qiskit.chemistry.components.bosonic_bases.HarmonicBasis¶

class HarmonicBasis(watson_hamiltonian, basis, truncation_order=3)[source]¶

Basis in which the Watson Hamiltonian is expressed.

This class uses the Hermite polynomials (eigenstates of the harmonic oscillator) as a modal basis for the expression of the Watson Hamiltonian or any bosonic operator.

References

[1] Ollitrault Pauline J., Chemical science 11 (2020): 6842-6855.

Parameters

watson_hamiltonian (WatsonHamiltonian) – A WatsonHamiltonian object which contains the hamiltonian information.
basis (List[int]) – Is a list defining the number of modals per mode. E.g. for a 3 modes system with 4 modals per mode basis = [4, 4, 4].
truncation_order (int) – where is the Hamiltonian expansion truncation (1 for having only 1-body terms, 2 for having on 1- and 2-body terms…)

__init__(watson_hamiltonian, basis, truncation_order=3)[source]¶

Parameters

watson_hamiltonian (WatsonHamiltonian) – A WatsonHamiltonian object which contains the hamiltonian information.
basis (List[int]) – Is a list defining the number of modals per mode. E.g. for a 3 modes system with 4 modals per mode basis = [4, 4, 4].
truncation_order (int) – where is the Hamiltonian expansion truncation (1 for having only 1-body terms, 2 for having on 1- and 2-body terms…)

Methods

__init__(watson_hamiltonian, basis[, …])

type watson_hamiltonian: WatsonHamiltonian

convert([threshold])

This prepares an array object representing a bosonic hamiltonian expressed in the harmonic basis.

convert(threshold=1e-06)[source]¶

This prepares an array object representing a bosonic hamiltonian expressed in the harmonic basis. This object can directly be given to the BosonicOperator class to be mapped to a qubit hamiltonian.

Parameters: threshold (float) – the matrix elements of value below this threshold are discarded
Return type: List[List[Tuple[List[List[int]], float]]]
Returns: List of modes for input to creation of a bosonic hamiltonian in the harmonic basis
Raises: ValueError – If problem with order value from computed modes