From 54d5d10c7b94b3e41807feb8d1f042a52ec262e6 Mon Sep 17 00:00:00 2001
From: sanderdemeyer <sander.demeyer@ugent.be>
Date: Fri, 26 Jun 2026 17:36:20 +0200
Subject: [PATCH 1/4] Exponential via MatrixAlgebraKit

---
 src/tensors/linalg.jl | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/src/tensors/linalg.jl b/src/tensors/linalg.jl
index 40a0e0024..c45c9f4f6 100644
--- a/src/tensors/linalg.jl
+++ b/src/tensors/linalg.jl
@@ -421,7 +421,16 @@ function exp!(t::TensorMap)
     domain(t) == codomain(t) ||
         error("Exponential of a tensor only exist when domain == codomain.")
     for (c, b) in blocks(t)
-        copy!(b, LinearAlgebra.exp!(b))
+        MatrixAlgebraKit.exponential!(b, b)
+    end
+    return t
+end
+
+function exp!((τ, t)::Tuple{Number, TensorMap})
+    domain(t) == codomain(t) ||
+        error("Exponential of a tensor only exist when domain == codomain.")
+    for (c, b) in blocks(t)
+        MatrixAlgebraKit.exponential!((τ, b), b)
     end
     return t
 end

From caab0e48fc066979c915035c3ac9991d4db4caf9 Mon Sep 17 00:00:00 2001
From: sanderdemeyer <sander.demeyer@ugent.be>
Date: Fri, 26 Jun 2026 17:58:15 +0200
Subject: [PATCH 2/4] include case where t is real and tau is complex

---
 src/tensors/linalg.jl | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/src/tensors/linalg.jl b/src/tensors/linalg.jl
index c45c9f4f6..f07f1b174 100644
--- a/src/tensors/linalg.jl
+++ b/src/tensors/linalg.jl
@@ -429,6 +429,13 @@ end
 function exp!((τ, t)::Tuple{Number, TensorMap})
     domain(t) == codomain(t) ||
         error("Exponential of a tensor only exist when domain == codomain.")
+    if eltype(t) <: Real && eltype(τ) <: Complex
+        t_complex = complex(t)
+        for ((cr, br), (cc, bc)) in zip(blocks(t), blocks(t_complex))
+            MatrixAlgebraKit.exponential!((τ, br), bc)
+        end
+        return t_complex
+    end
     for (c, b) in blocks(t)
         MatrixAlgebraKit.exponential!((τ, b), b)
     end

From 863ca6d28b709f16caafa96ab866b652d53c8214 Mon Sep 17 00:00:00 2001
From: sanderdemeyer <sander.demeyer@ugent.be>
Date: Fri, 26 Jun 2026 18:43:27 +0200
Subject: [PATCH 3/4] Add test

---
 test/tensors/exponential.jl | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)
 create mode 100644 test/tensors/exponential.jl

diff --git a/test/tensors/exponential.jl b/test/tensors/exponential.jl
new file mode 100644
index 000000000..cb5befb4e
--- /dev/null
+++ b/test/tensors/exponential.jl
@@ -0,0 +1,25 @@
+using Test, TestExtras
+using TensorKit
+using Random
+
+spaces = [ℂ^4, Vect[U1Irrep](0 => 1, 1 => 2), Vect[SU2Irrep](0 => 1, 1//2 => 1)]
+scalartypes = [Float64, ComplexF64]
+
+@timedtestset "exp!(τ,A) for $space, scalartype(A) = $st1, scalartype(τ) = $st2" for space = spaces, st1 = scalartypes, st2 = scalartypes
+    A = randn(st1, space, space)
+    τ = rand(st2)
+
+    @test exp!(copy(A)) == exp!((1.0, copy(A)))
+
+    A2 = exp!((τ,A))
+    if st1 <: Real && st2 <: Complex
+        @test objectid(A2) != objectid(A)
+    else
+        @test objectid(A2) == objectid(A)
+    end
+
+    expτA = exp!((τ,copy(A)))
+    expminτA = exp!((-τ,copy(A)))
+    @test expτA * expminτA ≈ id(scalartype(expτA), space)
+    @test expτA ≈ inv(expminτA)
+end

From bf8c3af6a3c254d21dbd599456c3d730668b00fc Mon Sep 17 00:00:00 2001
From: sanderdemeyer <sander.demeyer@ugent.be>
Date: Fri, 26 Jun 2026 18:44:06 +0200
Subject: [PATCH 4/4] Fix formatting

---
 test/tensors/exponential.jl | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/test/tensors/exponential.jl b/test/tensors/exponential.jl
index cb5befb4e..51fe1072b 100644
--- a/test/tensors/exponential.jl
+++ b/test/tensors/exponential.jl
@@ -2,24 +2,24 @@ using Test, TestExtras
 using TensorKit
 using Random
 
-spaces = [ℂ^4, Vect[U1Irrep](0 => 1, 1 => 2), Vect[SU2Irrep](0 => 1, 1//2 => 1)]
+spaces = [ℂ^4, Vect[U1Irrep](0 => 1, 1 => 2), Vect[SU2Irrep](0 => 1, 1 // 2 => 1)]
 scalartypes = [Float64, ComplexF64]
 
-@timedtestset "exp!(τ,A) for $space, scalartype(A) = $st1, scalartype(τ) = $st2" for space = spaces, st1 = scalartypes, st2 = scalartypes
+@timedtestset "exp!(τ,A) for $space, scalartype(A) = $st1, scalartype(τ) = $st2" for space in spaces, st1 in scalartypes, st2 in scalartypes
     A = randn(st1, space, space)
     τ = rand(st2)
 
     @test exp!(copy(A)) == exp!((1.0, copy(A)))
 
-    A2 = exp!((τ,A))
+    A2 = exp!((τ, A))
     if st1 <: Real && st2 <: Complex
         @test objectid(A2) != objectid(A)
     else
         @test objectid(A2) == objectid(A)
     end
 
-    expτA = exp!((τ,copy(A)))
-    expminτA = exp!((-τ,copy(A)))
+    expτA = exp!((τ, copy(A)))
+    expminτA = exp!((-τ, copy(A)))
     @test expτA * expminτA ≈ id(scalartype(expτA), space)
     @test expτA ≈ inv(expminτA)
 end