[BUG] SchodingerProblem does not support ForwardDiff

[hongyehu]

In simulation with Bloqade, one can use ForwardDiff.jl to do forward AD of parameters. This works with KrylovEvolution. But if one wants to simulate time-dependent Hamiltonian with Waveform, and SchodingerProblem. The ForwardDiff.gradient and ForwardDiff.jacobian breaks down and outputs NAN.

[Roger-luo]

do you have a minimum-not-working example to demonstrate this bug?

[ChenZhao44]

using Bloqade
using ForwardDiff

nsites = 5
scale = 5.0

function loss_detuning(Δ)
    atoms = generate_sites(ChainLattice(), nsites; scale = scale)
    reg = zero_state(Complex{typeof(Δ[1])}, nsites)
    rh = rydberg_h(atoms; Δ, Ω = 1)
    prob = SchrodingerProblem(reg, (0,1), rh)
    emulate!(prob)
    return real.(state(reg))
end
ForwardDiff.jacobian(loss_detuning, rand(nsites)) # Returns a matrix containing all NaNs.