convert to/from ITensors MPS

[starsfordummies]

It would be good to be able to convert between the two. An ITensorMPS.MPS is basically a list of ITensors plus a couple integers (llim, rlim) that localize the orthogonality center, but those should be added automatically when you create one.

The simplest way is probably to convert the tensors of Tenet's MPS into ITensors, and feed the list of ITensors into the ITensorMPS.MPS() constructor. The only thing I don't know how to do in Tenet,as always, is how to map the indices into the tensors. Here's a (non-working) attempt

 psi_tensors = [rand(2,10), rand(2,10,12), rand(2,12,4), rand(2,4)]
 psi_tenet = MPS(psi_tensors)

itensors = [] 
# this assumes some ordering of the Tenet tensor indices. one should also treat first and last separately but you get the idea
for (j,t) in enumerate(tensors(psi_tenet))
   it = ITensor(t, Index(dim("physical index of t"),"Site,n=$j"),Index(dim("left link index of t"),"Link,l=$j"),Index(dim("right link index of t"),"Link,l=$(j+1")
push!(itensors, it)
end 
psi_itensors = ITensorMPS.MPS(itensors)

the other way around is probably simpler (for me at least), here's one way to do it

psiten = ITensorMPS.random_mps(siteinds(4, 10), linkdims=7) 

# bring itensors to (o,l,r) and convert them

# first and last always annoying
first_ten = array(psiten[1], siteinds(psiten)[1], linkinds(psiten)[1])
last_ten = array(psiten[end], siteinds(psiten)[end], linkinds(psiten)[end])

ttensors = Array{}[array(psiten[jj], siteinds(psiten)[jj], linkinds(psiten)[jj-1],linkinds(psiten)[jj]) for jj in eachindex(psiten)[2:end-1]]
pushfirst!(ttensors, first_ten)
push!(ttensors,last_ten)

Tenet.MPS(ttensors)

[jofrevalles]

You can convert from Tenet.MPS to ITensorsMPS.MPS like this:

using Tenet
using ITensors
using Tenet: MPS, tensors
using ITensors: Index, ITensor, dim
using ITensorMPS

psi_tensors = [rand(2,10), rand(2,10,12), rand(2,12,4), rand(2,4)]
psi_tenet = MPS(psi_tensors)

itensors = ITensor[]

for (j,t) in enumerate(tensors(psi_tenet))
    it = if j == 1 || j == length(tensors(psi_tenet))
        ITensor(parent(t), Index(size(t, 1), "Site,n=$j"), Index(size(t, 2), "Link,l=$j"))
    else
        ITensor(parent(t), Index(size(t, 1), "Site,n=$j"), Index(size(t, 2), "Link,l=$j"), Index(size(t, 3), "Link,l=$(j+1)"))
    end

    push!(itensors, it)
end
psi_itensors = ITensorMPS.MPS(itensors)

Do you want to have this as an extension in Tenet? We should also store the ortogonality center information

[mofeing]

Conversion from/to ITensors.ITensor and Tenet.Tensor is already implemented. You can just do:

# Tensor -> ITensor
convert(ITensor, tensor)

# ITensor -> Tensor
convert(Tensor, itensor)

Furthermore, you can convert a Vector{ITensor} to a Tenet.TensorNetwork and viceversa.

What I'm not sure about is whether Index carries some site information. In that case, we currently lose it and we will need to do sth more for converting ITensorsMPS.MPS to our MPS and the other way around.