diff --git a/ext/QrochetChainRulesCoreExt.jl b/ext/QrochetChainRulesCoreExt.jl
index 12d8f92..3db9cd9 100644
--- a/ext/QrochetChainRulesCoreExt.jl
+++ b/ext/QrochetChainRulesCoreExt.jl
@@ -24,4 +24,51 @@ 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
 
+Base.zero(x::Dict{Site,Symbol}) = x
+
+ChainRulesCore.ProjectTo(x::T) where {T<:Ansatz} = ProjectTo{T}(; super = ProjectTo(Quantum(x)))
+(projector::ProjectTo{T})(Δ::Union{T,Tangent{T}}) where {T<:Ansatz} = T(projector.super(Δ.super), Δ.boundary)
+
+# NOTE edge case: `Product` has no `boundary`. should it?
+(projector::ProjectTo{T})(Δ::Union{T,Tangent{T}}) where {T<:Product} = T(projector.super(Δ.super))
+
+ChainRulesCore.frule((_, ẋ), ::Type{T}, x::Quantum) where {T<:Ansatz} = T(x), Tangent{T}(; super = ẋ)
+
+Ansatz_pullback(ȳ) = (NoTangent(), ȳ.super)
+Ansatz_pullback(ȳ::AbstractThunk) = Ansatz_pullback(unthunk(ȳ))
+function ChainRulesCore.rrule(::Type{T}, x::Quantum) where {T<:Ansatz}
+    y = T(x)
+    y, Ansatz_pullback
+end
+
+function ChainRulesCore.frule((_, ẋ, _), ::Type{T}, x::Quantum, boundary) where {T<:Ansatz}
+    T(x, boundary), Tangent{T}(; super = ẋ, boundary = NoTangent())
+end
+
+Ansatz_boundary_pullback(ȳ) = (NoTangent(), ȳ.super, NoTangent())
+Ansatz_boundary_pullback(ȳ::AbstractThunk) = Ansatz_boundary_pullback(unthunk(ȳ))
+function ChainRulesCore.rrule(::Type{T}, x::Quantum, boundary) where {T<:Ansatz}
+    T(x, boundary), Ansatz_boundary_pullback
+end
+
+# Ansatz_from_arrays_pullback(ȳ) = (NoTangent(), NoTangent(), NoTangent(), parent.(tensors(ȳ.super.tn)))
+# Ansatz_from_arrays_pullback(ȳ::AbstractThunk) = Ansatz_from_arrays_pullback(unthunk(ȳ))
+# function ChainRulesCore.rrule(
+#     ::Type{T},
+#     socket::Qrochet.Socket,
+#     boundary::Qrochet.Boundary,
+#     arrays;
+#     kwargs...,
+# ) where {T<:Ansatz}
+#     y = T(socket, boundary, arrays; kwargs...)
+#     y, Ansatz_from_arrays_pullback
+# end
+
+copy_pullback(ȳ) = (NoTangent(), ȳ)
+copy_pullback(ȳ::AbstractThunk) = unthunk(ȳ)
+function ChainRulesCore.rrule(::typeof(copy), x::Quantum)
+    y = copy(x)
+    y, copy_pullback
+end
+
 end
diff --git a/test/integration/ChainRulesCore_test.jl b/test/integration/ChainRulesCore_test.jl
index 619a189..01ab80f 100644
--- a/test/integration/ChainRulesCore_test.jl
+++ b/test/integration/ChainRulesCore_test.jl
@@ -4,7 +4,35 @@
     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))
+        test_frule(Quantum, TensorNetwork([Tensor(ones(2), [:i])]), Dict{Site,Symbol}(site"1" => :i))
+        test_rrule(Quantum, TensorNetwork([Tensor(ones(2), [:i])]), Dict{Site,Symbol}(site"1" => :i))
+    end
+
+    @testset "Ansatz" begin
+        @testset "Product" begin
+            tn = TensorNetwork([Tensor(ones(2), [:i]), Tensor(ones(2), [:j]), Tensor(ones(2), [:k])])
+            qtn = Quantum(tn, Dict([site"1" => :i, site"2" => :j, site"3" => :k]))
+
+            test_frule(Product, qtn)
+            test_rrule(Product, qtn)
+        end
+
+        @testset "Chain" begin
+            tn = Chain(State(), Open(), [ones(2, 2), ones(2, 2, 2), ones(2, 2)])
+            # test_frule(Chain, Quantum(tn), Open())
+            test_rrule(Chain, Quantum(tn), Open())
+
+            tn = Chain(State(), Periodic(), [ones(2, 2, 2), ones(2, 2, 2), ones(2, 2, 2)])
+            # test_frule(Chain, Quantum(tn), Periodic())
+            test_rrule(Chain, Quantum(tn), Periodic())
+
+            tn = Chain(Operator(), Open(), [ones(2, 2, 2), ones(2, 2, 2, 2), ones(2, 2, 2)])
+            # test_frule(Chain, Quantum(tn), Open())
+            test_rrule(Chain, Quantum(tn), Open())
+
+            tn = Chain(Operator(), Periodic(), [ones(2, 2, 2, 2), ones(2, 2, 2, 2), ones(2, 2, 2, 2)])
+            # test_frule(Chain, Quantum(tn), Periodic())
+            test_rrule(Chain, Quantum(tn), Periodic())
+        end
     end
 end