NaturalGradient

class qiskit.opflow.gradients.NaturalGradient(grad_method='lin_comb', qfi_method='lin_comb_full', regularization=None, **kwargs)

Bases: GradientBase

Deprecated: Convert an operator expression to the first-order gradient.

Given an ill-posed inverse problem

x = arg min{||Ax-C||^2} (1)

one can use regularization schemes can be used to stabilize the system and find a numerical solution

x_lambda = arg min{||Ax-C||^2 + lambda*R(x)} (2)

where R(x) represents the penalization term.

Deprecated since version 0.24.0: The class qiskit.opflow.gradients.natural_gradient.NaturalGradient is deprecated as of qiskit-terra 0.24.0. It will be removed no earlier than 3 months after the release date. For code migration guidelines, visit https://qisk.it/opflow_migration.

Parameters:

• grad_method (str | CircuitGradient) – The method used to compute the state gradient. Can be either 'param_shift' or 'lin_comb' or 'fin_diff'.

• qfi_method (str | CircuitQFI) – The method used to compute the QFI. Can be either 'lin_comb_full' or 'overlap_block_diag' or 'overlap_diag'.

• regularization (str | None) – Use the following regularization with a least square method to solve the underlying system of linear equations Can be either None or 'ridge' or 'lasso' or 'perturb_diag' 'ridge' and 'lasso' use an automatic optimal parameter search If regularization is None but the metric is ill-conditioned or singular then a least square solver is used without regularization

• kwargs (dict) – Optional parameters for a CircuitGradient

Attributes

grad_method

Returns CircuitGradient.

Returns:

CircuitGradient.

qfi_method

Returns CircuitQFI.

Returns: CircuitQFI.

regularization

Returns the regularization option.

Returns: the regularization option.

Methods

convert(operator, params=None)

Parameters:

• operator (OperatorBase) – The operator we are taking the gradient of.

• params (ParameterVector | ParameterExpression | List[ParameterExpression] | None) – The parameters we are taking the gradient with respect to. If not explicitly passed, they are inferred from the operator and sorted by name.

Returns:

An operator whose evaluation yields the NaturalGradient.

Raises:

• TypeError – If operator does not represent an expectation value or the quantum state is not CircuitStateFn.

• ValueError – If params contains a parameter not present in operator.

• ValueError – If operator is not parameterized.

Return type:

OperatorBase

static nat_grad_combo_fn(x, regularization=None)

Natural Gradient Function Implementation.

Parameters:

• x (tuple) – Iterable consisting of Gradient, Quantum Fisher Information.

• regularization (str | None) – Regularization method.

Returns:

Natural Gradient.

Raises:

ValueError – If the gradient has imaginary components that are non-negligible.

Return type:

ndarray