Support conversion to/from ITensors.jl and ITensorNetworks.jl

[mofeing]

CC @JoeyT1994

To do

•  Convert ITensor to Tensor
• Convert Tensor to ITensor
• Convert ITensorNetwork to TensorNetwork
• Convert TensorNetwork to ITensorNetwork
• Convert ITensorNetwork to Quantum
• Convert Quantum to ITensorNetwork
• Test conversions

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 24 lines in your changes missing coverage. Please review.

Project coverage is 72.46%. Comparing base (882049b) to head (50f5a4f).
Report is 3 commits behind head on master.

Files with missing lines	Patch %	Lines
ext/TenetITensorsExt.jl	0.00%	14 Missing ⚠️
ext/TenetITensorNetworksExt.jl	0.00%	10 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #200      +/-   ##
==========================================
- Coverage   72.73%   72.46%   -0.28%     
==========================================
  Files          27       31       +4     
  Lines        1944     1990      +46     
==========================================
+ Hits         1414     1442      +28     
- Misses        530      548      +18     

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[mofeing]

@starsfordummies would you mind checking this conversions with some code of your own?

You can just activate a temporary environment and add this version of Tenet with

]add Tenet#integration-itensornetworks

@jofrevalles I've added a sites method to get the site associated to an index. Currently it uses findfirst to search through the dictionary, but maybe we could use a bidirectional dictionary if we can assure that the 2 sets (the sites and the physical indices) are isomorphic. One case where they aren't is open indices without any tensor connected to it; it's a very edgy case anyway.

[starsfordummies]

I can test stuff, if you tell me what I should test!
I skimmed through the code, love how you decided to use convert() to make it impossible to find documentation 🦆

anyway, works for ITensor with data, breaks down with empty ITensor,

julia> a = random_itensor(Index(3),Index(4));
julia> at = convert(Tensor, a);   #works 

julia> a = ITensor(Index(3),Index(4))
ITensor ord=2 (dim=3|id=248) (dim=4|id=955)
NDTensors.EmptyStorage{NDTensors.EmptyNumber, NDTensors.Dense{NDTensors.EmptyNumber, Vector{NDTensors.EmptyNumber}}}

julia> at = convert(Tensor, a)
ERROR: StackOverflowError:

for MPS I don't know how to do it, with random attempts I was able to get it to do something but I don't know if that's the intended way

julia> psi = random_mps(siteinds("S=1/2", 10));

julia> tpsi = convert(Chain, psi)
ERROR: MethodError: Cannot `convert` an object of type ITensors.ITensorMPS.MPS to an object of type Chain
The function `convert` exists, but no method is defined for this combination of argument types.

julia> tpsi = convert(TensorNetwork, psi)
ERROR: MethodError: Cannot `convert` an object of type ITensors.ITensorMPS.MPS to an object of type TensorNetwork
The function `convert` exists, but no method is defined for this combination of argument types.

julia> tpsi = convert(Chain, psi.data)
ERROR: MethodError: Cannot `convert` an object of type Vector{ITensor} to an object of type Chain
The function `convert` exists, but no method is defined for this combination of argument types.


julia> tpsi = convert(TensorNetwork, psi.data)   # works 
TensorNetwork (#tensors=10, #inds=19)

[mofeing]

I can test stuff, if you tell me what I should test! I skimmed through the code, love how you decided to use convert() to make it impossible to find documentation 🦆

ups, sorry 😬😅

anyway, works for ITensor with data, breaks down with empty ITensor,

julia> a = random_itensor(Index(3),Index(4));
julia> at = convert(Tensor, a);   #works 

julia> a = ITensor(Index(3),Index(4))
ITensor ord=2 (dim=3|id=248) (dim=4|id=955)
NDTensors.EmptyStorage{NDTensors.EmptyNumber, NDTensors.Dense{NDTensors.EmptyNumber, Vector{NDTensors.EmptyNumber}}}

julia> at = convert(Tensor, a)
ERROR: StackOverflowError:

this is... kind of expected. what can we do with sth that doesn't even have an eltype?

for MPS I don't know how to do it, with random attempts I was able to get it to do something but I don't know if that's the intended way

yeah, MPS is not yet supported because I haven't add support for ITensorMPS package, just for ITensors and ITensorNetworks

i will once we have refactored Chain to MPS and MPO