Implement Infinite Boundary Conditions for MatrixProduct and ProjectedEntangledPair Types

[jofrevalles]

Summary

In this PR, we resolve #77 by extending our MatrixProduct and ProjectedEntangledPair types to include support for infinite boundary conditions, materialized in the infinite Matrix Product States (iMPS) and infinite Projected Entangled Pair States (iPEPS). This creates a structure where the tensors cycle periodically, emulating an infinite system by using a finite system unit cell that repeats itself.

The tensors, Base.show and Base.length functions have been extended to support TensorNetworks with Infinte boundary conditions. Additional unit tests have been added to ensure the proper functioning of these new boundary conditions for both the MPS and MPO structures.

Nevertheless, the visualization of infinite boundary types is not yet supported and we should think about how to implement this.

Example

Let's create a MatrixProduct{State, Infinite} which consists of a cell of three tensors that repeat indefinitely:

julia> _arrays = [rand(1, 1, 2), rand(1, 1, 2), rand(1, 1, 2)]
3-element Vector{Array{Float64, 3}}:
 [0.17136137178613753;;; 0.1659622523369414]
 [0.23387611601182623;;; 0.5187233455849274]
 [0.025368244393775274;;; 0.2701565528371912]

julia> ψ = MatrixProduct{State,Infinite}(_arrays, order = (:l, :r, :o))
TensorNetwork{MatrixProduct{State, Infinite}, NamedTuple{(:plug, :interlayer, :χ), Tuple{Type{<:Plug}, Vector{Bijection{Int64, Symbol}}, Union{Nothing, Int64}}}}(#tensors=∞, #labels=∞)

julia> tensors(ψ, 1) == tensors(ψ, 4) == tensors(ψ, -2)
true

[codecov]

Codecov Report

Merging #79 (0f14437) into master (9e5349d) will decrease coverage by 0.82%.
The diff coverage is 50.00%.

@@            Coverage Diff             @@
##           master      #79      +/-   ##
==========================================
- Coverage   78.27%   77.46%   -0.82%     
==========================================
  Files           9        9              
  Lines         695      701       +6     
==========================================
- Hits          544      543       -1     
- Misses        151      158       +7     

Files Changed	Coverage Δ
src/Quantum/PEP.jl	0.00% <0.00%> (ø)
src/Quantum/Quantum.jl	76.04% <ø> (ø)
src/Tenet.jl	25.00% <ø> (-75.00%)	⬇️
src/Quantum/MP.jl	90.10% <100.00%> (-0.80%)	⬇️

[mofeing]

In general is ok, but I think you mixed the PR #78. Please remove anything from that other PR so I can merge this.

[mofeing]

If it doesn't match any method signature, it's better to let Julia throw a MethodError.

Suggested change

	tensors(ψ::TensorNetwork{MatrixProduct{P,Infinite}}, args...) where {P<:Plug} =
	throw(ArgumentError("You need to specify the site for an infinite MatrixProduct$P"))

[jofrevalles]

Sorry, I cherry-picked the commits in #78 because I thought was necessary, I will try to remove them now.

[mofeing]

Same as in MP.jl

Suggested change

	tensors(ψ::TensorNetwork{ProjectedEntangledPair{P,Infinite}}, args...) where {P<:Plug} =
	throw(ArgumentError("You need to specify the site for an infinite MatrixProduct$P"))

[mofeing]

I think you mixed PRs.

Suggested change

	tensors(::Union{Type{Operator}, Type{State}}, tn::TensorNetwork{<:Quantum}, site) = select(tn, labels(tn, :plug, site)) |> only
	tensors(::Type{State}, tn::TensorNetwork{<:Quantum}, site) = select(tn, labels(tn, :plug, site)) |> only

[mofeing]

Again you mixed PRs.

Suggested change

	@testset "tensors" begin
	arrays = [rand(1, 2, 2), rand(1, 1, 2, 2), rand(1, 2, 2)]
	ψ = MatrixProduct{Operator,Open}(arrays, order = (:l, :r, :i, :o))
	@test tensors(ψ, 1) isa Tensor
	@test size(tensors(ψ)) |> first == length(ψ) == 3
	end

[jofrevalles]

@mofeing, your requested changes should be fixed