Reduce measurement cost using qubit-wise commutativity

[chmwzc]

Reduce the measurement cost of VQE by grouping Hamiltonian terms that commute qubit-wise, and obtaining their expectation value with a single set of measurements.

Reference paper: https://arxiv.org/abs/1907.03358

Checklist:

• Code (17 Apr - Currently refactoring)
• Documentation
• Example/Tutorial

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (81239b2) to head (4693517).

Additional details and impacted files

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  Coverage   100.00%   100.00%           
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  Files           12        12           
  Lines          587       620   +33     
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+ Hits           587       620   +33     

Flag	Coverage Δ
unittests	100.00% <100.00%> (ø)

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[chmwzc]

Note: I renamed expectation.py because I don't think it having the same name as the main function inside (expectation) was very nice. E.g. it's not clear what would import qibochem.measurement.expectation as expectation give, the module or the function.

Other than that, I think this is done, but I'll do a bit more testing locally to be sure .

[chmwzc]

The figures in the tutorial are ugly, but I wanted to finish this before the meeting early next week (A bit tired of working on this too 😛). Will redraw nicer looking figures to replace them in future👍

[damarkian]

The figures in the tutorial are ugly, but I wanted to finish this before the meeting early next week (A bit tired of working on this too 😛). Will redraw nicer looking figures to replace them in future👍

How's this?

[damarkian]

Added some small modifications to the expectations from shots tutorial. Rendering by sphinx now looks ok.