diff --git a/Project.toml b/Project.toml
index db12c9e..10d302f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -11,12 +11,17 @@ Tenet = "85d41934-b9cd-44e1-8730-56d86f15f3ec"
 ValSplit = "0625e100-946b-11ec-09cd-6328dd093154"
 
 [weakdeps]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
 Quac = "b9105292-1415-45cf-bff1-d6ccf71e6143"
 
 [extensions]
+QrochetChainRulesCoreExt = "ChainRulesCore"
+QrochetChainRulesTestUtilsExt = ["ChainRulesCore", "ChainRulesTestUtils"]
 QrochetQuacExt = "Quac"
 
 [compat]
+ChainRulesCore = "1.0"
 Muscle = "0.1"
 Quac = "0.3"
 Tenet = "0.5"
diff --git a/ext/QrochetChainRulesCoreExt.jl b/ext/QrochetChainRulesCoreExt.jl
new file mode 100644
index 0000000..b011d76
--- /dev/null
+++ b/ext/QrochetChainRulesCoreExt.jl
@@ -0,0 +1,27 @@
+module QrochetChainRulesCoreExt
+
+using Qrochet
+using ChainRulesCore
+using ChainRulesCore: AbstractTangent
+using Tenet
+
+@non_differentiable Qrochet.currindex()
+@non_differentiable Qrochet.nextindex()
+
+# WARN type-piracy
+@non_differentiable Base.setdiff(::Vector{Symbol}, ::Base.ValueIterator)
+
+ChainRulesCore.ProjectTo(qtn::Quantum) = ProjectTo{Quantum}(; tn = ProjectTo(qtn.tn))
+(projector::ProjectTo{Quantum})(Δ) = Quantum(projector.tn(Δ.tn), Δ.sites)
+
+function ChainRulesCore.frule((_, ẋ, _), ::Type{Quantum}, x::TensorNetwork, sites)
+    y = Quantum(x, sites)
+    ẏ = Tangent{Quantum}(; tn = ẋ)
+    y, ẏ
+end
+
+Quantum_pullback(ȳ) = (NoTangent(), ȳ.tn, NoTangent())
+Quantum_pullback(ȳ::AbstractThunk) = Quantum_pullback(unthunk(ȳ))
+ChainRulesCore.rrule(::Type{Quantum}, x::TensorNetwork, sites) = Quantum(x, sites), Quantum_pullback
+
+end
diff --git a/ext/QrochetChainRulesTestUtilsExt.jl b/ext/QrochetChainRulesTestUtilsExt.jl
new file mode 100644
index 0000000..8d9c14f
--- /dev/null
+++ b/ext/QrochetChainRulesTestUtilsExt.jl
@@ -0,0 +1,16 @@
+module QrochetChainRulesTestUtilsExt
+
+using Qrochet
+using ChainRulesCore
+using ChainRulesTestUtils
+using Random
+
+function ChainRulesTestUtils.rand_tangent(rng::AbstractRNG, x::Quantum)
+    return Tangent{Quantum}(; tn = rand_tangent(rng, x.tn), sites = NoTangent())
+end
+
+# WARN type-piracy
+# NOTE used in `Quantum` constructor
+ChainRulesTestUtils.rand_tangent(::AbstractRNG, x::Dict{<:Site,Symbol}) = NoTangent()
+
+end
diff --git a/test/Project.toml b/test/Project.toml
index dfed1ae..ff50946 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,5 +1,6 @@
 [deps]
+ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Quac = "b9105292-1415-45cf-bff1-d6ccf71e6143"
 Tenet = "85d41934-b9cd-44e1-8730-56d86f15f3ec"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-Quac = "b9105292-1415-45cf-bff1-d6ccf71e6143"
diff --git a/test/integration/ChainRulesCore_test.jl b/test/integration/ChainRulesCore_test.jl
new file mode 100644
index 0000000..dfe68fe
--- /dev/null
+++ b/test/integration/ChainRulesCore_test.jl
@@ -0,0 +1,10 @@
+@testset "ChainRulesCore" begin
+    using Qrochet
+    using Tenet
+    using ChainRulesTestUtils
+
+    @testset "Quantum" begin
+        test_frule(Quantum, TensorNetwork([Tensor(fill(1.0, 2), [:i])]), Dict{Site,Symbol}(site"1" => :i))
+        test_rrule(Quantum, TensorNetwork([Tensor(fill(1.0, 2), [:i])]), Dict{Site,Symbol}(site"1" => :i))
+    end
+end
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 021ef25..8a13796 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -10,6 +10,7 @@ end
 
 @testset "Integration tests" verbose = true begin
     include("integration/Quac_test.jl")
+    include("integration/ChainRulesCore_test.jl")
 end
 
 if haskey(ENV, "ENABLE_AQUA_TESTS")