Only one `TreeTensorNetwork`/`TTN` instead of seperate `TTNS`/`TTNO` types

[mtfishman]

It would be interesting to see if we can get away with just having a TreeTensorNetwork/TTN type that is treated as an operator or a state depending on the context.

In many ways the MPO/MPS types in ITensors.jl are nearly the same, and it can be awkward having both around.

If we really need to distinguish them for the sake of dispatch, we could have a wrapper type like Map(ttn) or Operator(ttn), which could be like an ITensorNetworkMap: https://github.com/ITensor/ITensors.jl/blob/v0.3.20/src/ITensorNetworkMaps/ITensorNetworkMaps.jl

Originally posted by @mtfishman in #18 (comment)

[emstoudenmire]

I like this sort of thing from a code design and maintenance perspective, especially because it would force us to be sure that a lot of the algorithms are fairly generic about e.g. MPS with extra indices on tensor and things.

One, I guess rather minor, concern is that when the types are printed they would look the same, or have perhaps an unusual name like "MatrixProductNetwork" for MPS and MPO if they were unified. Is there a way in Julia to know whether a type was referred to by an alias or the actual type for things like printing? I guess not.

[mtfishman]

In recent versions of Julia it prints both:

julia> Vector{Int}
Vector{Int64} (alias for Array{Int64, 1})

julia> versioninfo()
Julia Version 1.8.3
Commit 0434deb161e (2022-11-14 20:14 UTC)
Platform Info:
  OS: macOS (x86_64-apple-darwin21.4.0)
  CPU: 10 × Apple M1 Max
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-13.0.1 (ORCJIT, westmere)
  Threads: 1 on 10 virtual cores

[emstoudenmire]

Nice. Hopefully would do that for aliases like MPS and MPO if eventually they referred to the same type.