NaturalGradient

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.

Parameters

• grad_method (str (opens in a new tab) |CircuitGradient) – The method used to compute the state gradient. Can be either 'param_shift' or 'lin_comb' or 'fin_diff'.
• qfi_method (str (opens in a new tab) |CircuitQFI) – The method used to compute the QFI. Can be either 'lin_comb_full' or 'overlap_block_diag' or 'overlap_diag'.
• regularization (str (opens in a new tab) | 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 (opens in a new tab)) – Optional parameters for a CircuitGradient

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Attributes

grad_method

Returns CircuitGradient.

Returns

CircuitGradient.

qfi_method

Returns CircuitQFI.

Returns: CircuitQFI.

regularization

Returns the regularization option.

Returns: the regularization option.

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Methods

convert

convert(operator, params=None)

Parameters

• operator (OperatorBase) – The operator we are taking the gradient of.
• params (ParameterVector |ParameterExpression |List (opens in a new tab)[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 (opens in a new tab) – If operator does not represent an expectation value or the quantum state is not CircuitStateFn.
• ValueError (opens in a new tab) – If params contains a parameter not present in operator.
• ValueError (opens in a new tab) – If operator is not parameterized.

Return type

OperatorBase

nat_grad_combo_fn

static nat_grad_combo_fn(x, regularization=None)

Natural Gradient Function Implementation.

Parameters

• x (tuple (opens in a new tab)) – Iterable consisting of Gradient, Quantum Fisher Information.
• regularization (str (opens in a new tab) | None) – Regularization method.

Returns

Natural Gradient.

Raises

ValueError (opens in a new tab) – If the gradient has imaginary components that are non-negligible.

Return type

ndarray (opens in a new tab)