Description for the qutip-jax related package.

doc/development/ideas/jax_integrator.rst

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+JAX integrator
+--------------
+
+QuTiP has recently rewritten its solver module to extend its flexibility and
+allow different ``Integrator`` (ODE solvers). ``Integrator`` in qutip are the
+classes in responsible for the low level computation of the evolution of a
+Quantum state represented as a ``Qobj``. These are used in the QuTiP's solvers
+(see ``sesolve``, ``mesolve``, ``srmsolve``) to provide a user friendly
+interface for the computation of the time dynamics of a wide variety of
+systems. QuTiP also includes a data layer to represent its main class,
+``Qobj``, using different array interfaces. The data layer has been
+successfully extended in previous projects (some of them GSoC) giving birth to
+a family of packages ([TensorFlow](https://github.com/qutip/qutip-tensorflow),
+[CuPy](https://github.com/qutip/qutip-cupy) and most recently
+[Jax](https://github.com/qutip/qutip-jax)) that allow, among other things, GPU
+operation and autodifferentiation of QuTiP's ``Qobj``. Those data-layers open
+new avenues for quantum control applications in QuTiP, where the
+auto-differentiation of a system evolution is expected to improve the
+performance of quantum control algorithms. However, preliminary testing of
+these data-layers with QuTiPs solvers showed that a data-layer specific
+``Integrator`` is needed in order leverage the full potential of
+auto-differentiation. Your task as part of the GSoC will be to implement such
+``Integrator`` for the qutip-jax data layer, benchamark the result with
+existing integrators and provide an example of use of the auto-differentiation
+feature, possibly in the context of quantum control.
+
+
+Project size
+============
+
+- 350 hours
+
+Difficulty
+==========
+
+- Medium
+
+Deliverables
+============
+
+- Implement an Integrator based on jax integrators to allow
+- Support JAX `jax.jit` and `jax.grad` for automatic differentiation of
+  `Integrator` solutions.
+- Benchmark the new integrator with existing alternatives.
+- Use Jupyter notebook to demonstrate some simple examples, e.g.: a `jit`
+  in the control of a quantum system.
+
+Skills
+======
+
+- Familiar with QuTiP and its solvers (feel free to show us some code!)
+- Familiar with Python and Git.
+- Understand the concepts of Python closures and decorators (which are used
+  widely in JAX function transformations).
+- Familiar with JAX (beneficial, but not required)
+
+
+Mentors
+=======
+
+- Eric Giguère (eric.giguere@calculquebec.ca)
+- Shahnawaz Ahmed (shahnawaz.ahmed95@gmail.com)
+- Asier Galicia (agalicia1221@gmail.com)