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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` `nat_grad_combo_fn` Natural Gradient Function Implementation.

Attributes

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`]