ElectronicStructureProblem

class ElectronicStructureProblem(hamiltonian)

Bases: BaseProblem

The Electronic Structure Problem.

This class represents the problem of the electronic Schrödinger equation:

\[\hat{H_{el}}|\Psi\rangle = E_{el}|\Psi\rangle,\]

where \(\hat{H_{el}}\) is the qiskit_nature.second_q.hamiltonians.ElectronicEnergy hamiltonian, \(\Psi\) is the wave function of the system and \(E_{el}\) is the eigenvalue. When passed to a qiskit_nature.second_q.algorithms.GroundStateSolver, you will be solving for the ground-state energy, \(E_0\).

This class has various attributes (see below) which allow you to add additional information about the problem which you are trying to solve, which can be used by various modules in the stack. For example, specifying the number of particles in the system num_particles is useful (and even required) for many components that interact with this problem instance to make your life easier (for example the qiskit_nature.second_q.transformers.ActiveSpaceTransformer).

In the fermionic case the default filter ensures that the number of particles is being preserved.

নোট

The default filter_criterion assumes a singlet spin configuration. This means, that the number of alpha-spin electrons is equal to the number of beta-spin electrons. If the AngularMomentum property is available, one can correctly filter a non-singlet spin configuration with a custom filter_criterion similar to the following:

import numpy as np
from qiskit_algorithms import NumPyMinimumEigensolver

expected_spin = 2
expected_num_electrons = 6

def filter_criterion_custom(eigenstate, eigenvalue, aux_values):
    num_particles_aux = aux_values["ParticleNumber"][0]
    total_angular_momentum_aux = aux_values["AngularMomentum"][0]

    return (
        np.isclose(total_angular_momentum_aux, expected_spin) and
        np.isclose(num_particles_aux, expected_num_electrons)
    )

solver = NumPyEigensolver()
solver.filter_criterion = filter_criterion_custom

The following attributes can be read and updated once the ElectronicStructureProblem object has been constructed.

properties

a container for additional observable operator factories.

Type:

ElectronicStructureProblem

molecule

a container for molecular system data.

Type:

MoleculeInfo | None

basis

the electronic basis of all contained orbital coefficients.

Type:

ElectronicBasis | None

num_spatial_orbitals

the number of spatial orbitals in the system.

Type:

int | tuple[int, int] | None

reference_energy

a reference energy for the ground state of the problem.

Type:

float | None

orbital_energies

the energy values of the alpha-spin orbitals.

Type:

np.ndarray | None

orbital_energies_b

the energy values of the beta-spin orbitals.

Type:

np.ndarray | None

প্যারামিটার:

hamiltonian (ElectronicEnergy) -- the Hamiltonian of this problem.

Attributes

hamiltonian

nuclear_repulsion_energy

The nuclear repulsion energy.

See qiskit_nature.second_q.hamiltonians.ElectronicEnergy.nuclear_repulsion_energy for more details.

num_alpha

The number of alpha-spin particles.

num_beta

The number of beta-spin particles.

num_particles

The number of particles in alpha- and beta-spin.

num_spin_orbitals

The total number of spin orbitals.

orbital_occupations

The occupations of the alpha-spin orbitals.

orbital_occupations_b

The occupations of the beta-spin orbitals.

Methods

get_default_filter_criterion()

Returns a default filter criterion method to filter the eigenvalues computed by the eigensolver. For more information see also filter_criterion().

This particular default ensures that the total number of particles is conserved and that the angular momentum (if computed) evaluates to 0.

রিটার্ন টাইপ:

Callable[[List | ndarray, float, List[float] | None], bool] | None

get_tapered_mapper(mapper)

Builds a TaperedQubitMapper from one of the mappers. This simplifies the identification of the Pauli operator symmetries and of the symmetry sector in which lies the solution of the problem.

প্যারামিটার:

mapper (QubitMapper) -- QubitMapper object implementing the mapping of second quantized operators to Pauli operators.

রেইজেস:

ValueError -- If the mapper is a TaperedQubitMapper.

রিটার্নস:

A TaperedQubitMapper with pre-built symmetry specifications.

রিটার্ন টাইপ:

TaperedQubitMapper

interpret(raw_result)

Interprets an EigenstateResult in the context of this problem.

প্যারামিটার:

raw_result (EigenstateResult | EigensolverResult | MinimumEigensolverResult) -- an eigenstate result object.

রিটার্নস:

An electronic structure result.

রিটার্ন টাইপ:

ElectronicStructureResult

second_q_ops()

Returns the second quantized operators associated with this problem.

রিটার্নস:

A tuple, with the first object being the main operator and the second being a dictionary of auxiliary operators.

রিটার্ন টাইপ:

tuple[qiskit_nature.second_q.operators.sparse_label_op.SparseLabelOp, dict[str, qiskit_nature.second_q.operators.sparse_label_op.SparseLabelOp]]