diff --git a/Project.toml b/Project.toml
index 44440b84..2875b439 100644
--- a/Project.toml
+++ b/Project.toml
@@ -19,6 +19,7 @@ SafeTestsets = "0.0.1"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4"
 Test = "1"
+Zygote = "0.6.67"
 julia = "1.10"
 
 [extras]
@@ -27,6 +28,7 @@ Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "Pkg", "Test", "SafeTestsets", "StaticArrays"]
+test = ["Aqua", "Pkg", "Test", "SafeTestsets", "StaticArrays", "Zygote"]
diff --git a/test/runtests.jl b/test/runtests.jl
index eaf2ebe0..b91706cf 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -45,6 +45,9 @@ if GROUP == "All" || GROUP == "Core"
     @safetestset "BatchedInterface test" begin
         @time include("batched_interface_test.jl")
     end
+    @safetestset "Simple Adjoints test" begin
+        @time include("simple_adjoints_test.jl")
+    end
 end
 
 if GROUP == "All" || GROUP == "Downstream"
diff --git a/test/simple_adjoints_test.jl b/test/simple_adjoints_test.jl
new file mode 100644
index 00000000..329fd104
--- /dev/null
+++ b/test/simple_adjoints_test.jl
@@ -0,0 +1,17 @@
+using SymbolicIndexingInterface
+using Zygote
+
+sys = SymbolCache([:x, :y, :z], [:a, :b, :c], :t)
+pstate = ProblemState(; u = rand(3), p = rand(3), t = rand())
+
+getter = getu(sys, :x)
+@test Zygote.gradient(getter, pstate)[1].u == [1.0, 0.0, 0.0]
+
+getter = getu(sys, [:x, :z])
+@test Zygote.gradient(sum ∘ getter, pstate)[1].u == [1.0, 0.0, 1.0]
+
+getter = getu(sys, :a)
+@test Zygote.gradient(getter, pstate)[1].p == [1.0, 0.0, 0.0]
+
+getter = getu(sys, [:a, :c])
+@test Zygote.gradient(sum ∘ getter, pstate)[1].p == [1.0, 0.0, 1.0]