diff --git a/Project.toml b/Project.toml
index 51adadf9d..28cab4bf4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -36,7 +36,7 @@ MPSKitAdaptExt = "Adapt"
 [compat]
 Accessors = "0.1"
 Adapt = "4"
-BlockTensorKit = "0.3.11"
+BlockTensorKit = "0.3.14"
 Compat = "3.47, 4.10"
 DocStringExtensions = "0.9.3"
 HalfIntegers = "1.6.0"
@@ -49,7 +49,7 @@ OptimKit = "0.3.1, 0.4"
 Printf = "1"
 Random = "1"
 RecipesBase = "1.1"
-TensorKit = "0.16.5"
+TensorKit = "0.17"
 TensorKitManifolds = "0.7, 0.8"
 TensorOperations = "5.5.1"
 TimerOutputs = "0.5.29"
diff --git a/src/MPSKit.jl b/src/MPSKit.jl
index f30eb869f..f4d2fc6f8 100644
--- a/src/MPSKit.jl
+++ b/src/MPSKit.jl
@@ -59,7 +59,7 @@ using Compat: @compat
 # Imports
 # -------
 using TensorKit
-using TensorKit: BraidingTensor
+using TensorKit: BraidingTensor, promote_storagetype
 using TensorKit: TupleTools as TT
 using MatrixAlgebraKit
 using MatrixAlgebraKit: TruncationStrategy
diff --git a/src/operators/abstractmpo.jl b/src/operators/abstractmpo.jl
index 54ecf0358..41e5ea576 100644
--- a/src/operators/abstractmpo.jl
+++ b/src/operators/abstractmpo.jl
@@ -130,9 +130,10 @@ function _fuse_mpo_mpo(O1::MPOTensor, O2::MPOTensor, Fₗ, Fᵣ)
     return if O1 isa BraidingTensor && O2 isa BraidingTensor
         # shouldn't happen
         T = promote_type(scalartype(O1), scalartype(O2))
+        A = promote_storagetype(T, O1, O2)
         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)
     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])
@@ -159,9 +160,10 @@ function fuse_mul_mpo(O1, O2)
 end
 function fuse_mul_mpo(O1::BraidingTensor, O2::BraidingTensor)
     T = promote_type(scalartype(O1), scalartype(O2))
+    A = promote_storagetype(T, O1, O2)
     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 +200,7 @@ 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(O), 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..e4f77d8d7 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 +124,7 @@ end
 function jordanmpotensortype(::Type{S}, ::Type{E}) where {S <: VectorSpace, E}
     TA = tensormaptype(S, 2, 2, E)
     T = scalartype(TA)
-    Tτ = BraidingTensor{T, S}
+    Tτ = BraidingTensor{T, S, storagetype(TA)}
     TB = tensormaptype(S, 2, 1, E)
     TC = tensormaptype(S, 1, 2, E)
     TD = tensormaptype(S, 1, 1, E)
@@ -172,7 +172,7 @@ BlockTensorKit.issparse(W::JordanMPOTensor) = true
 # Converters
 # ----------
 function BlockTensorKit.SparseBlockTensorMap(W::JordanMPOTensor)
-    τ = BraidingTensor{scalartype(W)}(eachspace(W)[1])
+    τ = BraidingTensor{scalartype(W), spacetype(W), storagetype(W)}(eachspace(W)[1])
     W′ = SparseBlockTensorMap{AbstractTensorMap{scalartype(W), spacetype(W), 2, 2}}(
         undef_blocks, space(W)
     )
@@ -232,7 +232,7 @@ 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])
+        return BraidingTensor{scalartype(W), spacetype(W), storagetype(W)}(eachspace(W)[1])
     elseif i == 1 && j == size(W, 4)
         return insertrightunit(insertleftunit(only(W.D), 1), 3)
     elseif i == 1
diff --git a/src/operators/mpohamiltonian.jl b/src/operators/mpohamiltonian.jl
index daf7eb6a5..a2e39848f 100644
--- a/src/operators/mpohamiltonian.jl
+++ b/src/operators/mpohamiltonian.jl
@@ -140,7 +140,7 @@ 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])
+                τ = BraidingTensor{T, spacetype(W), storagetype(W)}(eachspace(W)[I])
                 W[I] = isone(v) ? τ : τ * v
             end
         end
@@ -261,7 +261,7 @@ 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])
+                τ = BraidingTensor{T, spacetype(W), storagetype(W)}(eachspace(W)[I])
                 W[I] = isone(v) ? τ : τ * v
             end
         end
@@ -477,7 +477,7 @@ 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])
+                τ = BraidingTensor{scalartype(TW), spacetype(TW), storagetype(TW)}(eachspace(O)[key_L, 1, 1, key_R])
                 isone(o) ? τ : τ * o
             else
                 o
@@ -600,7 +600,7 @@ 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])
+                τ = BraidingTensor{scalartype(TW), spacetype(TW), storagetype(TW)}(eachspace(O)[key_L, 1, 1, key_R])
                 isone(o) ? τ : τ * o
             else
                 o
diff --git a/test/Project.toml b/test/Project.toml
index da4cf3f70..562dd4339 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -24,7 +24,7 @@ MPSKit = {path = ".."}
 
 [compat]
 Aqua = "0.8.9"
-CUDA = "5.9"
+CUDA = "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 = "6"
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