add shot-noise to measurement

[multiphaseCFD]

This PR adds support for finite-shot measurement statistics (expval, var, and probs) for lightning.qubit and lightning.kokkos devices.

[sc-46423]

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (ea1c7b7) 99.54% compared to head (f9c3063) 99.56%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #392      +/-   ##
==========================================
+ Coverage   99.54%   99.56%   +0.01%     
==========================================
  Files          43       43              
  Lines        7302     7546     +244     
  Branches      497      497              
==========================================
+ Hits         7269     7513     +244     
  Misses         17       17              
  Partials       16       16              

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[josh146]

This is great @multiphaseCFD @maliasadi, great work!

Something I do wonder about though is testing. We know from experience that there are a lot of edge cases for measurements, such as:

• Single observables
• tensors on different wires
• linear combinations/hamiltonians
• new operator arithmetic
• differentiation
• expval/var

Should we have more extensive testing here?

[dime10]

Nice work 👍

[dime10]

🚀

[maliasadi]

Thanks @multiphaseCFD! 💯