Update Product manual

docs/src/manual/ansatz/product.md

@@ -1 +1,43 @@
 # `Product` ansatz
+
+```@setup examples
+using Tenet
+using Makie
+Makie.inline!(true)
+set_theme!(resolution=(800,400))
+using GraphMakie
+using CairoMakie
+CairoMakie.activate!(type = "svg")
+using NetworkLayout
+```
+
+A [`Product`](@ref) is the simplest [`Ansatz`](@ref) Tensor Network, which consists of a [`Tensor`](@ref) per [`Lane`](@ref) without any bonds, so all the sites are unconnected.
+The [`Socket`](@ref) type of a [`Product`](@ref) (whether it represents a [`State`](@ref) or an [`Operator`](@ref)) depends on the order of the tensors provided in the constructor.
+
+## `Product` State
+Each tensor is one-dimensional, with the only index being the output physical index.
+
+```@example examples
+fig = Figure() # hide
+
+qtn = Product([rand(2) for _ in 1:3])
+
+graphplot!(fig[1,1], qtn, layout=Spring(iterations=1000, C=0.5, seed=100)) # hide
+Label(fig[1,1, Bottom()], "Product State") # hide
+
+fig # hide
+```
+
+## `Product` Operator
+Each tensor is two-dimensional, with the indices being the input and output physical indices.
+
+```@example examples
+fig = Figure() # hide
+
+qtn = Product([rand(2, 2) for _ in 1:3])
+
+graphplot!(fig[1,1], qtn, layout=Spring(iterations=1000, C=0.5, seed=100)) # hide
+Label(fig[1,1, Bottom()], "Product Operator") # hide
+
+fig #hide
+```