diff --git a/test/cuda/mooncake.jl b/test/cuda/mooncake.jl
new file mode 100644
index 000000000..c0911c695
--- /dev/null
+++ b/test/cuda/mooncake.jl
@@ -0,0 +1,50 @@
+using Test, TestExtras
+using TensorKit
+using Mooncake
+using Random
+using CUDA, cuTENSOR, Adapt
+
+rng = Random.default_rng()
+
+spacelist = ad_spacelist(fast_tests)
+eltypes = (Float64, ComplexF64)
+
+is_ci = get(ENV, "CI", "false") == "true"
+
+@timedtestset "Mooncake - LinearAlgebra: $(TensorKit.type_repr(sectortype(eltype(V)))) ($T)" for V in spacelist, T in eltypes
+    atol = default_tol(T)
+    rtol = default_tol(T)
+
+    C = adapt(CuVector{T, CUDA.DeviceMemory}, randn(T, V[1] ⊗ V[2] ← (V[3] ⊗ V[4] ⊗ V[5])'))
+    A = adapt(CuVector{T, CUDA.DeviceMemory}, randn(T, codomain(C) ← V[5]' ⊗ V[4]'))
+    B = adapt(CuVector{T, CUDA.DeviceMemory}, randn(T, domain(A) ← domain(C)))
+    α = randn(T)
+    β = randn(T)
+
+    Mooncake.TestUtils.test_rule(rng, mul!, C, A, B, α, β; atol, rtol, interface_only = is_ci)
+    Mooncake.TestUtils.test_rule(rng, mul!, C, A, B; atol, rtol, is_primitive = false, interface_only = is_ci)
+
+    Mooncake.TestUtils.test_rule(rng, norm, C, 2; atol, rtol, interface_only = is_ci)
+    Mooncake.TestUtils.test_rule(rng, norm, C', 2; atol, rtol, interface_only = is_ci)
+
+    D1 = adapt(CuVector{T, CUDA.DeviceMemory}, randn(T, V[1] ← V[1]))
+    D2 = adapt(CuVector{T, CUDA.DeviceMemory}, randn(T, V[1] ⊗ V[2] ← V[1] ⊗ V[2]))
+    D3 = adapt(CuVector{T, CUDA.DeviceMemory}, randn(T, V[1] ⊗ V[2] ⊗ V[3] ← V[1] ⊗ V[2] ⊗ V[3]))
+
+    Mooncake.TestUtils.test_rule(rng, tr, D1; atol, rtol, interface_only = is_ci)
+    Mooncake.TestUtils.test_rule(rng, tr, D2; atol, rtol, interface_only = is_ci)
+    Mooncake.TestUtils.test_rule(rng, tr, D3; atol, rtol, interface_only = is_ci)
+
+    Mooncake.TestUtils.test_rule(rng, inv, D1; atol, rtol, interface_only = is_ci)
+    Mooncake.TestUtils.test_rule(rng, inv, D2; atol, rtol, interface_only = is_ci)
+    Mooncake.TestUtils.test_rule(rng, inv, D3; atol, rtol, interface_only = is_ci)
+
+    C = adapt(CuVector{T, CUDA.DeviceMemory}, randn(T, V[1] ← V[1]))
+    C′ = similar(C)
+    Mooncake.TestUtils.test_rule(rng, project_hermitian!, C, C′; atol, rtol, is_primitive = false, interface_only = is_ci)
+    Mooncake.TestUtils.test_rule(rng, project_hermitian!, C, C; atol, rtol, is_primitive = false, interface_only = is_ci)
+    Mooncake.TestUtils.test_rule(rng, project_hermitian, C; atol, rtol, is_primitive = false, interface_only = is_ci)
+    Mooncake.TestUtils.test_rule(rng, project_antihermitian!, C, C′; atol, rtol, is_primitive = false, interface_only = is_ci)
+    Mooncake.TestUtils.test_rule(rng, project_antihermitian!, C, C; atol, rtol, is_primitive = false, interface_only = is_ci)
+    Mooncake.TestUtils.test_rule(rng, project_antihermitian, C; atol, rtol, is_primitive = false, interface_only = is_ci)
+end