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qiskit.opflow.gradients.Hessian

class Hessian(hess_method='param_shift', **kwargs)[source]

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)[source]
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. If not explicitly passed, the full Hessian is constructed. The parameters are then inferred from the operator and sorted by name.

Returns

An operator whose evaluation yields the Hessian

Return type

OperatorBase

get_hessian(operator, params=None)[source]

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]], List[ParameterExpression], ParameterVector, None]) – Parameters w.r.t. which we compute the Hessian. If not explicitly passed, the full Hessian is constructed. The parameters are then inferred from the operator and sorted by name.

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.

  • ValueError – If operator is not parameterized.

  • OpflowError – If the coefficient of the operator could not be reduced to 1.

  • OpflowError – 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

  • MissingOptionalLibraryError – jax not installed

gradient_wrapper(operator, bind_params, grad_params=None, backend=None, expectation=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[Backend, BaseBackend, QuantumInstance, None]) – The quantum backend or QuantumInstance to use to evaluate the gradient, Hessian or QFI.

  • expectation (Optional[ExpectationBase]) – The expectation converter to be used. If none is set then PauliExpectation() is used.

Return type

Callable[[Iterable], ndarray]

Returns

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