Increase np.isclose tolerance for mitigated expectation value assertion

[ddddddanni]

This PR updates the tolerance of the np.isclose assertion used to validate the mitigated expectation value against its ideal value. The tolerance is being increased from 4 * mitigated_stddev to 10 * mitigated_stddev.
The nature of calculating a Pauli expectation is to statistically estimate the value by sampling from measurement outcomes a finite number of times, which by chance can lead to a small probability of the result deviate from the ideal value by > 4 * standard deviations. Increasing the tolerance to 10 * mitigated_stddev can makes the test much more robust against these statistical fluctuations.

Fixes #7612

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.40%. Comparing base (d0e2bc5) to head (dd51998).
⚠️ Report is 10 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #7627      +/-   ##
==========================================
- Coverage   97.50%   97.40%   -0.11%     
==========================================
  Files        1103     1103              
  Lines       99707    99915     +208     
==========================================
+ Hits        97222    97324     +102     
- Misses       2485     2591     +106     

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[pavoljuhas]

It feels a bit of an overkill to both increase the tolerance
and retry tests. I tried to run this test module repeatedly
~500 times without the retry decorator and it did not fail
once (the main branch would fail about 6 times).

Can you please remove the retry decorator?

[ddddddanni]

It feels a bit of an overkill to both increase the tolerance and retry tests. I tried to run this test module repeatedly ~500 times without the retry decorator and it did not fail once (the main branch would fail about 6 times).

Can you please remove the retry decorator?

Done ; )

[pavoljuhas]

Thank you!