qiskit.opflow.gradients.NaturalGradient¶

class NaturalGradient(grad_method='lin_comb', qfi_method='lin_comb_full', regularization=None, **kwargs)[source]¶

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

__init__(grad_method='lin_comb', qfi_method='lin_comb_full', regularization=None, **kwargs)[source]¶

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

`__init__`([grad_method, qfi_method, …])	type grad_method `Union`[`str`, `CircuitGradient`]
`convert`(operator[, params])	type operator `OperatorBase`
`gradient_wrapper`(operator, bind_params[, …])	Get a callable function which provides the respective gradient, Hessian or QFI for given parameter values.
`parameter_expression_grad`(param_expr, param)	Get the derivative of a parameter expression w.r.t.

Attributes

`grad_method`	Returns `CircuitGradient`.
`qfi_method`	Returns `CircuitQFI`.
`regularization`	Returns the regularization option.

convert(operator, params=None)[source]¶

Parameters

operator (OperatorBase) – The operator we are taking the gradient of.
params (Union[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.

Return type

OperatorBase

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.

property grad_method¶

Returns CircuitGradient.

Return type: CircuitGradient
Returns: CircuitGradient.

gradient_wrapper(operator, bind_params, grad_params=None, backend=None)¶

Get a callable function which provides the respective gradient, Hessian or QFI for given parameter values. This callable can be used as gradient function for optimizers.

Parameters

operator (OperatorBase) – The operator for which we want to get the gradient, Hessian or QFI.
bind_params (Union[ParameterExpression, ParameterVector, List[ParameterExpression]]) – The operator parameters to which the parameter values are assigned.
grad_params (Union[ParameterExpression, ParameterVector, List[ParameterExpression], Tuple[ParameterExpression, ParameterExpression], List[Tuple[ParameterExpression, ParameterExpression]], None]) – The parameters with respect to which we are taking the gradient, Hessian or QFI. If grad_params = None, then grad_params = bind_params
backend (Union[BaseBackend, QuantumInstance, None]) – The quantum backend or QuantumInstance to use to evaluate the gradient, Hessian or QFI.

Returns

Function to compute a gradient, Hessian or QFI. The function takes an iterable as argument which holds the parameter values.

Return type

callable(param_values)

static parameter_expression_grad(param_expr, param)¶

Get the derivative of a parameter expression w.r.t. the given parameter.

Parameters

param_expr (ParameterExpression) – The Parameter Expression for which we compute the derivative
param (ParameterExpression) – Parameter w.r.t. which we want to take the derivative

Return type

Union[ParameterExpression, float]

Returns

ParameterExpression representing the gradient of param_expr w.r.t. param

property qfi_method¶

Returns CircuitQFI.

Returns: CircuitQFI

Return type: CircuitQFI

property regularization¶

Returns the regularization option.

Returns: the regularization option.

Return type: Optional[str]