VibrationalEnergy#

class VibrationalEnergy(vibrational_integrals, *, truncation_order=None)[source]#

Bases: Hamiltonian

The vibrational energy Hamiltonian.

This class implements the following Hamiltonian:

\sum_{l = 1}^{L} \sum_{k_{l}, h_{l}}^{N_{l}} ⟨ ϕ_{k_{l}} | T (Q_{l}) + V^{[l]} (Q_{l}) | ϕ_{h_{l}} ⟩ a_{k_{l}}^{†} a_{h_{l}} + \sum_{l < m}^{L} \sum_{k_{l}, h_{l}}^{N_{l}} \sum_{k_{m}, h_{m}}^{N_{m}} ⟨ ϕ_{k_{l}} ϕ_{k_{m}} | V^{[l, m]} (Q_{l}, Q_{m}) | ϕ_{h_{l}} ϕ_{h_{m}} ⟩ a_{k_{l}}^{†} a_{k_{m}}^{†} a_{h_{l}} a_{h_{m}} + \dots

where $Q$ denotes a vibrational mode, $T$ denotes the kinetic term, and $V$ denotes the potential terms acting on multiple modes. The subscripts $k$ and $h$ are indexing the modals which each mode $l$ 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.

vibrational_integrals#

the integral coefficients.

Type:: VibrationalIntegrals

truncation_order#

the maximum order of multi-body terms to include in the operator.

Type:: int | None

References

[1]: P. Ollitrault et al. arXiv:2003.12578.

Parameters:

vibrational_integrals (VibrationalIntegrals) – the container with the integral coefficients.
truncation_order (int | None) – the maximum order of multi-body terms to include in the operator.

Attributes

register_length#

Methods

classmethod from_raw_integrals(integrals)[source]#

Constructs a hamiltonian instance from raw integrals.

This function simply calls qiskit_nature.second_q.operators.VibrationalIntegrals.from_raw_integrals(). See its documentation for more details.

Parameters:: integrals (dict[tuple[int, ...], complex]) – a mapping of matrix index tuples to coefficients.
Returns:: The resulting VibrationalEnergy instance.
Return type:: VibrationalEnergy

interpret(result)[source]#

Interprets an EigenstateResult.

Parameters:: result (qiskit_nature.second_q.problems.EigenstateResult) – The result to add meaning to.

second_q_op()[source]#

Returns the second quantized vibrational energy operator.

Returns:: A dict of VibrationalOp objects.
Return type:: VibrationalOp