qiskit.aqua.operators.gradients.Hessian

class Hessian(hess_method='param_shift', **kwargs)

Compute the Hessian of an expected value.

Parameters

• hess_method (Union[str, CircuitGradient]) – The method used to compute the state/probability gradient. Can be either 'param_shift' or 'lin_comb' or 'fin_diff'. Ignored for gradients w.r.t observable parameters.

• kwargs (dict) – Optional parameters for a CircuitGradient

Raises

ValueError – If method != fin_diff and epsilon is not None.

__init__(hess_method='param_shift', **kwargs)

Parameters

• hess_method (Union[str, CircuitGradient]) – The method used to compute the state/probability gradient. Can be either 'param_shift' or 'lin_comb' or 'fin_diff'. Ignored for gradients w.r.t observable parameters.

• kwargs (dict) – Optional parameters for a CircuitGradient

Raises

ValueError – If method != fin_diff and epsilon is not None.

Methods

__init__([hess_method])	type hess_method Union[str, CircuitGradient]
convert(operator[, params])	type operator OperatorBase
get_hessian(operator[, params])	Get the Hessian for the given operator w.r.t.
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

hess_method

Returns CircuitGradient.

convert(operator, params=None)

Parameters

• operator (OperatorBase) – The operator for which we compute the Hessian

• params (Union[Tuple[ParameterExpression, ParameterExpression], List[Tuple[ParameterExpression, ParameterExpression]], List[ParameterExpression], ParameterVector, None]) – The parameters we are computing the Hessian with respect to Either give directly the tuples/list of tuples for which the second order derivative is to be computed or give a list of parameters to build the full Hessian for those parameters.

Returns

An operator whose evaluation yields the Hessian

Return type

OperatorBase

Raises

ValueError – If params is not set.

get_hessian(operator, params=None)

Get the Hessian for the given operator w.r.t. the given parameters

Parameters

• operator (OperatorBase) – Operator w.r.t. which we take the Hessian.

• params (Union[Tuple[ParameterExpression, ParameterExpression], List[Tuple[ParameterExpression, ParameterExpression]], None]) – Parameters w.r.t. which we compute the Hessian.

Return type

OperatorBase

Returns

Operator which represents the gradient w.r.t. the given params.

Raises

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

• AquaError – If the coefficient of the operator could not be reduced to 1. AquaError: If the differentiation of a combo_fn requires JAX but the package is not installed.

• TypeError – If the operator does not include a StateFn given by a quantum circuit

• TypeError – If the parameters were given in an unsupported format.

• Exception – Unintended code is reached

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)

property hess_method

Returns CircuitGradient.

Return type

CircuitGradient

Returns

CircuitGradient.

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