Computing Quantum Fisher information

[oameye]

To compute the Quantum Fisher information of a state you need to have the the derivative of the density matrix compared to a parameter. I was wondering if someone already figured out how to compute that using QuantumToolbox. I know in the sciml ecosystem their exist tools like this for fitting routines. Does somebody have some experience with this?

[oameye]

I found this post :). Exactly what I needed. Could be an interesting example to add to the docs. A tutorial or user guide?

[albertomercurio]

Hi @oameye,

we are indeed planning to add the example about automatic differentiation. For the moment you can check the runtests here:

• https://github.com/qutip/QuantumToolbox.jl/blob/main/test/ext-test/cpu/autodiff/zygote.jl

or look at our paper:

• Quantum 9, 1866 (2025)

Be aware that it is totally experimental. But contributions are welcome of course.

[oameye]

I have added a tutorial where I got it working using FiniteDiff. With zygote the TFFX never finished (on my shitty laptop). But probably someone else can get it working if they follow you test file.

[albertomercurio]

I finally found some time to reply, sorry. I think that Zygote is very slow because Reverse mode is efficient only when a function is $R^n \to R^m$ with $n > m$. Otherwise, Forward mode is preferable.

Thus, I would say that one has to use ForwardDiff.jl or Diffractor.jl. I'm not an expert of autodiff, but I remember that ForwardDiff doesn't support complex numbers well. Also Enzyme.jl has the Forward mode BTW.

Anyhow, your tutorial is nice. @ytdHuang moved it into an internal repository, so that we can see the preview.

[oameye]

https://qutip.org/QuantumToolbox.jl/stable/users_guide/autodiff#doc:autodiff