Refactor classical postprocessing in shadows module

[natestemen]

Description

PR to refactor mitiq/shadows/classical_postprocessing.py.

Addresses some issues raised in #2129

Docs

Despite there being tests for the shadows module, as we saw in #2113 the tests do not cover everything and a change can pass tests despite making drastic changes to the results in a tutorial.

shadow tutorial before	after

Note there is a slight difference in the above plot. I'm not totally sure why.

rshadow tutorial before	after

All the other plots that I checked look either identical, or very close.

[codecov]

Codecov Report

Attention: 7 lines in your changes are missing coverage. Please review.

Comparison is base (e14a799) 98.20% compared to head (dd61f23) 98.26%.

Files	Patch %	Lines
mitiq/shadows/shadows_utils.py	69.56%	7 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2152      +/-   ##
==========================================
+ Coverage   98.20%   98.26%   +0.06%     
==========================================
  Files          88       88              
  Lines        4167     4143      -24     
==========================================
- Hits         4092     4071      -21     
+ Misses         75       72       -3     

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[Misty-W]

@Min-Li, we noticed some slight differences in the plots after the re-factor. Is this a concern, or do you think the module is working fine?

[FarLab]

Hi Nate, I had a look at your PR today by going over the commits and it looks good to me! The only concern is the very small difference in the first plots you show, but that might be some randomness that is not fixed.

[natestemen]

only concern is the very small difference in the first plots

Any idea where that change could be coming from? I have not been able to find it.

[FarLab]

only concern is the very small difference in the first plots

Any idea where that change could be coming from? I have not been able to find it.

looking at the shadows_tutorial notebook, the seed is fixed, and you didn't change that. So maybe that is not the cause.

[FarLab]

Looks good, not much to add besides the insignificant differences in the plot in the tutorial notebook.

[Min-Li]

@Min-Li, we noticed some slight differences in the plots after the re-factor. Is this a concern, or do you think the module is working fine?

Looks good to me, since there are some changes in the code, for me, this slight change of the figure seems to result from adding/removing stages of random sampling (especially in the quantum measurement). But overall, I don't think there are any issues here.