qiskit/releasenotes/notes/0.18/higher-order-spsa-f2eddb44b...

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---
features:
- |
A new optimizer class, :class:`~qiskit.algorithms.optimizers.QNSPSA`,
has been added to the :mod:`qiskit.algorithms.optimizers` module. This
class implements the
`Quantum Natural SPSA (QN-SPSA) <https://arxiv.org/abs/2103.09232>`__
algorithm, a generalization of the 2-SPSA algorithm, and estimates the
Quantum Fisher Information Matrix instead of the Hessian to obtain a
stochastic estimate of the Quantum Natural Gradient. For examples on
how to use this new optimizer refer to the
:class:`~qiskit.algorithms.optimizers.QNSPSA` class documentation.
- |
A new kwarg, ``second_order``, has been added to the constructor
of the :class:`~qiskit.algorithms.optimizers.SPSA` class in the
:mod:`qiskit.algorithms.optimizers` module. When set to ``True`` this
enables using
`second-order SPSA <https://ieeexplore.ieee.org/document/657661>`__.
Second order SPSA, or 2-SPSA, is an extension of the ordinary SPSA algorithm that
enables estimating the Hessian alongside the gradient, which is used
to precondition the gradient before the parameter update step. As a
second-order method, this tries to improve convergence of SPSA.
For examples on how to use this option refer to the
:class:`~qiskit.algorithms.optimizers.SPSA` class documentation.