diff --git a/Project.toml b/Project.toml
index 58f61d160..151b878f9 100644
--- a/Project.toml
+++ b/Project.toml
@@ -61,7 +61,7 @@ OrdinaryDiffEqTsit5 = "1"
 Pkg = "1"
 Random = "1"
 SciMLBase = "2"
-SciMLOperators = "0.3, 0.4"
+SciMLOperators = "1"
 SparseArrays = "1"
 SpecialFunctions = "2"
 StaticArraysCore = "1"
diff --git a/src/qobj/quantum_object_evo.jl b/src/qobj/quantum_object_evo.jl
index f1c4c58dc..32a06bcde 100644
--- a/src/qobj/quantum_object_evo.jl
+++ b/src/qobj/quantum_object_evo.jl
@@ -512,7 +512,8 @@ function (A::QuantumObjectEvolution)(
         )
     end
 
-    A.data(ψout.data, ψin.data, p, t)
+    # We put `nothing` in the place of `u` because the time-dependence doesn't depend on the state
+    A.data(ψout.data, ψin.data, nothing, p, t)
 
     return ψout
 end
diff --git a/src/qobj/superoperators.jl b/src/qobj/superoperators.jl
index 6bc9a71c3..6e17c904a 100644
--- a/src/qobj/superoperators.jl
+++ b/src/qobj/superoperators.jl
@@ -14,10 +14,6 @@ _sprepost(A::AbstractMatrix, B::AbstractMatrix) = kron(transpose(sparse(B)), spa
 _sprepost(A::AbstractMatrix, B::AbstractSparseMatrix) = kron(transpose(B), sparse(A))
 _sprepost(A::AbstractSparseMatrix, B::AbstractMatrix) = kron(transpose(sparse(B)), A)
 _sprepost(A::AbstractSparseMatrix, B::AbstractSparseMatrix) = kron(transpose(B), A)
-function _sprepost(A, B) # for any other input types
-    Id_cache = I(size(A, 1))
-    return _spre(A, Id_cache) * _spost(B, Id_cache)
-end
 
 ## if input is AbstractSciMLOperator 
 ## some of them are optimized to speed things up
@@ -25,7 +21,7 @@ end
 _spre(A::MatrixOperator, Id::AbstractMatrix) = MatrixOperator(_spre(A.A, Id))
 _spre(A::ScaledOperator, Id::AbstractMatrix) = ScaledOperator(A.λ, _spre(A.L, Id))
 _spre(A::AddedOperator, Id::AbstractMatrix) = AddedOperator(map(op -> _spre(op, Id), A.ops))
-function _spre(A::AbstractSciMLOperator, Id::AbstractMatrix)
+function _spre(A::AbstractSciMLOperator, Id::Union{AbstractMatrix,AbstractSciMLOperator})
     _lazy_tensor_warning(Id, A)
     return kron(Id, A)
 end
@@ -33,12 +29,17 @@ end
 _spost(B::MatrixOperator, Id::AbstractMatrix) = MatrixOperator(_spost(B.A, Id))
 _spost(B::ScaledOperator, Id::AbstractMatrix) = ScaledOperator(B.λ, _spost(B.L, Id))
 _spost(B::AddedOperator, Id::AbstractMatrix) = AddedOperator(map(op -> _spost(op, Id), B.ops))
-function _spost(B::AbstractSciMLOperator, Id::AbstractMatrix)
+function _spost(B::AbstractSciMLOperator, Id::Union{AbstractMatrix,AbstractSciMLOperator})
     B_T = transpose(B)
     _lazy_tensor_warning(B_T, Id)
     return kron(B_T, Id)
 end
 
+function _sprepost(A::AbstractSciMLOperator, B::AbstractSciMLOperator)
+    Id_cache = IdentityOperator(size(A, 1))
+    return _spre(A, Id_cache) * _spost(B, Id_cache)
+end
+
 ## intrinsic liouvillian 
 _liouvillian(H::MT, Id::AbstractMatrix) where {MT<:Union{AbstractMatrix,AbstractSciMLOperator}} =
     -1im * (_spre(H, Id) - _spost(H, Id))
diff --git a/test/core-test/quantum_objects_evo.jl b/test/core-test/quantum_objects_evo.jl
index a417f52ac..d726a3252 100644
--- a/test/core-test/quantum_objects_evo.jl
+++ b/test/core-test/quantum_objects_evo.jl
@@ -215,7 +215,7 @@
             coef2(p, t) * conj(coef3(p, t)) * (spre(a) * spost(X') - 0.5 * spre(X' * a) - 0.5 * spost(X' * a)) + # cross terms
             conj(coef2(p, t)) * coef3(p, t) * (spre(X) * spost(a') - 0.5 * spre(a' * X) - 0.5 * spost(a' * X))   # cross terms
         L_ti = liouvillian(H_ti) + D1_ti + D2_ti
-        L_td = @test_logs (:warn,) (:warn,) liouvillian(H_td, c_ops) # warnings from lazy tensor in `lindblad_dissipator(c_op2)`
+        L_td = @test_logs (:warn,) (:warn,) (:warn,) (:warn,) liouvillian(H_td, c_ops) # warnings from lazy tensor in `lindblad_dissipator(c_op2)`
         ρvec = mat2vec(rand_dm(N))
         @test L_td(p, t) ≈ L_ti
         @test iscached(L_td) == false