qiskit.algorithms.gradients.FiniteDiffEstimatorGradient(estimator, epsilon, options=None, *, method='central')

Compute the gradients of the expectation values by finite difference method [1].

Reference: [1] Finite difference method (opens in a new tab)

Parameters

• estimator (BaseEstimator) – The estimator used to compute the gradients.

• epsilon (float (opens in a new tab)) – The offset size for the finite difference gradients.

• options (Options | None) – Primitive backend runtime options used for circuit execution. The order of priority is: options in run method > gradient’s default options > primitive’s default setting. Higher priority setting overrides lower priority setting

• method (Literal['central', 'forward', 'backward']) –

The computation method of the gradients.

• central computes $\frac{f(x+e)-f(x-e)}{2e}$,
• forward computes $\frac{f(x+e) - f(x)}{e}$,
• backward computes $\frac{f(x)-f(x-e)}{e}$

where $e$ is epsilon.

Raises

## Attributes

### derivative_type

Return the derivative type (real, imaginary or complex).

Returns

The derivative type.

### options

Return the union of estimator options setting and gradient default options, where, if the same field is set in both, the gradient’s default options override the primitive’s default setting.

Returns

The gradient default + estimator options.

## Methods

### run

run(circuits, observables, parameter_values, parameters=None, **options)

Run the job of the estimator gradient on the given circuits.

Parameters

• circuits (Sequence[QuantumCircuit]) – The list of quantum circuits to compute the gradients.
• observables (Sequence[BaseOperator | PauliSumOp]) – The list of observables.
• parameter_values (Sequence[Sequence[float (opens in a new tab)]]) – The list of parameter values to be bound to the circuit.
• parameters (Sequence[Sequence[Parameter] | None] | None) – The sequence of parameters to calculate only the gradients of the specified parameters. Each sequence of parameters corresponds to a circuit in circuits. Defaults to None, which means that the gradients of all parameters in each circuit are calculated. None in the sequence means that the gradients of all parameters in the corresponding circuit are calculated.
• options – Primitive backend runtime options used for circuit execution. The order of priority is: options in run method > gradient’s default options > primitive’s default setting. Higher priority setting overrides lower priority setting

Returns

The job object of the gradients of the expectation values. The i-th result corresponds to circuits[i] evaluated with parameters bound as parameter_values[i]. The j-th element of the i-th result corresponds to the gradient of the i-th circuit with respect to the j-th parameter.

Raises

ValueError (opens in a new tab) – Invalid arguments are given.

Return type

AlgorithmJob

### update_default_options

update_default_options(**options)

Update the gradient’s default options setting.

Parameters

**options – The fields to update the default options.