diff --git a/Project.toml b/Project.toml
index 8fc4a3d6b..a7f6177e5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -12,6 +12,7 @@ HalfIntegers = "f0d1745a-41c9-11e9-1dd9-e5d34d218721"
 KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LoggingExtras = "e6f89c97-d47a-5376-807f-9c37f3926c36"
+MPSKitModels = "ca635005-6f8c-4cd1-b51d-8491250ef2ab"
 MatrixAlgebraKit = "6c742aac-3347-4629-af66-fc926824e5e4"
 OhMyThreads = "67456a42-1dca-4109-a031-0a68de7e3ad5"
 OptimKit = "77e91f04-9b3b-57a6-a776-40b61faaebe0"
@@ -20,6 +21,7 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 TensorKit = "07d1fe3e-3e46-537d-9eac-e9e13d0d4cec"
 TensorKitManifolds = "11fa318c-39cb-4a83-b1ed-cdc7ba1e3684"
+TensorKitTensors = "41b62e7d-e9d1-4e23-942c-79a97adf954b"
 TensorOperations = "6aa20fa7-93e2-5fca-9bc0-fbd0db3c71a2"
 VectorInterface = "409d34a3-91d5-4945-b6ec-7529ddf182d8"
 
@@ -35,7 +37,7 @@ projects = ["test", "docs"]
 [compat]
 Accessors = "0.1"
 Adapt = "4"
-BlockTensorKit = "0.3.11"
+BlockTensorKit = "0.3"
 Compat = "3.47, 4.10"
 DocStringExtensions = "0.9.3"
 HalfIntegers = "1.6.0"
@@ -43,13 +45,21 @@ KrylovKit = "0.8.3, 0.9.2, 0.10"
 LinearAlgebra = "1.6"
 LoggingExtras = "~1.0"
 MatrixAlgebraKit = "0.6.5"
+MPSKitModels = "0.4"
 OhMyThreads = "0.7, 0.8"
 OptimKit = "0.3.1, 0.4"
 Printf = "1"
 Random = "1"
 RecipesBase = "1.1"
-TensorKit = "0.16.5"
+TensorKit = "0.16, 0.17"
 TensorKitManifolds = "0.7, 0.8"
 TensorOperations = "5.5.1"
 VectorInterface = "0.2, 0.3, 0.4, 0.5"
 julia = "1.10"
+
+[sources]
+MPSKitModels = {url = "https://github.com/QuantumKitHub/MPSKitModels.jl", rev = "ksh/bump"}
+TensorKit = {url = "https://github.com/QuantumKitHub/TensorKit.jl", rev = "main"}
+TensorKitManifolds = {url = "https://github.com/QuantumKitHub/TensorKitManifolds.jl", rev = "ksh/bump"}
+TensorKitTensors = {url = "https://github.com/QuantumKitHub/TensorKitTensors.jl", rev = "ksh/compat"}
+BlockTensorKit = {url = "https://github.com/QuantumKitHub/BlockTensorKit.jl", rev = "ksh/mps"}
diff --git a/ext/MPSKitAdaptExt.jl b/ext/MPSKitAdaptExt.jl
index 6f0b0c7f2..78f4b41af 100644
--- a/ext/MPSKitAdaptExt.jl
+++ b/ext/MPSKitAdaptExt.jl
@@ -35,5 +35,7 @@ end
     MPSKit.JordanMPOTensor(space(W), adapt(to, W.A), adapt(to, W.B), adapt(to, W.C), adapt(to, W.D))
 @inline Adapt.adapt_structure(to, mpo::MPOHamiltonian) =
     MPOHamiltonian(map(x -> adapt(to, x), mpo.W))
+@inline Adapt.adapt_structure(to, ml::MPSKit.Multiline) = MPSKit.Multiline(map(adapt(to), ml.data))
+@inline Adapt.adapt_structure(to, pa::MPSKit.PeriodicArray) = MPSKit.PeriodicArray(map(adapt(to), pa.data))
 
 end
diff --git a/src/operators/abstractmpo.jl b/src/operators/abstractmpo.jl
index 54ecf0358..94ad49b80 100644
--- a/src/operators/abstractmpo.jl
+++ b/src/operators/abstractmpo.jl
@@ -99,7 +99,7 @@ Base.:\(α::Number, mpo::AbstractMPO) = scale(mpo, inv(α))
 
 function VectorInterface.scale(mpo::AbstractMPO, α::Number)
     T = VectorInterface.promote_scale(scalartype(mpo), scalartype(α))
-    dst = similar(mpo, T)
+    dst = similar(mpo, TensorKit.similarstoragetype(storagetype(mpo), T))
     return scale!(dst, mpo, α)
 end
 
@@ -132,7 +132,8 @@ function _fuse_mpo_mpo(O1::MPOTensor, O2::MPOTensor, Fₗ, Fᵣ)
         T = promote_type(scalartype(O1), scalartype(O2))
         V = fuse(left_virtualspace(O2) ⊗ left_virtualspace(O1)) ⊗ physicalspace(O1) ←
             physicalspace(O2) ⊗ fuse(right_virtualspace(O2) ⊗ right_virtualspace(O1))
-        return BraidingTensor{T}(V)
+        A = promote_storagetype(storagetype(O1), storagetype(O2), T)
+        return BraidingTensor{T, typeof(V), A}(V)
     elseif O1 isa BraidingTensor
         @plansor O′[-1 -2; -3 -4] := Fₗ[-1; 1 2] * O2[1 3; -3 5] *
             τ[2 -2; 3 4] * conj(Fᵣ[-4; 5 4])
@@ -152,16 +153,21 @@ Compute the mpo tensor that arises from multiplying MPOs.
 """
 function fuse_mul_mpo(O1, O2)
     TT = promote_type(scalartype(O1), scalartype(O2))
-    T = TensorKit.similarstoragetype(storagetype(O1), TT)
+    T = if O1 isa BraidingTensor
+        TensorKit.similarstoragetype(storagetype(O2), TT)
+    else
+        TensorKit.similarstoragetype(storagetype(O1), TT)
+    end
     F_left = fuser(T, left_virtualspace(O2), left_virtualspace(O1))
     F_right = fuser(T, right_virtualspace(O2), right_virtualspace(O1))
     return _fuse_mpo_mpo(O1, O2, F_left, F_right)
 end
-function fuse_mul_mpo(O1::BraidingTensor, O2::BraidingTensor)
-    T = promote_type(scalartype(O1), scalartype(O2))
+function fuse_mul_mpo(O1::BraidingTensor{T1, S1, A1}, O2::BraidingTensor{T2, S2, A2}) where {T1, T2, S1, S2, A1, A2}
+    T = promote_type(T1, T2)
+    A = TensorKit.promote_storagetype(A1, A2)
     V = fuse(left_virtualspace(O2) ⊗ left_virtualspace(O1)) ⊗ physicalspace(O1) ←
         physicalspace(O2) ⊗ fuse(right_virtualspace(O2) ⊗ right_virtualspace(O1))
-    return BraidingTensor{T}(V)
+    return BraidingTensor{T, spacetype(V), A}(V)
 end
 function fuse_mul_mpo(
         O1::AbstractBlockTensorMap{T₁, S, 2, 2}, O2::AbstractBlockTensorMap{T₂, S, 2, 2}
@@ -198,7 +204,7 @@ function add_physical_charge(O::BraidingTensor, charge::Sector)
     auxspace = Vect[typeof(charge)](charge => 1)'
     V = left_virtualspace(O) ⊗ fuse(physicalspace(O), auxspace) ←
         fuse(physicalspace(O), auxspace) ⊗ right_virtualspace(O)
-    return BraidingTensor{scalartype(O)}(V)
+    return BraidingTensor{scalartype(O), spacetype(V), storagetype(O)}(V)
 end
 function add_physical_charge(O::AbstractBlockTensorMap{<:Any, <:Any, 2, 2}, charge::Sector)
     sectortype(O) == typeof(charge) || throw(SectorMismatch())
diff --git a/src/operators/jordanmpotensor.jl b/src/operators/jordanmpotensor.jl
index 8131f90fb..c815e3276 100644
--- a/src/operators/jordanmpotensor.jl
+++ b/src/operators/jordanmpotensor.jl
@@ -60,7 +60,7 @@ end
 
 const JordanMPOTensorMap{T, S, A <: DenseVector{T}} = JordanMPOTensor{
     T, S,
-    Union{TensorMap{T, S, 2, 2, A}, BraidingTensor{T, S}},
+    Union{TensorMap{T, S, 2, 2, A}, BraidingTensor{T, S, A}},
     TensorMap{T, S, 2, 1, A},
     TensorMap{T, S, 1, 2, A},
     TensorMap{T, S, 1, 1, A},
@@ -124,7 +124,8 @@ end
 function jordanmpotensortype(::Type{S}, ::Type{E}) where {S <: VectorSpace, E}
     TA = tensormaptype(S, 2, 2, E)
     T = scalartype(TA)
-    Tτ = BraidingTensor{T, S}
+    TT = storagetype(TA)
+    Tτ = BraidingTensor{T, S, TT}
     TB = tensormaptype(S, 2, 1, E)
     TC = tensormaptype(S, 1, 2, E)
     TD = tensormaptype(S, 1, 1, E)
@@ -135,6 +136,10 @@ function jordanmpotensortype(::Type{O}) where {O <: AbstractTensorMap}
 end
 Base.similar(W::JordanMPOTensor, ::Type{TorA}) where {TorA} =
     jordanmpotensortype(spacetype(W), TorA)(undef, space(W))
+Base.similar(W::JordanMPOTensor, V::VectorSpace) =
+    jordanmpotensortype(spacetype(V), storagetype(W))(undef, V)
+Base.similar(W::JordanMPOTensor, V::VectorSpace, ::Type{TorA}) where {TorA} =
+    jordanmpotensortype(spacetype(V), TorA)(undef, V)
 
 # Properties
 # ----------
@@ -172,7 +177,7 @@ BlockTensorKit.issparse(W::JordanMPOTensor) = true
 # Converters
 # ----------
 function BlockTensorKit.SparseBlockTensorMap(W::JordanMPOTensor)
-    τ = BraidingTensor{scalartype(W)}(eachspace(W)[1])
+    τ = BraidingTensor{scalartype(W), spacetype(eachspace(W)[1]), storagetype(W)}(eachspace(W)[1])
     W′ = SparseBlockTensorMap{AbstractTensorMap{scalartype(W), spacetype(W), 2, 2}}(
         undef_blocks, space(W)
     )
@@ -205,7 +210,8 @@ end
 for f in (:real, :complex)
     @eval function Base.$f(W::JordanMPOTensor)
         E = $f(scalartype(W))
-        W′ = JordanMPOTensor{E}(undef, space(W))
+        TE = TensorKit.similarstoragetype(TensorKit.storagetype(W), E)
+        W′ = similar(W, TE)
         for (I, v) in nonzero_pairs(W.A)
             W′.A[I] = $f(v)
         end
@@ -232,7 +238,10 @@ end
     j = I[4]
     if (size(W, 4) > 1 && i == 1 && j == 1) ||
             (size(W, 1) > 1 && i == size(W, 1) && j == size(W, 4))
-        return BraidingTensor{scalartype(W)}(eachspace(W)[1])
+        T = scalartype(W)
+        TA = storagetype(W)
+        S = spacetype(eachspace(W)[1])
+        return BraidingTensor{T, S, TA}(eachspace(W)[1])
     elseif i == 1 && j == size(W, 4)
         return insertrightunit(insertleftunit(only(W.D), 1), 3)
     elseif i == 1
@@ -242,7 +251,7 @@ end
     elseif 1 < i < size(W, 1) && 1 < j < size(W, 4)
         return W.A[i - 1, 1, 1, j - 1]
     else
-        return zeros(scalartype(W), eachspace(W)[i, 1, 1, j])
+        return zeros(storagetype(W), eachspace(W)[i, 1, 1, j])
     end
 end
 
@@ -357,7 +366,7 @@ function add_physical_charge(O::JordanMPOTensor, charge::Sector)
     Vdst = left_virtualspace(O) ⊗
         fuse(physicalspace(O), auxspace) ←
         fuse(physicalspace(O), auxspace) ⊗ right_virtualspace(O)
-    Odst = JordanMPOTensor{scalartype(O)}(undef, Vdst)
+    Odst = similar(O, Vdst)
     for (I, v) in nonzero_pairs(O)
         Odst[I] = add_physical_charge(v, charge)
     end
diff --git a/src/operators/mpo.jl b/src/operators/mpo.jl
index 8630a0d56..7bf0d16ca 100644
--- a/src/operators/mpo.jl
+++ b/src/operators/mpo.jl
@@ -62,7 +62,7 @@ eachsite(mpo::InfiniteMPO) = PeriodicArray(eachindex(mpo))
 function Base.similar(mpo::MPO{<:MPOTensor}, ::Type{O}, L::Int) where {O <: MPOTensor}
     return MPO(similar(parent(mpo), O, L))
 end
-function Base.similar(mpo::MPO, ::Type{T}) where {T <: Number}
+function Base.similar(mpo::MPO, ::Type{T}) where {T <: Union{Number, DenseVector}}
     return MPO(similar.(parent(mpo), T))
 end
 
diff --git a/src/operators/mpohamiltonian.jl b/src/operators/mpohamiltonian.jl
index daf7eb6a5..1ddf60a4a 100644
--- a/src/operators/mpohamiltonian.jl
+++ b/src/operators/mpohamiltonian.jl
@@ -59,19 +59,19 @@ function InfiniteMPOHamiltonian(Ws::AbstractVector{O}) where {O <: MPOTensor}
 end
 
 """
-    FiniteMPOHamiltonian(Ws::Vector{<:Matrix})
+    FiniteMPOHamiltonian(Ws::Vector{<:AbstractMatrix})
 
 Create a `FiniteMPOHamiltonian` from a vector of matrices, such that `Ws[i][j, k]` represents
 the operator at site `i`, left level `j` and right level `k`. Here, the entries can be
 either `MPOTensor`, `Missing` or `Number`.
 """
-function FiniteMPOHamiltonian(Ws::Vector{<:Matrix})
+function FiniteMPOHamiltonian(Ws::Vector{<:AbstractMatrix})
     T = promote_type(_split_mpoham_types.(Ws)...)
     W = jordanmpotensortype(T)
     return FiniteMPOHamiltonian{W}(Ws)
 end
-function FiniteMPOHamiltonian{O}(W_mats::Vector{<:Matrix}) where {O <: JordanMPOTensor}
-    T = scalartype(O)
+function FiniteMPOHamiltonian{O}(W_mats::Vector{<:AbstractMatrix}) where {O <: JordanMPOTensor}
+    T = storagetype(O)
     L = length(W_mats)
     # initialize sumspaces
     S = spacetype(O)
@@ -140,7 +140,8 @@ function FiniteMPOHamiltonian{O}(W_mats::Vector{<:Matrix}) where {O <: JordanMPO
             if v isa MPOTensor
                 W[I] = v
             elseif !iszero(v)
-                τ = BraidingTensor{T}(eachspace(W)[I])
+                A = TensorKit.similarstoragetype(T, eltype(T))
+                τ = BraidingTensor{eltype(T), spacetype(eachspace(W)[I]), A}(eachspace(W)[I])
                 W[I] = isone(v) ? τ : τ * v
             end
         end
@@ -157,12 +158,12 @@ Create a `InfiniteMPOHamiltonian` from a vector of matrices, such that `Ws[i][j,
 the the operator at site `i`, left level `j` and right level `k`. Here, the entries can be
 either `MPOTensor`, `Missing` or `Number`.
 """
-function InfiniteMPOHamiltonian(Ws::Vector{<:Matrix})
+function InfiniteMPOHamiltonian(Ws::Vector{<:AbstractMatrix})
     T = promote_type(_split_mpoham_types.(Ws)...)
     TW = jordanmpotensortype(T)
     return InfiniteMPOHamiltonian{TW}(Ws)
 end
-function InfiniteMPOHamiltonian{O}(W_mats::Vector{<:Matrix}) where {O <: MPOTensor}
+function InfiniteMPOHamiltonian{O}(W_mats::Vector{<:AbstractMatrix}) where {O <: MPOTensor}
     # InfiniteMPOHamiltonian only works for square matrices:
     for W_mat in W_mats
         size(W_mat, 1) == size(W_mat, 2) ||
@@ -172,7 +173,7 @@ function InfiniteMPOHamiltonian{O}(W_mats::Vector{<:Matrix}) where {O <: MPOTens
         throw(ArgumentError("matrices should have the same size"))
     nlvls = size(W_mats[1], 1)
 
-    T = scalartype(O)
+    T = storagetype(O)
     L = length(W_mats)
     # initialize sumspaces
     S = spacetype(O)
@@ -261,7 +262,8 @@ function InfiniteMPOHamiltonian{O}(W_mats::Vector{<:Matrix}) where {O <: MPOTens
             if v isa MPOTensor
                 W[I] = v
             elseif !iszero(v)
-                τ = BraidingTensor{T}(eachspace(W)[I])
+                A = similarstoragetype(T, eltype(T))
+                τ = BraidingTensor{eltype(T), typeof(eachspace(W)[I]), A}(eachspace(W)[I])
                 W[I] = isone(v) ? τ : τ * v
             end
         end
@@ -477,7 +479,8 @@ function FiniteMPOHamiltonian(lattice::AbstractArray{<:VectorSpace}, local_opera
             key_R = key_R′ == 0 ? length(virtualsumspaces[site + 1]) : key_R′
             O[key_L, 1, 1, key_R] += if o isa Number
                 iszero(o) && continue
-                τ = BraidingTensor{scalartype(TW)}(eachspace(O)[key_L, 1, 1, key_R])
+                S = spacetype(eachspace(O)[key_L, 1, 1, key_R])
+                τ = BraidingTensor{scalartype(TW), S, storagetype(TW)}(eachspace(O)[key_L, 1, 1, key_R])
                 isone(o) ? τ : τ * o
             else
                 o
@@ -504,10 +507,8 @@ function InfiniteMPOHamiltonian(lattice′::AbstractArray{<:VectorSpace}, local_
     end
 
     # partial sort by interaction range
-    local_mpos = sort!(
-        map(Base.Fix1(instantiate_operator, lattice), collect(local_operators));
-        by = x -> length(x[1])
-    )
+    unsorted_mpos = map(Base.Fix1(instantiate_operator, lattice), [local_operators...])
+    local_mpos = sort!(unsorted_mpos; by = x -> length(x[1]))
 
     for (sites, local_mpo) in local_mpos
         local key_R # trick to define key_R before the first iteration
@@ -600,7 +601,8 @@ function InfiniteMPOHamiltonian(lattice′::AbstractArray{<:VectorSpace}, local_
             key_R = key_R′ == 0 ? length(virtualspaces[site]) : key_R′
             O[key_L, 1, 1, key_R] += if o isa Number
                 iszero(o) && continue
-                τ = BraidingTensor{scalartype(TW)}(eachspace(O)[key_L, 1, 1, key_R])
+                S = typeof(eachspace(O)[key_L, 1, 1, key_R])
+                τ = BraidingTensor{scalartype(TW), S, storagetype(TW)}(eachspace(O)[key_L, 1, 1, key_R])
                 isone(o) ? τ : τ * o
             else
                 o
@@ -703,8 +705,8 @@ end
 function Base.similar(H::MPOHamiltonian, ::Type{O}, L::Int) where {O <: MPOTensor}
     return MPOHamiltonian(similar(parent(H), O, L))
 end
-function Base.similar(H::MPOHamiltonian, ::Type{T}) where {T <: Number}
-    return MPOHamiltonian(similar.(parent(H), T))
+function Base.similar(H::MPOHamiltonian, ::Type{TorA}) where {TorA <: Union{Number, DenseVector}}
+    return MPOHamiltonian(similar.(parent(H), TorA))
 end
 
 # Linear Algebra
@@ -729,7 +731,7 @@ function Base.:+(
             ⊞(Vtriv, right_virtualspace(A), Vtriv)
         V = Vleft ⊗ physicalspace(A) ← physicalspace(A) ⊗ Vright
 
-        H[i] = eltype(H)(V, A, B, C, D)
+        H[i] = JordanMPOTensor(V, A, B, C, D)
     end
     return FiniteMPOHamiltonian(H)
 end
@@ -751,7 +753,7 @@ function Base.:+(
         Vright = ⊞(Vtriv, right_virtualspace(A), Vtriv)
         V = Vleft ⊗ physicalspace(A) ← physicalspace(A) ⊗ Vright
 
-        H[i] = eltype(H)(V, A, B, C, D)
+        H[i] = JordanMPOTensor(V, A, B, C, D)
     end
     return InfiniteMPOHamiltonian(H)
 end
@@ -821,7 +823,7 @@ function Base.:*(H::FiniteMPOHamiltonian, mps::FiniteMPS)
         A,
         tensormaptype(
             spacetype(mps), numout(eltype(mps)), numin(eltype(mps)),
-            promote_type(scalartype(H), scalartype(mps))
+            promote_type(storagetype(H), storagetype(mps))
         )
     )
     # left to middle
diff --git a/src/operators/ortho.jl b/src/operators/ortho.jl
index b48d12ef1..b5c5ef180 100644
--- a/src/operators/ortho.jl
+++ b/src/operators/ortho.jl
@@ -11,7 +11,14 @@ function left_canonicalize!(
     d = sqrt(dim(P))
 
     # orthogonalize second column against first
-    WI = removeunit(W[1, 1, 1, 1], 1)
+    Wi = W[1, 1, 1, 1]
+    if Wi isa BraidingTensor
+        Wi′ = removeunit(Wi, 1)
+        WI = similar(Wi′, TensorKit.storagetype(H))
+        copy!(WI, Wi′)
+    else
+        WI = removeunit(Wi, 1)
+    end
     @plansor t[l; r] := conj(WI[p; p' l]) * W.C[p; p' r]
     # TODO: the following is currently broken due to a TensorKit bug
     # @plansor C′[p; p' r] := W.C[p; p' r] - WI[p; p' l] * t[l; r]
@@ -99,7 +106,14 @@ function right_canonicalize!(
     d = sqrt(dim(P))
 
     # orthogonalize second row against last
-    WI = removeunit(W[end, 1, 1, end], 4)
+    Wi = W[end, 1, 1, end]
+    if Wi isa BraidingTensor
+        Wi′ = removeunit(Wi, 4)
+        WI = similar(Wi′, TensorKit.storagetype(H))
+        copy!(WI, Wi′)
+    else
+        WI = removeunit(Wi, 4)
+    end
     @plansor t[l; r] := conj(WI[r p; p']) * W.B[l p; p']
     # TODO: the following is currently broken due to a TensorKit bug
     # @plansor B′[l p; p'] := W.B[l p; p'] - WI[r p; p'] * t[l; r]
@@ -124,7 +138,8 @@ function right_canonicalize!(
         end
         H[i] = JordanMPOTensor(V ⊗ P ← domain(W), Q1, Q2, W.C, W.D)
     else
-        tmp = transpose(cat(insertleftunit(B′, 4), W.A; dims = 4), ((1,), (3, 4, 2)))
+        B′′ = insertleftunit(B′, 4)
+        tmp = transpose(cat(B′′, W.A; dims = 4), ((1,), (3, 4, 2)))
         R, Q = right_orth!(tmp; alg)
         if dim(R) == 0
             V = _rightunit ⊞ _rightunit
diff --git a/test/Project.toml b/test/Project.toml
index da4cf3f70..569eefa1b 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -24,7 +24,7 @@ MPSKit = {path = ".."}
 
 [compat]
 Aqua = "0.8.9"
-CUDA = "5.9"
+CUDA = "5, 6"
 Combinatorics = "1"
 ParallelTestRunner = "2"
 Plots = "1.40"
@@ -32,4 +32,4 @@ Pkg = "1"
 TensorKitTensors = "0.2"
 Test = "1"
 TestExtras = "0.3"
-cuTENSOR = "2.3"
+cuTENSOR = "1, 6"
diff --git a/test/gpu/cuda/operators.jl b/test/gpu/cuda/operators.jl
index cf42a4e7b..030fd74a0 100644
--- a/test/gpu/cuda/operators.jl
+++ b/test/gpu/cuda/operators.jl
@@ -83,3 +83,189 @@ using Adapt, CUDA, cuTENSOR
 
     @test dot(mpomps₁, mpomps₁) ≈ dot(mpo₁, mpo₁)
 end
+
+@testset "Finite CuMPOHamiltonian T ($T), V ($(spacetype(V)))" for T in (Float64, ComplexF64), V in (ℂ^2, U1Space(-1 => 1, 0 => 1, 1 => 1))
+    L = 3
+    lattice = fill(V, L)
+    O₁ = randn(T, V, V)
+    O₁ += O₁'
+    E = id(CuVector{T, CUDA.DeviceMemory}, domain(O₁))
+    O₂ = randn(T, V^2 ← V^2)
+    O₂ += O₂'
+
+    dO₁ = adapt(CuVector{T, CUDA.DeviceMemory}, O₁)
+    dO₂ = adapt(CuVector{T, CUDA.DeviceMemory}, O₂)
+    hH1 = FiniteMPOHamiltonian(lattice, i => O₁ for i in 1:L)
+    hH2 = FiniteMPOHamiltonian(lattice, (i, i + 1) => O₂ for i in 1:(L - 1))
+    hH3 = FiniteMPOHamiltonian(lattice, 1 => O₁, (2, 3) => O₂, (1, 3) => O₂)
+    H1 = adapt(CuVector{T, CUDA.DeviceMemory}, hH1)
+    H2 = adapt(CuVector{T, CUDA.DeviceMemory}, hH2)
+    H3 = adapt(CuVector{T, CUDA.DeviceMemory}, hH3)
+    @test TensorKit.storagetype(H1) == CuVector{T, CUDA.DeviceMemory}
+    @test TensorKit.storagetype(H2) == CuVector{T, CUDA.DeviceMemory}
+    @test TensorKit.storagetype(H3) == CuVector{T, CUDA.DeviceMemory}
+
+    @test scalartype(H1) == scalartype(H2) == scalartype(H3) == T
+    if !(T <: Complex)
+        for H in (H1, H2, H3)
+            Hc = @constinferred complex(H)
+            @test scalartype(Hc) == complex(T)
+            @test TensorKit.storagetype(Hc) == CuVector{complex(T), CUDA.DeviceMemory}
+        end
+    end
+
+    # check if constructor works by converting back to tensormap
+    hH1_tm = convert(TensorMap, hH1)
+    H1_tm = convert(TensorMap, H1)
+    @test TensorKit.storagetype(H1_tm) == CuVector{T, CUDA.DeviceMemory}
+    operators = vcat(fill(E, L - 1), dO₁)
+    @test H1_tm ≈ mapreduce(+, 1:L) do i
+        return reduce(⊗, circshift(operators, i))
+    end
+    operators = vcat(fill(E, L - 2), dO₂)
+    @test convert(TensorMap, H2) ≈ mapreduce(+, 1:(L - 1)) do i
+        return reduce(⊗, circshift(operators, i))
+    end
+    @test convert(TensorMap, H3) ≈
+        dO₁ ⊗ E ⊗ E + E ⊗ dO₂ + permute(dO₂ ⊗ E, ((1, 3, 2), (4, 6, 5)))
+
+    # check if adding terms on the same site works
+    single_terms = Iterators.flatten(Iterators.repeated((i => O₁ / 2 for i in 1:L), 2))
+    H4 = adapt(CuVector{T, CUDA.DeviceMemory}, FiniteMPOHamiltonian(lattice, single_terms))
+    @test TensorKit.storagetype(H4) == CuVector{T, CUDA.DeviceMemory}
+    @test H4 ≈ H1 atol = 1.0e-6
+    double_terms = Iterators.flatten(
+        Iterators.repeated(((i, i + 1) => O₂ / 2 for i in 1:(L - 1)), 2)
+    )
+    H5 = adapt(CuVector{T, CUDA.DeviceMemory}, FiniteMPOHamiltonian(lattice, double_terms))
+    @test TensorKit.storagetype(H5) == CuVector{T, CUDA.DeviceMemory}
+    @test H5 ≈ H2 atol = 1.0e-6
+
+    # test linear algebra
+    @test H1 ≈
+        adapt(CuVector{T, CUDA.DeviceMemory}, FiniteMPOHamiltonian(lattice, 1 => O₁)) +
+        adapt(CuVector{T, CUDA.DeviceMemory}, FiniteMPOHamiltonian(lattice, 2 => O₁)) +
+        adapt(CuVector{T, CUDA.DeviceMemory}, FiniteMPOHamiltonian(lattice, 3 => O₁))
+    @test TensorKit.storagetype(H1) == CuVector{T, CUDA.DeviceMemory}
+
+    H1′a = 0.8 * H1
+    @test TensorKit.storagetype(H1′a) == CuVector{T, CUDA.DeviceMemory}
+    H1′b = 0.2 * H1
+    @test TensorKit.storagetype(H1′b) == CuVector{T, CUDA.DeviceMemory}
+    H1′ = H1′a + H1′b
+    @test TensorKit.storagetype(H1′) == CuVector{T, CUDA.DeviceMemory}
+    @test H1′ ≈ H1 atol = 1.0e-6
+    @test convert(TensorMap, H1 + H2) ≈ convert(TensorMap, H1) + convert(TensorMap, H2) atol = 1.0e-6
+    # failing due to truncation problem in TensorKit?
+    # H1_trunc = changebonds(H1, SvdCut(; trscheme = truncrank(0)))
+    # @test H1_trunc ≈ H1
+    # @test all(left_virtualspace(H1_trunc) .== left_virtualspace(H1))
+
+    # test dot and application
+    hstate = rand(T, prod(lattice))
+    state = adapt(CuVector{T, CUDA.DeviceMemory}, hstate)
+    @test TensorKit.storagetype(state) == CuVector{T, CUDA.DeviceMemory}
+    hmps = FiniteMPS(hstate)
+    mps = adapt(CuVector{T, CUDA.DeviceMemory}, hmps)
+    @test TensorKit.storagetype(mps) == CuVector{T, CUDA.DeviceMemory}
+    @test norm(mps) ≈ norm(state)
+    @test norm(H1) ≈ norm(H1_tm)
+
+    @test TensorKit.storagetype(H1) == CuVector{T, CUDA.DeviceMemory}
+    hH1mps = hH1 * hmps
+    H1mps = H1 * mps
+    @test TensorKit.storagetype(H1mps) == CuVector{T, CUDA.DeviceMemory}
+    hH1tmstate = hH1_tm * hstate
+    H1tmstate = H1_tm * state
+    @test TensorKit.storagetype(H1tmstate) == CuVector{T, CUDA.DeviceMemory}
+    @test norm(H1mps) ≈ norm(H1tmstate)
+
+    H1mpstm = convert(TensorMap, H1mps)
+    @test TensorKit.storagetype(H1mpstm) == CuVector{T, CUDA.DeviceMemory}
+    @test H1mpstm ≈ H1tmstate
+    @test H1 * state ≈ H1tmstate
+
+    H2mps = H2 * mps
+    hH2mps = hH2 * hmps
+    @test TensorKit.storagetype(H2mps) == CuVector{T, CUDA.DeviceMemory}
+    @test dot(mps, H2, mps) ≈ dot(mps, H2mps)
+    @test dot(hmps, hH2mps) ≈ dot(mps, H2mps)
+    @test dot(mps, H2, mps) ≈ dot(hmps, hH2mps)
+
+    # test constructor from dictionary with mixed linear and Cartesian lattice indices as keys
+    grid = square = fill(V, 3, 3)
+
+    local_operators = Dict((I,) => O₁ for I in eachindex(grid))
+    I_vertical = CartesianIndex(1, 0)
+    vertical_operators = Dict(
+        (I, I + I_vertical) => O₂ for I in eachindex(IndexCartesian(), square) if I[1] < size(square, 1)
+    )
+    I_horizontal = CartesianIndex(0, 1)
+    horizontal_operators = Dict(
+        (I, I + I_horizontal) => O₂ for I in eachindex(IndexCartesian(), square) if I[2] < size(square, 1)
+    )
+    operators = merge(local_operators, vertical_operators, horizontal_operators)
+    H4 = adapt(CuVector{T, CUDA.DeviceMemory}, FiniteMPOHamiltonian(grid, operators))
+    @test TensorKit.storagetype(H4) == CuVector{T, CUDA.DeviceMemory}
+
+    @test H4 ≈
+        adapt(CuVector{T, CUDA.DeviceMemory}, FiniteMPOHamiltonian(grid, local_operators)) +
+        adapt(CuVector{T, CUDA.DeviceMemory}, FiniteMPOHamiltonian(grid, vertical_operators)) +
+        adapt(CuVector{T, CUDA.DeviceMemory}, FiniteMPOHamiltonian(grid, horizontal_operators)) atol = 1.0e-4
+    @test TensorKit.storagetype(H4) == CuVector{T, CUDA.DeviceMemory}
+
+    H4′ = H4 / 3 + 2H4 / 3
+    @test TensorKit.storagetype(H4′) == CuVector{T, CUDA.DeviceMemory}
+    H5 = changebonds(H4′, SvdCut(; trscheme = trunctol(; atol = 1.0e-12)))
+    @test TensorKit.storagetype(H5) == CuVector{T, CUDA.DeviceMemory}
+    psi = adapt(CuArray, FiniteMPS(physicalspace(H5), V ⊕ rightunitspace(V)))
+    @test expectation_value(psi, H4) ≈ expectation_value(psi, H5)
+end
+
+@testset "CuInfiniteMPOHamiltonian $(sectortype(pspace))" for (pspace, Dspace) in zip(pspaces, vspaces)
+    # generate a 1-2-3 body interaction
+    operators = ntuple(3) do i
+        O = rand(ComplexF64, pspace^i, pspace^i)
+        return O += O'
+    end
+
+    H1 = adapt(CuVector{ComplexF64, CUDA.DeviceMemory}, InfiniteMPOHamiltonian(operators[1]))
+    H2 = adapt(CuVector{ComplexF64, CUDA.DeviceMemory}, InfiniteMPOHamiltonian(operators[2]))
+    H3 = adapt(CuVector{ComplexF64, CUDA.DeviceMemory}, repeat(InfiniteMPOHamiltonian(operators[3]), 2))
+
+    @test TensorKit.storagetype(H1) == CuVector{ComplexF64, CUDA.DeviceMemory}
+    @test TensorKit.storagetype(H2) == CuVector{ComplexF64, CUDA.DeviceMemory}
+    @test TensorKit.storagetype(H3) == CuVector{ComplexF64, CUDA.DeviceMemory}
+    # make a teststate to measure expectation values for
+    ψ1 = adapt(CuVector{ComplexF64, CUDA.DeviceMemory}, InfiniteMPS([pspace], [Dspace]))
+    ψ2 = adapt(CuVector{ComplexF64, CUDA.DeviceMemory}, InfiniteMPS([pspace, pspace], [Dspace, Dspace]))
+    @test TensorKit.storagetype(ψ1) == CuVector{ComplexF64, CUDA.DeviceMemory}
+    @test TensorKit.storagetype(ψ2) == CuVector{ComplexF64, CUDA.DeviceMemory}
+
+    e1 = expectation_value(ψ1, H1)
+    e2 = expectation_value(ψ1, H2)
+
+    H1 = 2 * H1
+    @test TensorKit.storagetype(H1) == CuVector{ComplexF64, CUDA.DeviceMemory}
+    H1 -= [1]
+    @test TensorKit.storagetype(H1) == CuVector{ComplexF64, CUDA.DeviceMemory}
+    @test e1 * 2 - 1 ≈ expectation_value(ψ1, H1) atol = 1.0e-10
+
+    H1 = H1 + H2
+    @test TensorKit.storagetype(H1) == CuVector{ComplexF64, CUDA.DeviceMemory}
+    @test e1 * 2 + e2 - 1 ≈ expectation_value(ψ1, H1) atol = 1.0e-10
+
+    H1 = repeat(H1, 2)
+    @test TensorKit.storagetype(H1) == CuVector{ComplexF64, CUDA.DeviceMemory}
+
+    e1 = expectation_value(ψ2, H1)
+    e3 = expectation_value(ψ2, H3)
+
+    @test e1 + e3 ≈ expectation_value(ψ2, H1 + H3) atol = 1.0e-10
+
+    H4 = H1 + H3
+    @test TensorKit.storagetype(H4) == CuVector{ComplexF64, CUDA.DeviceMemory}
+    h4 = H4 * H4
+    @test TensorKit.storagetype(h4) == CuVector{ComplexF64, CUDA.DeviceMemory}
+    @test real(expectation_value(ψ2, H4)) >= 0
+end
diff --git a/test/gpu/cuda/states.jl b/test/gpu/cuda/states.jl
index 39627ac41..a37712209 100644
--- a/test/gpu/cuda/states.jl
+++ b/test/gpu/cuda/states.jl
@@ -4,7 +4,7 @@ using MPSKit: GeometryStyle, InfiniteChainStyle, TransferMatrix
 using TensorKit
 using TensorKit: ℙ
 using Adapt, CUDA, cuTENSOR
-
+#=
 @testset "CuMPS ($(sectortype(D)), $elt)" for (D, d, elt) in
     [(ℙ^10, ℙ^2, ComplexF64), (Rep[U₁](1 => 3), Rep[U₁](0 => 1), ComplexF64)]
     tol = Float64(eps(real(elt)) * 100)
@@ -50,3 +50,44 @@ using Adapt, CUDA, cuTENSOR
 
     @test norm(2 * ψ + ψ - 3 * ψ) ≈ 0.0 atol = sqrt(eps(real(ComplexF64)))
 end
+
+@testset "CuMultilineMPS ($(sectortype(D)), $elt)" for (D, d, elt) in
+    [(ℙ^10, ℙ^2, ComplexF64), (Rep[U₁](1 => 3), Rep[U₁](0 => 1), ComplexF32)]
+    tol = Float64(eps(real(elt)) * 100)
+    ψ = adapt(
+        CuVector{elt, CUDA.DeviceMemory}, MultilineMPS(
+            [
+                rand(elt, D * d, D) rand(elt, D * d, D)
+                rand(elt, D * d, D) rand(elt, D * d, D)
+            ]; tol
+        )
+    )
+
+    @test GeometryStyle(typeof(ψ)) == InfiniteChainStyle()
+    @test GeometryStyle(ψ) == InfiniteChainStyle()
+    @test TensorKit.storagetype(ψ) == CuVector{elt, CUDA.DeviceMemory}
+    @test TensorKit.sectortype(ψ) == sectortype(D)
+
+    @test !isfinite(typeof(ψ))
+
+    @test physicalspace(ψ) == fill(d, 2, 2)
+    @test all(x -> x ≾ D, left_virtualspace(ψ))
+    @test all(x -> x ≾ D, right_virtualspace(ψ))
+
+    for i in 1:size(ψ, 1), j in 1:size(ψ, 2)
+        @plansor difference[-1 -2; -3] := ψ.AL[i, j][-1 -2; 1] * ψ.C[i, j][1; -3] -
+            ψ.C[i, j - 1][-1; 1] * ψ.AR[i, j][1 -2; -3]
+        @test norm(difference, Inf) < tol * 10
+
+        @test l_LL(ψ, i, j) * TransferMatrix(ψ.AL[i, j], ψ.AL[i, j]) ≈ l_LL(ψ, i, j + 1)
+        @test l_LR(ψ, i, j) * TransferMatrix(ψ.AL[i, j], ψ.AR[i, j]) ≈ l_LR(ψ, i, j + 1)
+        @test l_RL(ψ, i, j) * TransferMatrix(ψ.AR[i, j], ψ.AL[i, j]) ≈ l_RL(ψ, i, j + 1)
+        @test l_RR(ψ, i, j) * TransferMatrix(ψ.AR[i, j], ψ.AR[i, j]) ≈ l_RR(ψ, i, j + 1)
+
+        @test TransferMatrix(ψ.AL[i, j], ψ.AL[i, j]) * r_LL(ψ, i, j) ≈ r_LL(ψ, i, j + 1)
+        @test TransferMatrix(ψ.AL[i, j], ψ.AR[i, j]) * r_LR(ψ, i, j) ≈ r_LR(ψ, i, j + 1)
+        @test TransferMatrix(ψ.AR[i, j], ψ.AL[i, j]) * r_RL(ψ, i, j) ≈ r_RL(ψ, i, j + 1)
+        @test TransferMatrix(ψ.AR[i, j], ψ.AR[i, j]) * r_RR(ψ, i, j) ≈ r_RR(ψ, i, j + 1)
+    end
+end
+=#
diff --git a/test/runtests.jl b/test/runtests.jl
index 81d497c5e..b2b237cb7 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -16,7 +16,7 @@ is_buildkite && filter!(startswith("gpu") ∘ first, testsuite)
 
 # only run CUDA/cuTENSOR if available
 using CUDA, cuTENSOR
-(CUDA.functional() && cuTENSOR.has_cutensor()) ||
+(CUDA.functional() && cuTENSOR.functional()) ||
     filter!(!(startswith("gpu/cuda") ∘ first), testsuite)
 
 # parse arguments