are
given.
- normalize_output : bool
Normalize output state to hide ODE numerical errors.
- progress_bar : str {'text', 'enhanced', 'tqdm', ''}
How to present the solver progress.
'tqdm' uses the python module of the same name and raise an error
if not installed. Empty string or False will disable the bar.
- progress_kwargs : dict
kwargs to pass to the progress_bar. Qutip's bars use `chunk_size`.
- method : str ["adams", "bdf", "lsoda", "dop853", "vern9", etc.]
Which differential equation integration method to use.
- atol, rtol : float
Absolute and relative tolerance of the ODE integrator.
- nsteps :
Maximum number of (internally defined) steps allowed in one ``tlist``
step.
- max_step : float, 0
Maximum lenght of one internal step. When using pulses, it should be
less than half the width of the thinnest pulse.
Other options could be supported depending on the integration method,
see `Integrator <./classes.html#classes-ode>`_.
Returns
-------
result: :class:`qutip.Result`
An instance of the class :class:`qutip.Result`, which contains
a *list of array* `result.expect` of expectation values for the times
specified by `tlist`, and/or a *list* `result.states` of state vectors
or density matrices corresponding to the times in `tlist` [if `e_ops`
is an empty list of `store_states=True` in options].
"""
H = QobjEvo(H, args=args, tlist=tlist)
solver = SESolver(H, options=options)
return solver.run(psi0, tlist, e_ops=e_ops)
[docs]class SESolver(Solver):
"""
Schrodinger equation evolution of a state vector or unitary matrix
for a given Hamiltonian.
Parameters
----------
H : :class:`Qobj`, :class:`QobjEvo`
System Hamiltonian as a Qobj or QobjEvo for time-dependent
Hamiltonians. List of [:class:`Qobj`, :class:`Coefficient`] or callable
that can be made into :class:`QobjEvo` are also accepted.
options : dict, optional
Options for the solver, see :obj:`SESolver.options` and
`Integrator <./classes.html#classes-ode>`_ for a list of all options.
attributes
----------
stats: dict
Diverse diagnostic statistics of the evolution.
"""
name = "sesolve"
_avail_integrators = {}
solver_options = {
"progress_bar": "text",
"progress_kwargs": {"chunk_size":10},
"store_final_state": False,
"store_states": None,
"normalize_output": True,
'method': 'adams',
}
def __init__(self, H, *, options=None):
_time_start = time()
if not isinstance(H, (Qobj, QobjEvo)):
raise TypeError("The Hamiltonian must be a Qobj or QobjEvo")
rhs = -1j * H
if not rhs.isoper:
raise ValueError("The hamiltonian must be an operator")
super().__init__(rhs, options=options)
def _initialize_stats(self):
stats = super()._initialize_stats()
stats.update({
"solver": "Schrodinger Evolution",
})
return stats
@property
def options(self):
"""
Solver's options:
store_final_state: bool, default=False
Whether or not to store the final state of the evolution in the
result class.
store_states: bool, default=None
Whether or not to store the state vectors or density matrices.
On `None` the states will be saved if no expectation operators are
given.
normalize_output: bool, default=True
Normalize output state to hide ODE numerical errors.
progress_bar: str {'text', 'enhanced', 'tqdm', ''}, {}
How to present the solver progress.
'tqdm' uses the python module of the same name and raise an error
if not installed. Empty string or False will disable the bar.
progress_kwargs: dict, default={"chunk_size": 10}
Arguments to pass to the progress_bar. Qutip's bars use
``chunk_size``.
method: str, default="adams"
Which ordinary differential equation integration method to use.
"""
return self._options
@options.setter
def options(self, new_options):
Solver.options.fset(self, new_options)