OrbitalOptimizationVQE

class OrbitalOptimizationVQE(transformation, solver, initial_point=None, orbital_rotation=None, bounds=None, iterative_oo=True, iterative_oo_iterations=2)

Bases: qiskit.chemistry.algorithms.ground_state_solvers.ground_state_eigensolver.GroundStateEigensolver

A ground state calculation employing the OOVQE algorithm. The Variational Quantum Eigensolver (VQE) algorithm enhanced with the Orbital Optimization (OO). The core of the approach resides in the optimization of orbitals through the AO-to-MO coefficients matrix C. In the usual VQE, the latter remains constant throughout the simulation. Here, its elements are modified according to C=Ce^(-kappa) where kappa is an anti-hermitian matrix. This transformation preserves the spectrum but modifies the amplitudes of the ground state of given operator such that in the end a given ansatz can be closest to that ground state, producing larger overlap and lower eigenvalue than conventional VQE. Kappa is parametrized and optimized inside the OOVQE in the same way as the gate angles. Therefore, at each step of OOVQE the coefficient matrix C is modified and the operator is recomputed, unlike usual VQE where operator remains constant. Iterative OO refers to optimization in two steps, first the wavefunction and then the orbitals. It allows for faster optimization as the operator is not recomputed when wavefunction is optimized. It is recommended to use the iterative method on real device/qasm simulator with noise to facilitate the convergence of the classical optimizer. For more details of this method refer to: https://aip.scitation.org/doi/10.1063/1.5141835

Parameters

• transformation (FermionicTransformation) – a fermionic driver to operator transformation strategy.

• solver (Union[MinimumEigensolver, MinimumEigensolverFactory]) – a VQE instance or a factory for the VQE solver employing any custom variational form, such as the VQEUCCSDFactory. Both need to use the UCCSD variational form.

• initial_point (Optional[ndarray]) – An optional initial point (i.e. initial parameter values) for the optimizer. If None then VQE will look to the variational form for a preferred point and if not will simply compute a random one.

• orbital_rotation (Optional[OrbitalRotation]) – instance of OrbitalRotation class that creates the matrices that rotate the orbitals needed to produce the rotated MO coefficients C as C = C0 * exp(-kappa).

• bounds (Optional[ndarray]) – bounds for variational form and orbital rotation parameters given to a classical optimizer.

• iterative_oo (bool) – when True optimize first the variational form and then the orbitals, iteratively. Otherwise, the wavefunction ansatz and orbitals are optimized simultaneously.

• iterative_oo_iterations (int) – number of iterations in the iterative procedure, set larger to be sure to converge to the global minimum.

Raises

AquaError – if the number of orbital optimization iterations is less or equal to zero.

Methods

evaluate_operators	Evaluates additional operators at the given state.
returns_groundstate	Whether the eigensolver returns the ground state or only ground state energy.
solve	Compute Ground State properties.

Attributes

solver

Returns the minimum eigensolver or factory.

Return type

Union[MinimumEigensolver, MinimumEigensolverFactory]

transformation

Returns the transformation used to obtain a qubit operator from the molecule.

Return type

Transformation