Reimplement MPS and MPO

ext/TenetAdaptExt.jl

@@ -9,5 +9,7 @@ Adapt.adapt_structure(to, x::TensorNetwork) = TensorNetwork(adapt.(Ref(to), tens
 Adapt.adapt_structure(to, x::Quantum) = Quantum(adapt(to, TensorNetwork(x)), x.sites)
 Adapt.adapt_structure(to, x::Ansatz) = Ansatz(adapt(to, Quantum(x)), Tenet.lattice(x))
 Adapt.adapt_structure(to, x::Product) = Product(adapt(to, Ansatz(x)))
+Adapt.adapt_structure(to, x::MPS) = MPS(adapt(to, Ansatz(x)), form(x))
+Adapt.adapt_structure(to, x::MPO) = MPO(adapt(to, Ansatz(x)), form(x))
 
 end

ext/TenetChainRulesCoreExt/frules.jl

@@ -18,6 +18,8 @@ end
 
 # `AbstractAnsatz`-subtype constructors
 ChainRulesCore.frule((_, ẋ), ::Type{Product}, x::Ansatz) = Product(x), Tangent{Product}(; tn=ẋ)
+ChainRulesCore.frule((_, ẋ), ::Type{MPS}, x::Ansatz, form) = MPS(x, form), Tangent{MPS}(; tn=ẋ, lattice=NoTangent())
+ChainRulesCore.frule((_, ẋ), ::Type{MPO}, x::Ansatz, form) = MPO(x, form), Tangent{MPO}(; tn=ẋ, lattice=NoTangent())
 
 # `Base.conj` methods
 ChainRulesCore.frule((_, Δ), ::typeof(Base.conj), tn::Tensor) = conj(tn), conj(Δ)

ext/TenetChainRulesCoreExt/rrules.jl

@@ -25,6 +25,14 @@ Product_pullback(ȳ) = (NoTangent(), ȳ.tn)
 Product_pullback(ȳ::AbstractThunk) = Product_pullback(unthunk(ȳ))
 ChainRulesCore.rrule(::Type{Product}, x::Ansatz) = Product(x), Product_pullback
 
+MPS_pullback(ȳ) = (NoTangent(), ȳ.tn, NoTangent())
+MPS_pullback(ȳ::AbstractThunk) = MPS_pullback(unthunk(ȳ))
+ChainRulesCore.rrule(::Type{MPS}, x::Ansatz, form) = MPS(x, form), MPS_pullback
+
+MPO_pullback(ȳ) = (NoTangent(), ȳ.tn, NoTangent())
+MPO_pullback(ȳ::AbstractThunk) = MPO_pullback(unthunk(ȳ))
+ChainRulesCore.rrule(::Type{MPO}, x::Ansatz, form) = MPO(x, form), MPO_pullback
+
 # `Base.conj` methods
 conj_pullback(Δ::Tensor) = (NoTangent(), conj(Δ))
 conj_pullback(Δ::Tangent{Tensor}) = (NoTangent(), conj(Δ))

ext/TenetReactantExt.jl

@@ -42,6 +42,13 @@ function Reactant.make_tracer(seen, prev::Tenet.Product, path::Tuple, mode::Reac
     return Tenet.Product(tracetn)
 end
 
+for A in (MPS, MPO)
+    @eval function Reactant.make_tracer(seen, prev::$A, path::Tuple, mode::Reactant.TraceMode; kwargs...)
+        tracetn = Reactant.make_tracer(seen, Ansatz(prev), Reactant.append_path(path, :tn), mode; kwargs...)
+        return $A(tracetn, form(prev))
+    end
+end
+
 function Reactant.create_result(@nospecialize(tocopy::Tensor), @nospecialize(path), result_stores)
     data = Reactant.create_result(parent(tocopy), Reactant.append_path(path, :data), result_stores)
     return :($Tensor($data, $(inds(tocopy))))
@@ -70,6 +77,13 @@ function Reactant.create_result(tocopy::Tenet.Product, @nospecialize(path), resu
     return :($(Tenet.Product)($tn))
 end
 
+for A in (MPS, MPO)
+    @eval function Reactant.create_result(tocopy::A, @nospecialize(path), result_stores) where {A<:$A}
+        tn = Reactant.create_result(Ansatz(tocopy), Reactant.append_path(path, :tn), result_stores)
+        return :($A($tn, $(Tenet.form(tocopy))))
+    end
+end
+
 # TODO try rely on generic fallback for ansatzes
 # function Reactant.create_result(tocopy::Tenet.Product, @nospecialize(path), result_stores)
 #     tn = Reactant.create_result(Ansatz(tocopy), Reactant.append_path(path, :tn), result_stores)

src/Ansatz.jl

@@ -192,13 +192,49 @@ Contract the virtual bond between two [`Site`](@ref)s in a [`AbstractAnsatz`](@r
 """
 @kwmethod contract!(tn::AbstractAnsatz; bond) = contract!(tn, inds(tn; bond))
 
+"""
+    canonize!(tn::AbstractAnsatz)
+
+Transform an [`AbstractAnsatz`](@ref) Tensor Network into the canonical form (aka Vidal gauge); i.e. the singular values matrix Λᵢ between each tensor Γᵢ₋₁ and Γᵢ.
+"""
+function canonize! end
+
+"""
+    canonize(tn::AbstractAnsatz)
+
+Like [`canonize!`](@ref), but returns a new Tensor Network instead of modifying the original one.
+"""
 canonize(tn::AbstractAnsatz, args...; kwargs...) = canonize!(deepcopy(tn), args...; kwargs...)
+
+"""
+    mixed_canonize!(tn::AbstractAnsatz, orthog_center)
+
+Transform an [`AbstractAnsatz`](@ref) Tensor Network into the mixed-canonical form, that is,
+for `i < orthog_center` the tensors are left-canonical and for `i >= orthog_center` the tensors are right-canonical,
+and in the `orthog_center` there is a tensor with the Schmidt coefficients in it.
+"""
+function mixed_canonize! end
+
+"""
+    mixed_canonize(tn::AbstractAnsatz, orthog_center)
+
+Like [`mixed_canonize!`](@ref), but returns a new Tensor Network instead of modifying the original one.
+"""
+mixed_canonize(tn::AbstractAnsatz, args...; kwargs...) = mixed_canonize!(deepcopy(tn), args...; kwargs...)
+
 canonize_site(tn::AbstractAnsatz, args...; kwargs...) = canonize_site!(deepcopy(tn), args...; kwargs...)
 
+"""
+    isisometry(tn::AbstractAnsatz, site; kwargs...)
+
+Check if the tensor at a given [`Site`](@ref) in a [`AbstractAnsatz`](@ref) Tensor Network is an isometry.
+"""
+function isisometry end
+
 """
     truncate(tn::AbstractAnsatz, bond; threshold = nothing, maxdim = nothing)
 
-Like [`truncate!`](@ref), but returns a new tensor network instead of modifying the original one.
+Like [`truncate!`](@ref), but returns a new Tensor Network instead of modifying the original one.
 """
 truncate(tn::AbstractAnsatz, args...; kwargs...) = truncate!(deepcopy(tn), args...; kwargs...)