Compute the gradients of the sampling probability by finite difference method [1].

Reference: [1] Finite difference method

Parameters:
• sampler (BaseSampler) â€“ The sampler used to compute the gradients.

• epsilon (float) â€“ The offset size for the finite difference gradients.

• options (Options | None) â€“ Primitive backend runtime options used for circuit execution. The order of priority is: options in run method > gradientâ€™s default options > primitiveâ€™s default setting. Higher priority setting overrides lower priority setting

• method (Literal['central', 'forward', 'backward']) â€“

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:
• ValueError â€“ If epsilon is not positive.

• TypeError â€“ If method is invalid.

Attributes

options#

Return the union of sampler options setting and gradient default options, where, if the same field is set in both, the gradientâ€™s default options override the primitiveâ€™s default setting.

Returns:

The gradient default + sampler options.

Methods

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

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

Parameters:
• circuits (Sequence[QuantumCircuit]) â€“ The list of quantum circuits to compute the gradients.

• parameter_values (Sequence[Sequence[float]]) â€“ The list of parameter values to be bound to the circuit.

• parameters (Sequence[Sequence[Parameter] | None] | None) â€“ 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 â€“ Primitive backend runtime options used for circuit execution. The order of priority is: options in run method > gradientâ€™s default options > primitiveâ€™s default setting. Higher priority setting overrides lower priority setting

Returns:

The job object of the gradients of the sampling probability. The i-th result corresponds to circuits[i] evaluated with parameters bound as parameter_values[i]. The j-th quasi-probability distribution in the i-th result corresponds to the gradients of the sampling probability for the j-th parameter in circuits[i].

Raises:

ValueError â€“ Invalid arguments are given.

Return type:

AlgorithmJob

update_default_options(**options)#

Update the gradientâ€™s default options setting.

Parameters:

**options â€“ The fields to update the default options.