From 78553899dee059870ec14f081f850315942c05b7 Mon Sep 17 00:00:00 2001
From: Lukas Devos <ldevos98@gmail.com>
Date: Wed, 27 Aug 2025 15:14:14 +0200
Subject: [PATCH 1/5] Add package extension

---
 Project.toml                            | 7 +++++++
 ext/TensorAlgebraTensorOperationsExt.jl | 3 +++
 2 files changed, 10 insertions(+)
 create mode 100644 ext/TensorAlgebraTensorOperationsExt.jl

diff --git a/Project.toml b/Project.toml
index 1c77028..647b015 100644
--- a/Project.toml
+++ b/Project.toml
@@ -20,6 +20,13 @@ EllipsisNotation = "1.8.0"
 LinearAlgebra = "1.10"
 MatrixAlgebraKit = "0.2"
 TensorProducts = "0.1.5"
+TensorOperations = "5"
 TupleTools = "1.6.0"
 TypeParameterAccessors = "0.2.1, 0.3, 0.4"
 julia = "1.10"
+
+[weakdeps]
+TensorOperations = "6aa20fa7-93e2-5fca-9bc0-fbd0db3c71a2"
+
+[extensions]
+TensorAlgebraTensorOperationsExt = "TensorOperations"
diff --git a/ext/TensorAlgebraTensorOperationsExt.jl b/ext/TensorAlgebraTensorOperationsExt.jl
new file mode 100644
index 0000000..2bb6c92
--- /dev/null
+++ b/ext/TensorAlgebraTensorOperationsExt.jl
@@ -0,0 +1,3 @@
+module TensorAlgebraTensorOperationsExt
+
+end

From 5cfaaf29fbf3225cc990c8e70d9dd56a724e0637 Mon Sep 17 00:00:00 2001
From: Lukas Devos <ldevos98@gmail.com>
Date: Wed, 27 Aug 2025 15:15:09 +0200
Subject: [PATCH 2/5] TensorAlgebra for TensorOperations

---
 ext/TensorAlgebraTensorOperationsExt.jl | 44 +++++++++++++++++++++++++
 1 file changed, 44 insertions(+)

diff --git a/ext/TensorAlgebraTensorOperationsExt.jl b/ext/TensorAlgebraTensorOperationsExt.jl
index 2bb6c92..e56d805 100644
--- a/ext/TensorAlgebraTensorOperationsExt.jl
+++ b/ext/TensorAlgebraTensorOperationsExt.jl
@@ -1,3 +1,47 @@
 module TensorAlgebraTensorOperationsExt
 
+using TensorAlgebra: TensorAlgebra, BlockedPermutation, Algorithm
+using TupleTools
+using TensorOperations
+using TensorOperations: AbstractBackend as TOAlgorithm
+
+TensorAlgebra.Algorithm(backend::TOAlgorithm) = backend
+
+trivtuple(n) = ntuple(identity, n)
+
+function _index2tuple(p::BlockedPermutation{2})
+  N₁, N₂ = blocklengths(p)
+  return (
+    TupleTools.getindices(Tuple(p), trivtuple(N₁)),
+    TupleTools.getindices(Tuple(p), N₁ .+ trivtuple(N₂)),
+  )
 end
+
+_blockedpermutation(p::Index2Tuple) = TensorAlgebra.blockedpermvcat(p...)
+
+# Using TensorAlgebra implementations as TensorOperations backends
+# ----------------------------------------------------------------
+function TensorOperations.tensorcontract!(
+  C::AbstractArray,
+  A::AbstractArray,
+  pA::Index2Tuple,
+  conjA::Bool,
+  B::AbstractArray,
+  pB::Index2Tuple,
+  conjB::Bool,
+  pAB::Index2Tuple,
+  α::Number,
+  β::Number,
+  backend::Algorithm,
+  allocator,
+)
+  bipermA = _blockedpermutation(pA)
+  bipermB = _blockedpermutation(pB)
+  ipAB = invperm((pAB[1]..., pAB[2]...))
+  bipermAB = _blockedpermutation((TupleTools.getindices(ipAB, trivtuple(length(pA[1]))),
+  TupleTools.getindices(ipAB, trivtuple(length(pB[2])) .+ length(pA[1]))))
+  A′ = conjA ? conj(A) : A
+  B′ = conjB ? conj(B) : B
+  return TensorAlgebra.contract!(backend, C, bipermAB, A′, bipermA, B′, bipermB, α, β)
+end
+

From 3ee9224392d38956ab94efd379baadaf4dafb31e Mon Sep 17 00:00:00 2001
From: Lukas Devos <ldevos98@gmail.com>
Date: Wed, 27 Aug 2025 15:22:24 +0200
Subject: [PATCH 3/5] TensorOperations for TensorAlgebra

---
 ext/TensorAlgebraTensorOperationsExt.jl | 79 ++++++++++++++++++++++++-
 1 file changed, 77 insertions(+), 2 deletions(-)

diff --git a/ext/TensorAlgebraTensorOperationsExt.jl b/ext/TensorAlgebraTensorOperationsExt.jl
index e56d805..f677c14 100644
--- a/ext/TensorAlgebraTensorOperationsExt.jl
+++ b/ext/TensorAlgebraTensorOperationsExt.jl
@@ -19,6 +19,78 @@ end
 
 _blockedpermutation(p::Index2Tuple) = TensorAlgebra.blockedpermvcat(p...)
 
+# Using TensorOperations backends as TensorAlgebra implementations
+# ----------------------------------------------------------------
+
+# not in-place
+function TensorAlgebra.contract(
+  backend::TOAlgorithm,
+  bipermAB::BlockedPermutation,
+  A::AbstractArray,
+  bipermA::BlockedPermutation,
+  B::AbstractArray,
+  bipermB::BlockedPermutation,
+  α::Number,
+)
+  pA = _index2tuple(bipermA)
+  pB = _index2tuple(bipermB)
+
+  # TODO: this assumes biperm of output because not enough information!
+  ipermAB = invperm(Tuple(bipermAB))
+  pAB = (TupleTools.getindices(ipermAB, length(ipermAB)), ())
+
+  return tensorcontract(A, pA, false, B, pB, false, pAB, α, backend)
+end
+
+function TensorAlgebra.contract(
+  backend::TOAlgorithm,
+  labelsC,
+  A::AbstractArray,
+  labelsA,
+  B::AbstractArray,
+  labelsB,
+  α::Number,
+)
+  return tensorcontract(labelsC, A, labelsA, B, labelsB, α; backend)
+end
+
+# in-place
+function TensorAlgebra.contract!(
+  backend::TOAlgorithm,
+  C::AbstractArray,
+  bipermAB::BlockedPermutation,
+  A::AbstractArray,
+  bipermA::BlockedPermutation,
+  B::AbstractArray,
+  bipermB::BlockedPermutation,
+  α::Number,
+  β::Number,
+)
+  pA = _index2tuple(bipermA)
+  pB = _index2tuple(bipermB)
+
+  # TODO: this assumes biperm of output because not enough information!
+  ipermAB = invperm(Tuple(bipermAB))
+  pAB = (TupleTools.getindices(ipermAB, length(ipermAB)), ())
+
+  return tensorcontract!(C, A, pA, false, B, pB, false, pAB, α, β, backend)
+end
+
+function TensorAlgebra.contract!(
+  backend::TOAlgorithm,
+  C::AbstractArray,
+  labelsC,
+  A::AbstractArray,
+  labelsA,
+  B::AbstractArray,
+  labelsB,
+  α::Number,
+  β::Number,
+)
+  pA, pB, pAB = TensorOperations.contract_indices(labelsA, labelsB, labelsC)
+  return TensorOperations.tensorcontract!(C, A, pA, false, B, pB, false, pAB, α, β, backend)
+end
+
 # Using TensorAlgebra implementations as TensorOperations backends
 # ----------------------------------------------------------------
 function TensorOperations.tensorcontract!(
@@ -38,10 +110,13 @@ function TensorOperations.tensorcontract!(
   bipermA = _blockedpermutation(pA)
   bipermB = _blockedpermutation(pB)
   ipAB = invperm((pAB[1]..., pAB[2]...))
-  bipermAB = _blockedpermutation((TupleTools.getindices(ipAB, trivtuple(length(pA[1]))),
-  TupleTools.getindices(ipAB, trivtuple(length(pB[2])) .+ length(pA[1]))))
+  bipermAB = _blockedpermutation((
+    TupleTools.getindices(ipAB, trivtuple(length(pA[1]))),
+    TupleTools.getindices(ipAB, trivtuple(length(pB[2])) .+ length(pA[1])),
+  ))
   A′ = conjA ? conj(A) : A
   B′ = conjB ? conj(B) : B
   return TensorAlgebra.contract!(backend, C, bipermAB, A′, bipermA, B′, bipermB, α, β)
 end
 
+end

From 3c06f1e3477e7a81e7cede297d1d99e7eb902496 Mon Sep 17 00:00:00 2001
From: Lukas Devos <ldevos98@gmail.com>
Date: Wed, 27 Aug 2025 15:22:28 +0200
Subject: [PATCH 4/5] Add tests

---
 test/test_tensoroperations.jl | 41 +++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)
 create mode 100644 test/test_tensoroperations.jl

diff --git a/test/test_tensoroperations.jl b/test/test_tensoroperations.jl
new file mode 100644
index 0000000..067ef1e
--- /dev/null
+++ b/test/test_tensoroperations.jl
@@ -0,0 +1,41 @@
+using Test: @test, @testset
+using TensorOperations: @tensor, ncon
+using TensorAlgebra: Matricize
+
+elts = (Float32, Float64, ComplexF32, ComplexF64)
+
+@testset "tensor network examples ($T)" for T in elts
+  D1, D2, D3 = 30, 40, 20
+  d1, d2 = 2, 3
+  A1 = rand(T, D1, d1, D2) .- 1//2
+  A2 = rand(T, D2, d2, D3) .- 1//2
+  rhoL = rand(T, D1, D1) .- 1//2
+  rhoR = rand(T, D3, D3) .- 1//2
+  H = rand(T, d1, d2, d1, d2) .- 1//2
+
+  @tensor HrA12[a, s1, s2, c] :=
+    rhoL[a, a'] * A1[a', t1, b] * A2[b, t2, c'] * rhoR[c', c] * H[s1, s2, t1, t2]
+  @tensor backend = Matricize() HrA12′[a, s1, s2, c] :=
+    rhoL[a, a'] * A1[a', t1, b] * A2[b, t2, c'] * rhoR[c', c] * H[s1, s2, t1, t2]
+
+  @test HrA12 ≈ HrA12′
+  @test HrA12 ≈ ncon(
+    [rhoL, H, A2, rhoR, A1],
+    [[-1, 1], [-2, -3, 4, 5], [2, 5, 3], [3, -4], [1, 4, 2]];
+    backend=Matricize(),
+  )
+  E = @tensor rhoL[a', a] *
+    A1[a, s, b] *
+    A2[b, s', c] *
+    rhoR[c, c'] *
+    H[t, t', s, s'] *
+    conj(A1[a', t, b']) *
+    conj(A2[b', t', c'])
+  @test E ≈ @tensor backend = Matricize() rhoL[a', a] *
+    A1[a, s, b] *
+    A2[b, s', c] *
+    rhoR[c, c'] *
+    H[t, t', s, s'] *
+    conj(A1[a', t, b']) *
+    conj(A2[b', t', c'])
+end

From fa81eca26f77718ecf77f08a5470ed0ff020d924 Mon Sep 17 00:00:00 2001
From: Lukas Devos <ldevos98@gmail.com>
Date: Wed, 27 Aug 2025 15:47:02 +0200
Subject: [PATCH 5/5] Bump v0.3.12

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 647b015..263a613 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 = "0.3.11"
+version = "0.3.12"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"