# This code is part of a Qiskit project.
#
# (C) Copyright IBM 2021, 2023.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
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"""The vibrational energy Hamiltonian."""
from __future__ import annotations
import qiskit_nature # pylint: disable=unused-import
from qiskit_nature.second_q.operators import VibrationalIntegrals, VibrationalOp
from .hamiltonian import Hamiltonian
[docs]class VibrationalEnergy(Hamiltonian):
r"""The vibrational energy Hamiltonian.
This class implements the following Hamiltonian:
.. math::
\sum_{l=1}^L \sum_{k_l,h_l}^{N_l}
\langle \phi_{k_l} | T(Q_l) + V^{[l]}(Q_l) | \phi_{h_l} \rangle a^\dagger_{k_l} a_{h_l}
+ \sum_{l<m}^L \sum_{k_l,h_l}^{N_l} \sum_{k_m,h_m}^{N_m}
\langle \phi_{k_l} \phi_{k_m} | V^{[l,m]}(Q_l, Q_m) | \phi_{h_l} \phi_{h_m} \rangle
a^\dagger_{k_l} a^\dagger_{k_m} a_{h_l} a_{h_m}
+ \ldots
where :math:`Q` denotes a vibrational mode, :math:`T` denotes the kinetic term, and :math:`V`
denotes the potential terms acting on multiple modes. The subscripts :math:`k` and :math:`h` are
indexing the modals which each mode :math:`l` gets expanded into.
For a detailed explanation please refer to reference [1].
The following attributes can be set via the initializer but can also be read and updated once
the ``VibrationalEnergy`` object has been constructed.
Attributes:
vibrational_integrals (VibrationalIntegrals): the integral coefficients.
truncation_order (int | None): the maximum order of multi-body terms to include in the
operator.
References:
[1]: P. Ollitrault et al. `arXiv:2003.12578 <https://arxiv.org/abs/2003.12578>`_.
"""
def __init__(
self,
vibrational_integrals: VibrationalIntegrals,
*,
truncation_order: int | None = None,
) -> None:
"""
Args:
vibrational_integrals: the container with the integral coefficients.
truncation_order: the maximum order of multi-body terms to include in the operator.
"""
self.vibrational_integrals = vibrational_integrals
self.truncation_order = truncation_order
@property
def register_length(self) -> int | None:
return None
[docs] @classmethod
def from_raw_integrals(cls, integrals: dict[tuple[int, ...], complex]) -> VibrationalEnergy:
"""Constructs a hamiltonian instance from raw integrals.
This function simply calls
:meth:`qiskit_nature.second_q.operators.VibrationalIntegrals.from_raw_integrals`.
See its documentation for more details.
Args:
integrals: a mapping of matrix index tuples to coefficients.
Returns:
The resulting ``VibrationalEnergy`` instance.
"""
return cls(VibrationalIntegrals.from_raw_integrals(integrals))
[docs] def second_q_op(self) -> VibrationalOp:
"""Returns the second quantized vibrational energy operator.
Returns:
A ``dict`` of ``VibrationalOp`` objects.
"""
truncated_integrals = self.vibrational_integrals
if self.truncation_order is not None:
truncated_integrals = VibrationalIntegrals(
{
key: value
for key, value in self.vibrational_integrals.items()
if len(key) <= 3 * self.truncation_order
},
validate=False,
)
return VibrationalOp.from_polynomial_tensor(truncated_integrals)
[docs] def interpret(
self, result: "qiskit_nature.second_q.problems.EigenstateResult" # type: ignore[name-defined]
) -> None:
"""Interprets an :class:`~qiskit_nature.second_q.problems.EigenstateResult`.
Args:
result: The result to add meaning to.
"""