Belief Propagation Version 3

[JoeyT1994]

This PR introduces a more generalized version of belief propagation where the message tensors are now ITensorNetworks whose structure can be specified by the user.
Message tensor updates therefore can utilize the approx_itensornetwork() function and thus there is a new degree of freedom one can utilise for belief propagation. Default behaviour (not specifying contraction arguments for update_mt()) is to have the message tensors take the form of an ITensorNetwork containing a single ITensor

Corresponding tests and examples have been updated to reflect these changes.

Within beliefpropagation.jl, the calculate_contraction function has been replaced with calculate_contraction_network and it is then up to the user to decide how to contract the resulting network to obtain, e.g., an expectation value.

I have also defined ITensorNetwork(t::ITensor) to default to ITensorNetwork(ITensor[t])

[codecov-commenter]

Codecov Report

Merging #85 (4866b6a) into main (480b2c7) will increase coverage by 0.18%.
The diff coverage is 87.87%.

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@@            Coverage Diff             @@
##             main      #85      +/-   ##
==========================================
+ Coverage   77.75%   77.94%   +0.18%     
==========================================
  Files          62       62              
  Lines        3273     3287      +14     
==========================================
+ Hits         2545     2562      +17     
+ Misses        728      725       -3     

Impacted Files	Coverage Δ
src/abstractitensornetwork.jl	81.84% <66.66%> (-0.47%)	⬇️
src/beliefpropagation.jl	87.27% <90.00%> (-6.17%)	⬇️
src/apply.jl	91.66% <100.00%> (+0.08%)	⬆️
src/gauging.jl	100.00% <100.00%> (ø)
src/itensornetwork.jl	86.66% <100.00%> (+0.45%)	⬆️

... and 2 files with indirect coverage changes

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[mtfishman]

@JoeyT1994 besides the function renaming I raised in the comments above, over all it looks good! Nice to see it involves pretty minimal changes. Is there anything in particular you think I should look at?

[JoeyT1994]

No I think it all seems straightforward and there is nothing else in particular for you to look at. Just let me know what you want to do with the output type of get_environment.

[JoeyT1994]

Okay I think I have made the belief propagation interface much simpler following your suggestions. Initialisation now always gives a rank 1 MPS with the on-site tensor constructor specificable by the user.
The datagraph passed to message_tensor() must always have ITensorNetworks directly as the vertex data and thus should be the output of the partition() function.
There is also the option of message_tensors(tn::ITensorNetwork; partition_args) for handling the partitioning within belief_propagation.jl

[mtfishman]

Looks great, thanks!