mesolve fails when collapse operator contains a sum of constant and time-dependent operators (A + f(t)B)

[hckim012]

Bug Description

I encountered an error when trying to define a collapse operator in c_ops that is a sum of a constant operator and a time-dependent operator (e.g., $L(t)=a+f(t)a$).
While QuantumToolbox.jl handles QuantumObject (static) and simple QuantumObjectEvolution (single time-dependent term) correctly in c_ops, it fails with a cache error when the operator is a sum of constant and QuantumObjectEvolution or sum of two or more QuantumObjectEvolution.
This logic works in QuTiP (where c_ops =[ [a, [a, func]]] implies $L=a+f(t)a$), so there should be a workaround.

Code to Reproduce the Bug

using QuantumToolbox

N = 5
a = destroy(N)
H = a' * a

# Define a time-dependent function
func(p, t) = sin(t)

# 1. Create a Jump Operator L(t) = a + sin(t)*a
L_sum = a + QobjEvo(a, func)

# 2. Setup simulation
c_ops = [L_sum]
psi0 = fock(N, 0)
tlist = range(0, 10, length=100)

# 3. Run mesolve
# Expectation: Solves the master equation with D[L_sum]
# Actual: Throws AssertionError regarding Cache for ComposedOperator
mesolve(H, psi0, tlist, c_ops)

Code Output

┌ Warning: using lazy tensor (which can hurt performance) between data types: LinearAlgebra.Diagonal and SciMLOperators.ComposedOperator
└ @ QuantumToolbox ~/.julia/packages/QuantumToolbox/uRmBI/src/utilities.jl:170
┌ Warning: using lazy tensor (which can hurt performance) between data types: SciMLOperators.ComposedOperator and LinearAlgebra.Diagonal
└ @ QuantumToolbox ~/.julia/packages/QuantumToolbox/uRmBI/src/utilities.jl:170
ERROR: LoadError: AssertionError: Cache needs to be set up for ComposedOperator. Call cache_operator(L, u) first.
Stacktrace:
  [1] (::SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing})(w::Vector{ComplexF64}, v::Vector{ComplexF64}, u::Vector{ComplexF64}, p::SciMLBase.NullParameters, t::Float64, α::Bool, β::Bool; kwargs::@Kwargs{})
    @ SciMLOperators ~/.julia/packages/SciMLOperators/Qj6Wy/src/basic.jl:1042
  [2] (::SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing})(w::Vector{ComplexF64}, v::Vector{ComplexF64}, u::Vector{ComplexF64}, p::SciMLBase.NullParameters, t::Float64, α::Bool, β::Bool)
    @ SciMLOperators ~/.julia/packages/SciMLOperators/Qj6Wy/src/basic.jl:1039
  [3] macro expansion
    @ ~/.julia/packages/SciMLOperators/Qj6Wy/src/basic.jl:669 [inlined]
  [4] (::SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}}, Nothing}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}, Nothing}}}})(w::Vector{ComplexF64}, v::Vector{ComplexF64}, u::Vector{ComplexF64}, p::SciMLBase.NullParameters, t::Float64; kwargs::@Kwargs{})
    @ SciMLOperators ~/.julia/packages/SciMLOperators/Qj6Wy/src/basic.jl:658
  [5] (::SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}}, Nothing}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}, Nothing}}}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing})(du::Vector{ComplexF64}, u::Vector{ComplexF64}, p::SciMLBase.NullParameters, t::Float64)        
    @ SciMLBase ~/.julia/packages/SciMLBase/Dau5z/src/scimlfunctions.jl:2595
  [6] initialize!(integrator::OrdinaryDiffEqCore.ODEIntegrator{OrdinaryDiffEqLowOrderRK.DP5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, true, Vector{ComplexF64}, Nothing, Float64, SciMLBase.NullParameters, Float64, Float64, Float64, Float64, Vector{Vector{ComplexF64}}, SciMLBase.ODESolution{ComplexF64, 2, Vector{Vector{ComplexF64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{ComplexF64}}}, Nothing, SciMLBase.ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, true, SciMLBase.NullParameters, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}}, Nothing}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}, Nothing}}}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}, @Kwargs{abstol::Float64, reltol::Float64, save_everystep::Bool, save_end::Bool, saveat::Vector{Float64}, alg::OrdinaryDiffEqLowOrderRK.DP5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, tstops::Vector{Float64}, callback::SciMLBase.DiscreteCallback{typeof(DiffEqCallbacks.true_condition), DiffEqCallbacks.FunctionCallingAffect{QuantumToolbox.SaveFuncMESolve{Nothing, ProgressMeter.Progress, Base.RefValue{Int64}, Nothing}, Vector{Float64}, Vector{Float64}}, typeof(DiffEqCallbacks.functioncalling_initialize), typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}}, SciMLBase.StandardODEProblem}, OrdinaryDiffEqLowOrderRK.DP5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, OrdinaryDiffEqCore.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}}, Nothing}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}, Nothing}}}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}, Vector{Vector{ComplexF64}}, Vector{Float64}, Vector{Vector{Vector{ComplexF64}}}, Nothing, OrdinaryDiffEqLowOrderRK.DP5Cache{Vector{ComplexF64}, Vector{ComplexF64}, Vector{ComplexF64}, typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, Nothing}, SciMLBase.DEStats, Nothing, Nothing, Nothing, Nothing}, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}}, Nothing}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}, Nothing}}}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}, OrdinaryDiffEqLowOrderRK.DP5Cache{Vector{ComplexF64}, Vector{ComplexF64}, Vector{ComplexF64}, typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, OrdinaryDiffEqCore.DEOptions{Float64, Float64, Float64, Float64, OrdinaryDiffEqCore.PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Bool, SciMLBase.CallbackSet{Tuple{}, Tuple{SciMLBase.DiscreteCallback{typeof(DiffEqCallbacks.true_condition), DiffEqCallbacks.FunctionCallingAffect{QuantumToolbox.SaveFuncMESolve{Nothing, ProgressMeter.Progress, Base.RefValue{Int64}, Nothing}, Vector{Float64}, Vector{Float64}}, typeof(DiffEqCallbacks.functioncalling_initialize), typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Int64, Vector{Float64}, Vector{Float64}, Tuple{}}, Vector{ComplexF64}, ComplexF64, Nothing, DiffEqBase.DefaultInit, Nothing}, cache::OrdinaryDiffEqLowOrderRK.DP5Cache{Vector{ComplexF64}, Vector{ComplexF64}, Vector{ComplexF64}, typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False})
    @ OrdinaryDiffEqLowOrderRK ~/.julia/packages/OrdinaryDiffEqLowOrderRK/uKHOH/src/low_order_rk_perform_step.jl:630     
  [7] __init(prob::SciMLBase.ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, true, SciMLBase.NullParameters, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}}, Nothing}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}, Nothing}}}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}, @Kwargs{abstol::Float64, reltol::Float64, save_everystep::Bool, save_end::Bool, saveat::Vector{Float64}, alg::OrdinaryDiffEqLowOrderRK.DP5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, tstops::Vector{Float64}, callback::SciMLBase.DiscreteCallback{typeof(DiffEqCallbacks.true_condition), DiffEqCallbacks.FunctionCallingAffect{QuantumToolbox.SaveFuncMESolve{Nothing, ProgressMeter.Progress, Base.RefValue{Int64}, Nothing}, Vector{Float64}, Vector{Float64}}, typeof(DiffEqCallbacks.functioncalling_initialize), typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}}, SciMLBase.StandardODEProblem}, alg::OrdinaryDiffEqLowOrderRK.DP5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}; saveat::Vector{Float64}, tstops::Vector{Float64}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_discretes::Bool, save_start::Bool, save_end::Bool, callback::SciMLBase.DiscreteCallback{typeof(DiffEqCallbacks.true_condition), DiffEqCallbacks.FunctionCallingAffect{QuantumToolbox.SaveFuncMESolve{Nothing, ProgressMeter.Progress, Base.RefValue{Int64}, Nothing}, Vector{Float64}, Vector{Float64}}, typeof(DiffEqCallbacks.functioncalling_initialize), typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}, dense::Bool, calck::Bool, dt::Float64, dtmin::Float64, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{Int64}, abstol::Float64, reltol::Float64, qmin::Rational{Int64}, qmax::Int64, qsteady_min::Int64, qsteady_max::Int64, beta1::Nothing, beta2::Nothing, qoldinit::Rational{Int64}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(LinearAlgebra.opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), progress_id::Symbol, userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias::SciMLBase.ODEAliasSpecifier, initializealg::DiffEqBase.DefaultInit, kwargs::@Kwargs{alg::OrdinaryDiffEqLowOrderRK.DP5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/GMkz9/src/solve.jl:578
  [8] __init (repeats 2 times)
    @ ~/.julia/packages/OrdinaryDiffEqCore/GMkz9/src/solve.jl:11 [inlined]
  [9] #__solve#60
    @ ~/.julia/packages/OrdinaryDiffEqCore/GMkz9/src/solve.jl:6 [inlined]
 [10] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/GMkz9/src/solve.jl:1 [inlined]
 [11] solve_call(_prob::SciMLBase.ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, true, SciMLBase.NullParameters, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}}, Nothing}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}, Nothing}}}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}, @Kwargs{abstol::Float64, reltol::Float64, save_everystep::Bool, save_end::Bool, saveat::Vector{Float64}, alg::OrdinaryDiffEqLowOrderRK.DP5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, tstops::Vector{Float64}, callback::SciMLBase.DiscreteCallback{typeof(DiffEqCallbacks.true_condition), DiffEqCallbacks.FunctionCallingAffect{QuantumToolbox.SaveFuncMESolve{Nothing, ProgressMeter.Progress, Base.RefValue{Int64}, Nothing}, Vector{Float64}, Vector{Float64}}, typeof(DiffEqCallbacks.functioncalling_initialize), typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}}, SciMLBase.StandardODEProblem}, args::OrdinaryDiffEqLowOrderRK.DP5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/aB45d/src/solve.jl:127
 [12] solve_call
    @ ~/.julia/packages/DiffEqBase/aB45d/src/solve.jl:84 [inlined]
 [13] #solve_up#39
    @ ~/.julia/packages/DiffEqBase/aB45d/src/solve.jl:563 [inlined]
 [14] solve_up
    @ ~/.julia/packages/DiffEqBase/aB45d/src/solve.jl:540 [inlined]
 [15] #solve#38
    @ ~/.julia/packages/DiffEqBase/aB45d/src/solve.jl:530 [inlined]
 [16] solve
    @ ~/.julia/packages/DiffEqBase/aB45d/src/solve.jl:520 [inlined]
 [17] #mesolve#170
    @ ~/.julia/packages/QuantumToolbox/uRmBI/src/time_evolution/mesolve.jl:231 [inlined]
 [18] mesolve(prob::QuantumToolbox.TimeEvolutionProblem{SciMLBase.ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, true, SciMLBase.NullParameters, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}}, Nothing}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.FilterKwargs{typeof(SciMLOperators.DEFAULT_UPDATE_FUNC), Val{()}}}, SciMLOperators.TensorProductOperator{ComplexF64, Tuple{SciMLOperators.ComposedOperator{ComplexF64, Tuple{SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, SciMLOperators.var"#45#47"{SciMLOperators.var"#45#46#48"{SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}}}}, SciMLOperators.MatrixOperator{ComplexF64, LinearAlgebra.Transpose{ComplexF64, LinearAlgebra.Adjoint{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}, Nothing}, SciMLOperators.MatrixOperator{Float64, LinearAlgebra.Diagonal{Float64, FillArrays.Ones{Float64, 1, Tuple{Base.OneTo{Int64}}}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}, Nothing}}}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}, @Kwargs{abstol::Float64, reltol::Float64, save_everystep::Bool, save_end::Bool, saveat::Vector{Float64}, alg::OrdinaryDiffEqLowOrderRK.DP5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, tstops::Vector{Float64}, callback::SciMLBase.DiscreteCallback{typeof(DiffEqCallbacks.true_condition), DiffEqCallbacks.FunctionCallingAffect{QuantumToolbox.SaveFuncMESolve{Nothing, ProgressMeter.Progress, Base.RefValue{Int64}, Nothing}, Vector{Float64}, Vector{Float64}}, typeof(DiffEqCallbacks.functioncalling_initialize), typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}}, SciMLBase.StandardODEProblem}, Vector{Float64}, Dimensions{1, Tuple{Space}}, @NamedTuple{isoperket::Val{false}}}, alg::OrdinaryDiffEqLowOrderRK.DP5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False})
    @ QuantumToolbox ~/.julia/packages/QuantumToolbox/uRmBI/src/time_evolution/mesolve.jl:230
 [19] mesolve(H::QuantumObject{Operator, Dimensions{1, Tuple{Space}}, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, ψ0::QuantumObject{Ket, Dimensions{1, Tuple{Space}}, Vector{ComplexF64}}, tlist::StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, c_ops::Vector{QuantumObjectEvolution{Operator, Dimensions{1, Tuple{Space}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}}; alg::OrdinaryDiffEqLowOrderRK.DP5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, e_ops::Nothing, params::SciMLBase.NullParameters, progress_bar::Val{true}, inplace::Val{true}, kwargs::@Kwargs{})
    @ QuantumToolbox ~/.julia/packages/QuantumToolbox/uRmBI/src/time_evolution/mesolve.jl:224
 [20] mesolve(H::QuantumObject{Operator, Dimensions{1, Tuple{Space}}, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, ψ0::QuantumObject{Ket, Dimensions{1, Tuple{Space}}, Vector{ComplexF64}}, tlist::StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, c_ops::Vector{QuantumObjectEvolution{Operator, Dimensions{1, Tuple{Space}}, SciMLOperators.AddedOperator{ComplexF64, Tuple{SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}, SciMLOperators.ScaledOperator{ComplexF64, SciMLOperators.ScalarOperator{ComplexF64, QuantumToolbox.var"#35#36"{var"#1#2"}}, SciMLOperators.MatrixOperator{ComplexF64, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{Nothing, Val{()}}}}}}}})
    @ QuantumToolbox ~/.julia/packages/QuantumToolbox/uRmBI/src/time_evolution/mesolve.jl:180
 [21] top-level scope
    @ ~/minimal_example.jl:18

Expected Behaviour

Should solve the master equation

Your Environment

Package information:
====================================
Julia              Ver. 1.11.6
QuantumToolbox     Ver. 0.39.0
SciMLOperators     Ver. 1.12.0
LinearSolve        Ver. 3.45.0
OrdinaryDiffEqCore Ver. 1.36.0

System information:
====================================
OS       : Linux (x86_64-linux-gnu)
WORD_SIZE: 64
LIBM     : libopenlibm
LLVM     : libLLVM-16.0.6 (ORCJIT, tigerlake)
BLAS     : libopenblas64_.so (ilp64)
Threads  : 1 (on 8 virtual cores)

Additional Context

No response

[ytdHuang]

Hi @hckim012

Actually, we just solved this bug in PR #596 yesterday.

There are two solutions:

Sol 1.

if you can wait until our next release PR #599, the above code you provide will be able to execute directly.

Sol 2.

If you would like to run it now, you can use the following code:

L = liouvillian(H, c_ops)
u = mat2vec(rand_dm(N))
L_cached = cache_operator(L, u)
mesolve(L_cached, psi0, tlist)

In this case, you generate the liouvillian and cache it by yourself. Note that this method still uses lazy tensor, which might hurt performances, while our fix in PR #596 address this issue.

[hckim012]

This is great! I'll be happy to wait a few days then.

[albertomercurio]

Hi @hckim012,

A new version has just been released. If you update the package, you error should not be there.

I'm closing the issue now. Feel free to reopen it if it still doesn't work.