Promote TimeDependentSum to Dual when using ForwardDiff (#378)

* promote TimeDependentSum in schroedinger_dynamics

src/schroedinger.jl

@@ -56,7 +56,13 @@ end
 
 function schroedinger_dynamic(tspan, psi0::T, H::AbstractTimeDependentOperator;
     kwargs...) where {B,Bp,T<:Union{AbstractOperator{B,Bp},StateVector{B}}}
-    schroedinger_dynamic(tspan, psi0, schroedinger_dynamic_function(H); kwargs...)
+    promoted_tspan, psi0 = _promote_time_and_state(psi0, H, tspan)
+    if promoted_tspan !== tspan # promote H
+        promoted_H = TimeDependentSum(H.coefficients, H.static_op.operators; init_time=first(promoted_tspan))
+        return schroedinger_dynamic(promoted_tspan, psi0, schroedinger_dynamic_function(promoted_H); kwargs...)
+    else
+        return schroedinger_dynamic(promoted_tspan, psi0, schroedinger_dynamic_function(H); kwargs...)
+    end
 end
 
 """

test/test_ForwardDiff.jl

@@ -50,3 +50,26 @@ for u0 = (psi, psi', psi⊗psi') # test all methods of `rebuild`
 end
 
 end # testset
+
+@testset "ForwardDiff with schroedinger using TimeDependentSum" begin
+
+base=SpinBasis(1/2)
+ψi = spinup(base)
+ψt = spindown(base)
+function Ftdop(q)
+    H = TimeDependentSum([q, abs2∘sinpi], [sigmaz(base), sigmax(base)])
+    _, ψf = timeevolution.schroedinger_dynamic(range(0,1,2), ψi, H)
+    abs2(ψt'last(ψf))
+end
+Ftdop(1.0)
+@test ForwardDiff.derivative(Ftdop, 1.0) isa Any
+
+function Ftdop(q)
+    H = TimeDependentSum([1, abs2∘sinpi], [sigmaz(base), q*sigmax(base)])
+    _, ψf = timeevolution.schroedinger_dynamic(range(0,1,2), ψi, H)
+    abs2(ψt'last(ψf))
+end
+Ftdop(1.0)
+@test ForwardDiff.derivative(Ftdop, 1.0) isa Any
+
+end # testset