class ReverseEstimatorGradient(derivative_type=DerivativeType.REAL)[source]#

Bases: BaseEstimatorGradient

Estimator gradients with the classically efficient reverse mode.


This gradient implementation is based on statevector manipulations and scales exponentially with the number of qubits. However, for small system sizes it can be very fast compared to circuit-based gradients.

This class implements the calculation of the expectation gradient as described in [1]. By keeping track of two statevectors and iteratively sweeping through each parameterized gate, this method scales only linearly with the number of parameters.


[1]: Jones, T. and Gacon, J. “Efficient calculation of gradients in classical simulations

of variational quantum algorithms” (2020). arXiv:2009.02823.


derivative_type (DerivativeType) – Defines whether the real, imaginary or real plus imaginary part of the gradient is returned.


SUPPORTED_GATES = ['rx', 'ry', 'rz', 'cp', 'crx', 'cry', 'crz']#

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


The derivative type.


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.


The gradient default + estimator options.


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

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

  • circuits (Sequence[QuantumCircuit]) – The list of quantum circuits to compute the gradients.

  • observables (Sequence[BaseOperator]) – The list of observables.

  • parameter_values (Sequence[Sequence[float]]) – 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


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.


ValueError – Invalid arguments are given.

Return type:



Update the gradient’s default options setting.


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