excited state vmc and tests added

[victor11235]

Hi,
Based on https://github.com/orgs/netket/discussions/1593, I have drafted some code for penalty-based excited state protocol. This first version still uses a new driver (instead of a new operator suggested for better integration), so I have put them into experimental features.

I have also modified the tests for groundstate to mainly test the penalty-based gradient (central difference v.s. sample-estimated). Some of the tests are omitted (and for some reasons variational state with real parameters do not pass the test). Might be a bit messy but let me know what you think and I will try to find time to fix up!

[codecov]

Codecov Report

Attention: 18 lines in your changes are missing coverage. Please review.

Comparison is base (45d334e) 83.74% compared to head (f45db46) 84.83%.

❗ Current head f45db46 differs from pull request most recent head 975567c. Consider uploading reports for the commit 975567c to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1612      +/-   ##
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+ Coverage   83.74%   84.83%   +1.08%     
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  Files         262      265       +3     
  Lines       14636    15256     +620     
  Branches     2210     2238      +28     
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+ Hits        12257    12942     +685     
+ Misses       1832     1775      -57     
+ Partials      547      539       -8     

Files	Coverage Δ
netket/experimental/excited/__init__.py	100.00% <100.00%> (ø)
netket/experimental/excited/expect_grad_ex.py	93.65% <93.65%> (ø)
netket/experimental/excited/vmc_ex.py	73.58% <73.58%> (ø)

... and 69 files with indirect coverage changes

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[gcarleo]

Can we call this VMC_Excited or something more explicit?

[PhilipVinc]

Hi @victor11235 , thanks for the contribution!

I adapted a bit your PR to the style that we want to keep in netket, mainly having those 'objects' that behave as operators follow the operator interface such that we can do vstate.expect and vstate.expect_and_grad.

I have not really tested thoroughly that it works correctly right now, so please do that!

From am high level point of view I agree with the proposal.
The main three things that I need to reflect upon are

• returning both the energy and the 'loss' that is being optimised or loss + infidelity
• I don't know where to put the excited module. I would like to hide it a bit because in a (not so close) future I would like to do this tricks with Fidelity operator that eventually we'll bring into netket.
• The interface. I think it's ok but some extra documentation is needed (for example, what should be a good starting beta... etc),

Changes that would be nice to have would be the possibility to update the states/betas, which following my changes do not work anymore but are easy to restore with a setter, and the support for variational states with different 'ansatze', which should be very simple to implement...

I will get back to you with a few more formalised comments in the next few days