NaturalGradient

class NaturalGradient(grad_method='lin_comb', qfi_method='lin_comb_full', regularization=None, **kwargs)

Bases: qiskit.opflow.gradients.gradient_base.GradientBase

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.

Parameters

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

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

• regularization (Optional[str]) – 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

Methods Defined Here

convert

type operator OperatorBase

Attributes

grad_method

Returns CircuitGradient.

Return type

CircuitGradient

Returns

CircuitGradient.

qfi_method

Returns CircuitQFI.

Returns: CircuitQFI

Return type

CircuitQFI

regularization

Returns the regularization option.

Returns: the regularization option.

Return type

Optional[str]