GRAPE on open quantum system
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johny maartin
Jan 18, 2023, 8:36:51 PM1/18/23
to QuTiP: Quantum Toolbox in Python
Does Qutip currently support GRAPE (or other methods of optimal control) for open quantum systems? I haven't seen any example Jupyter notebook that deals with the open dynamics.
Gerardo Suarez
Jan 23, 2023, 8:41:27 AM1/23/23
to QuTiP: Quantum Toolbox in Python
I don't know if qutip GRAPE does, but krotov has its own library based on qutip and can be implemented for open quantum systems https://qucontrol.github.io/krotov/v1.0.0/01_overview.html in the examples you will find open lindblad dynamics
if you want to know more about the Krotov algorithm you can use the references in the library or for selfish self promotion reasons check this article https://arxiv.org/abs/2207.00094
That being said, for most of optimal control algorithms even if not done you can adapt their readily done libraries by writing your open lindblad dynamics as a schrodinger equation with an effective non hermitian hamiltonian as done in the arxiv above (adapt your open dynamics to first order differential equations in Liouville space) and update your overlaps (inner products ) for the appropriate ones, if you want to do it in general then you can follow https://arxiv.org/pdf/1312.0111.pdf and adapt you algorithm of choice to Liouville space
if you want to know more about the Krotov algorithm you can use the references in the library or for selfish self promotion reasons check this article https://arxiv.org/abs/2207.00094
That being said, for most of optimal control algorithms even if not done you can adapt their readily done libraries by writing your open lindblad dynamics as a schrodinger equation with an effective non hermitian hamiltonian as done in the arxiv above (adapt your open dynamics to first order differential equations in Liouville space) and update your overlaps (inner products ) for the appropriate ones, if you want to do it in general then you can follow https://arxiv.org/pdf/1312.0111.pdf and adapt you algorithm of choice to Liouville space
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