VibrationalEnergy

class VibrationalEnergy(vibrational_integrals, *, truncation_order=None)

Bases: Hamiltonian

The vibrational energy Hamiltonian.

This class implements the following Hamiltonian:

$$\sum _{l=1}^L\sum _{k_l,h_l}^{N_l}⟨{\varphi }_{k_l}|T(Q_l)+V^{[l]}(Q_l)|{\varphi }_{h_l}⟩a_{k_l}^{†}{a}_{h_l}+\sum _{l<m}^L\sum _{k_l,h_l}^{N_l}\sum _{k_m,h_m}^{N_m}⟨{\varphi }_{k_l}{\varphi }_{k_m}|V^{[l,m]}(Q_l,Q_m)|{\varphi }_{h_l}{\varphi }_{h_m}⟩a_{k_l}^{†}{a}_{k_m}^{†}{a}_{h_l}{a}_{h_m}+\dots$$

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

Referencias

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

Parámetros:

• 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)

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.

Parámetros:

integrals (dict[tuple[int, ...], complex]) – a mapping of matrix index tuples to coefficients.

Devuelve:

The resulting VibrationalEnergy instance.

Tipo del valor devuelto:

VibrationalEnergy

interpret(result)

Interprets an EigenstateResult.

Parámetros:

result (EigenstateResult) – The result to add meaning to.

second_q_op()

Returns the second quantized vibrational energy operator.

Devuelve:

A dict of VibrationalOp objects.

Tipo del valor devuelto:

VibrationalOp