Generalize the definition of liouvillian

[ytdHuang]

Checklist

Thank you for contributing to QuantumToolbox.jl! Please make sure you have finished the following tasks before opening the PR.

• Please read Contributing to Quantum Toolbox in Julia.
• Any code changes were done in a way that does not break public API.
• Appropriate tests were added and tested locally by running: make test.
• Any code changes should be julia formatted by running: make format.
• All documents (in docs/ folder) related to code changes were updated and able to build locally by running: make docs.
• (If necessary) the CHANGELOG.md should be updated (regarding to the code changes) and built by running: make changelog.

Request for a review after you have completed all the tasks. If you have not finished them all, you can also open a Draft Pull Request to let the others know this on-going work.

Description

Start from QuTiP v5.2.1, they have generalize the definition of liouvillian as

$$\mathcal{L} [\cdot] =-i\left(\hat{H}[\cdot] - [\cdot]\hat{H}^\dagger\right)$$

see also the PR in qutip: qutip/qutip#2658

That is, we should not expect the Hamiltonian to be Hermitian. This could be beneficial for people working on non-Hermitian physics.

All the test passes, the only problem is the type instability from our original test:

H_td2 = H_td + QobjEvo(destroy(N) + create(N), coef3)
c_ops1 = (destroy(N), create(N))
c_ops2 = (destroy(N), QobjEvo(create(N), coef1))

@inferred liouvillian(H_td, c_ops1)   # pass
@inferred liouvillian(H_td, c_ops2)   # fail
@inferred liouvillian(H_td2, c_ops1)  # pass
@inferred liouvillian(H_td2, c_ops2)  # fail

This is super weird cause I only change the definition of liouvilian, how come it fails for c_ops2 but pass for c_ops1.

[ytdHuang]

We can remove the implementation for ScaledOperator, since it should just call the first method (for AbstractSciMLOperator)

[albertomercurio]

Actually by removing this we have issues with Enzyme.jl

[albertomercurio]

Ok we actually need it, otherwise we don't apply conj to the ScalarOperator. This creates some errors in Enzyme.jl

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 93.95%. Comparing base (be147e5) to head (dc46a4f).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #541      +/-   ##
==========================================
+ Coverage   93.15%   93.95%   +0.79%     
==========================================
  Files          51       51              
  Lines        3566     3558       -8     
==========================================
+ Hits         3322     3343      +21     
+ Misses        244      215      -29     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[albertomercurio]

When this PR will be merged

• Fix type instabilities on complex AddedOperators and add new methods SciML/SciMLOperators.jl#310

the code should not show these error anymore.