diff --git a/.github/workflows/IntegrationTest.yml b/.github/workflows/IntegrationTest.yml
index cdf36ec..fdafe6c 100644
--- a/.github/workflows/IntegrationTest.yml
+++ b/.github/workflows/IntegrationTest.yml
@@ -18,6 +18,7 @@ jobs:
        matrix:
          pkg:
            - 'BlockSparseArrays'
+           - 'FusionTensors'
            - 'NamedDimsArrays'
     uses: "ITensor/ITensorActions/.github/workflows/IntegrationTest.yml@main"
     with:
diff --git a/Project.toml b/Project.toml
index 79ae9d2..c0b41e7 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "TensorAlgebra"
 uuid = "68bd88dc-f39d-4e12-b2ca-f046b68fcc6a"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.3.16"
+version = "0.4.0"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
diff --git a/docs/Project.toml b/docs/Project.toml
index 661cea0..db836a0 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -6,4 +6,4 @@ TensorAlgebra = "68bd88dc-f39d-4e12-b2ca-f046b68fcc6a"
 [compat]
 Documenter = "1.8.1"
 Literate = "2.20.1"
-TensorAlgebra = "0.3.0"
+TensorAlgebra = "0.4.0"
diff --git a/examples/Project.toml b/examples/Project.toml
index 0c257a8..bb98e64 100644
--- a/examples/Project.toml
+++ b/examples/Project.toml
@@ -2,4 +2,4 @@
 TensorAlgebra = "68bd88dc-f39d-4e12-b2ca-f046b68fcc6a"
 
 [compat]
-TensorAlgebra = "0.3.0"
+TensorAlgebra = "0.4.0"
diff --git a/ext/TensorAlgebraTensorOperationsExt.jl b/ext/TensorAlgebraTensorOperationsExt.jl
index 2b25095..2edf43a 100644
--- a/ext/TensorAlgebraTensorOperationsExt.jl
+++ b/ext/TensorAlgebraTensorOperationsExt.jl
@@ -1,9 +1,8 @@
 module TensorAlgebraTensorOperationsExt
 
-using TensorAlgebra: TensorAlgebra, BlockedPermutation, Algorithm
-using TupleTools
-using TensorOperations
-using TensorOperations: AbstractBackend, DefaultBackend
+using TensorAlgebra: TensorAlgebra, BlockedPermutation, Algorithm, blocklengths
+using TupleTools: TupleTools
+using TensorOperations: TensorOperations, AbstractBackend, DefaultBackend, Index2Tuple
 
 """
     TensorOperationsAlgorithm(backend::AbstractBackend)
@@ -44,8 +43,9 @@ function TensorAlgebra.contract(
   pA = _index2tuple(bipermA)
   pB = _index2tuple(bipermB)
   pAB = _index2tuple(bipermAB)
-
-  return tensorcontract(A, pA, false, B, pB, false, pAB, α, algorithm.backend)
+  return TensorOperations.tensorcontract(
+    A, pA, false, B, pB, false, pAB, α, algorithm.backend
+  )
 end
 
 function TensorAlgebra.contract(
@@ -62,7 +62,7 @@ function TensorAlgebra.contract(
 end
 
 # in-place
-function TensorAlgebra.contract!(
+function TensorAlgebra.contractadd!(
   algorithm::TensorOperationsAlgorithm,
   C::AbstractArray,
   bipermAB::BlockedPermutation,
@@ -76,10 +76,12 @@ function TensorAlgebra.contract!(
   pA = _index2tuple(bipermA)
   pB = _index2tuple(bipermB)
   pAB = _index2tuple(bipermAB)
-  return tensorcontract!(C, A, pA, false, B, pB, false, pAB, α, β, algorithm.backend)
+  return TensorOperations.tensorcontract!(
+    C, A, pA, false, B, pB, false, pAB, α, β, algorithm.backend
+  )
 end
 
-function TensorAlgebra.contract!(
+function TensorAlgebra.contractadd!(
   algorithm::TensorOperationsAlgorithm,
   C::AbstractArray,
   labelsC,
@@ -117,7 +119,7 @@ function TensorOperations.tensorcontract!(
   bipermAB = _blockedpermutation(pAB)
   A′ = conjA ? conj(A) : A
   B′ = conjB ? conj(B) : B
-  return TensorAlgebra.contract!(backend, C, bipermAB, A′, bipermA, B′, bipermB, α, β)
+  return TensorAlgebra.contractadd!(backend, C, bipermAB, A′, bipermA, B′, bipermB, α, β)
 end
 
 # For now no trace/add is supported, so simply reselect default backend from TensorOperations
diff --git a/src/contract/allocate_output.jl b/src/contract/allocate_output.jl
index 7284ffa..f1b311d 100644
--- a/src/contract/allocate_output.jl
+++ b/src/contract/allocate_output.jl
@@ -22,7 +22,6 @@ function output_axes(
   biperm1::AbstractBlockPermutation{2},
   a2::AbstractArray,
   biperm2::AbstractBlockPermutation{2},
-  α::Number=one(Bool),
 )
   axes_codomain, axes_contracted = blocks(axes(a1)[biperm1])
   axes_contracted2, axes_domain = blocks(axes(a2)[biperm2])
@@ -40,9 +39,8 @@ function allocate_output(
   biperm1::AbstractBlockPermutation,
   a2::AbstractArray,
   biperm2::AbstractBlockPermutation,
-  α::Number=one(Bool),
 )
   check_input(contract, a1, biperm1, a2, biperm2)
-  axes_dest = output_axes(contract, biperm_dest, a1, biperm1, a2, biperm2, α)
-  return similar(a1, promote_type(eltype(a1), eltype(a2), typeof(α)), axes_dest)
+  axes_dest = output_axes(contract, biperm_dest, a1, biperm1, a2, biperm2)
+  return similar(a1, promote_type(eltype(a1), eltype(a2)), axes_dest)
 end
diff --git a/src/contract/contract.jl b/src/contract/contract.jl
index 02665ca..abdcd85 100644
--- a/src/contract/contract.jl
+++ b/src/contract/contract.jl
@@ -10,7 +10,7 @@ default_contract_alg() = Matricize()
 
 # Required interface if not using
 # matricized contraction.
-function contract!(
+function contractadd!(
   alg::Algorithm,
   a_dest::AbstractArray,
   biperm_dest::AbstractBlockPermutation,
@@ -28,53 +28,59 @@ function contract(
   a1::AbstractArray,
   labels1,
   a2::AbstractArray,
-  labels2,
-  α::Number=one(Bool);
+  labels2;
   alg=default_contract_alg(),
   kwargs...,
 )
-  return contract(Algorithm(alg), a1, labels1, a2, labels2, α; kwargs...)
+  return contract(Algorithm(alg), a1, labels1, a2, labels2; kwargs...)
 end
 
 function contract(
-  alg::Algorithm,
+  alg::Algorithm, a1::AbstractArray, labels1, a2::AbstractArray, labels2; kwargs...
+)
+  labels_dest = output_labels(contract, alg, a1, labels1, a2, labels2; kwargs...)
+  return contract(alg, labels_dest, a1, labels1, a2, labels2; kwargs...), labels_dest
+end
+
+function contract(
+  labels_dest,
   a1::AbstractArray,
   labels1,
   a2::AbstractArray,
-  labels2,
-  α::Number=one(Bool);
+  labels2;
+  alg=default_contract_alg(),
   kwargs...,
 )
-  labels_dest = output_labels(contract, alg, a1, labels1, a2, labels2, α; kwargs...)
-  return contract(alg, labels_dest, a1, labels1, a2, labels2, α; kwargs...), labels_dest
+  return contract(Algorithm(alg), labels_dest, a1, labels1, a2, labels2; kwargs...)
 end
 
-function contract(
+function contract!(
+  a_dest::AbstractArray,
   labels_dest,
   a1::AbstractArray,
   labels1,
   a2::AbstractArray,
-  labels2,
-  α::Number=one(Bool);
-  alg=default_contract_alg(),
+  labels2;
   kwargs...,
 )
-  return contract(Algorithm(alg), labels_dest, a1, labels1, a2, labels2, α; kwargs...)
+  return contractadd!(a_dest, labels_dest, a1, labels1, a2, labels2, true, false; kwargs...)
 end
 
-function contract!(
+function contractadd!(
   a_dest::AbstractArray,
   labels_dest,
   a1::AbstractArray,
   labels1,
   a2::AbstractArray,
   labels2,
-  α::Number=one(Bool),
-  β::Number=zero(Bool);
+  α::Number,
+  β::Number;
   alg=default_contract_alg(),
   kwargs...,
 )
-  contract!(Algorithm(alg), a_dest, labels_dest, a1, labels1, a2, labels2, α, β; kwargs...)
+  contractadd!(
+    Algorithm(alg), a_dest, labels_dest, a1, labels1, a2, labels2, α, β; kwargs...
+  )
   return a_dest
 end
 
@@ -84,16 +90,30 @@ function contract(
   a1::AbstractArray,
   labels1,
   a2::AbstractArray,
-  labels2,
-  α::Number=one(Bool);
+  labels2;
   kwargs...,
 )
   check_input(contract, a1, labels1, a2, labels2)
   biperm_dest, biperm1, biperm2 = blockedperms(contract, labels_dest, labels1, labels2)
-  return contract(alg, biperm_dest, a1, biperm1, a2, biperm2, α; kwargs...)
+  return contract(alg, biperm_dest, a1, biperm1, a2, biperm2; kwargs...)
 end
 
 function contract!(
+  alg::Algorithm,
+  a_dest::AbstractArray,
+  labels_dest,
+  a1::AbstractArray,
+  labels1,
+  a2::AbstractArray,
+  labels2;
+  kwargs...,
+)
+  return contractadd!(
+    alg, a_dest, labels_dest, a1, labels1, a2, labels2, true, false; kwargs...
+  )
+end
+
+function contractadd!(
   alg::Algorithm,
   a_dest::AbstractArray,
   labels_dest,
@@ -107,7 +127,7 @@ function contract!(
 )
   check_input(contract, a_dest, labels_dest, a1, labels1, a2, labels2)
   biperm_dest, biperm1, biperm2 = blockedperms(contract, labels_dest, labels1, labels2)
-  return contract!(alg, a_dest, biperm_dest, a1, biperm1, a2, biperm2, α, β; kwargs...)
+  return contractadd!(alg, a_dest, biperm_dest, a1, biperm1, a2, biperm2, α, β; kwargs...)
 end
 
 function contract(
@@ -116,12 +136,11 @@ function contract(
   a1::AbstractArray,
   biperm1::AbstractBlockPermutation,
   a2::AbstractArray,
-  biperm2::AbstractBlockPermutation,
-  α::Number;
+  biperm2::AbstractBlockPermutation;
   kwargs...,
 )
   check_input(contract, a1, biperm1, a2, biperm2)
-  a_dest = allocate_output(contract, biperm_dest, a1, biperm1, a2, biperm2, α)
-  contract!(alg, a_dest, biperm_dest, a1, biperm1, a2, biperm2, α, zero(Bool); kwargs...)
+  a_dest = allocate_output(contract, biperm_dest, a1, biperm1, a2, biperm2)
+  contract!(alg, a_dest, biperm_dest, a1, biperm1, a2, biperm2; kwargs...)
   return a_dest
 end
diff --git a/src/contract/contract_matricize/contract.jl b/src/contract/contract_matricize/contract.jl
index 77db7e8..be4f26c 100644
--- a/src/contract/contract_matricize/contract.jl
+++ b/src/contract/contract_matricize/contract.jl
@@ -1,6 +1,6 @@
 using LinearAlgebra: mul!
 
-function contract!(
+function contractadd!(
   ::Matricize,
   a_dest::AbstractArray,
   biperm_dest::AbstractBlockPermutation{2},
@@ -17,6 +17,6 @@ function contract!(
   a1_mat = matricize(a1, biperm1)
   a2_mat = matricize(a2, biperm2)
   a_dest_mat = a1_mat * a2_mat
-  unmatricize_add!(a_dest, a_dest_mat, invbiperm, α, β)
+  unmatricizeadd!(a_dest, a_dest_mat, invbiperm, α, β)
   return a_dest
 end
diff --git a/src/contract/output_labels.jl b/src/contract/output_labels.jl
index 68525c5..c9c18bf 100644
--- a/src/contract/output_labels.jl
+++ b/src/contract/output_labels.jl
@@ -5,7 +5,6 @@ function output_labels(
   labels1,
   a2::AbstractArray,
   labels2,
-  α,
 )
   return output_labels(f, alg, labels1, labels2)
 end
diff --git a/src/matricize.jl b/src/matricize.jl
index c67ff9a..d812d92 100644
--- a/src/matricize.jl
+++ b/src/matricize.jl
@@ -122,7 +122,7 @@ function unmatricize!(a_dest, m::AbstractMatrix, invbiperm::AbstractBlockPermuta
   return permuteblockeddims!(a_dest, a_perm, biperm_dest)
 end
 
-function unmatricize_add!(a_dest, a_dest_mat, invbiperm, α, β)
+function unmatricizeadd!(a_dest, a_dest_mat, invbiperm, α, β)
   a12 = unmatricize(a_dest_mat, axes(a_dest), invbiperm)
   a_dest .= α .* a12 .+ β .* a_dest
   return a_dest
diff --git a/test/Project.toml b/test/Project.toml
index c6f8f73..656853a 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -23,7 +23,7 @@ Random = "1.10"
 SafeTestsets = "0.1"
 StableRNGs = "1.0.2"
 Suppressor = "0.2"
-TensorAlgebra = "0.3.0"
+TensorAlgebra = "0.4.0"
 TensorOperations = "5.1.4"
 Test = "1.10"
 TestExtras = "0.3.1"
diff --git a/test/test_basics.jl b/test/test_basics.jl
index 26fe98b..3a75cec 100644
--- a/test/test_basics.jl
+++ b/test/test_basics.jl
@@ -10,6 +10,7 @@ using TensorAlgebra:
   blockedpermvcat,
   contract,
   contract!,
+  contractadd!,
   length_codomain,
   length_domain,
   matricize,
@@ -213,9 +214,9 @@ const elts = (Float32, Float64, Complex{Float32}, Complex{Float64})
       β = elt_dest(2.4) # randn(elt_dest)
       a_dest_init = randn(elt_dest, map(i -> dims[i], d_dests))
       a_dest = copy(a_dest_init)
-      contract!(a_dest, labels_dest, a1, labels1, a2, labels2, α, β)
+      contractadd!(a_dest, labels_dest, a1, labels1, a2, labels2, α, β)
       a_dest_tensoroperations = copy(a_dest_init)
-      contract!(
+      contractadd!(
         alg_tensoroperations,
         a_dest_tensoroperations,
         labels_dest,