Correct QVFitter confidence level threshold to 0.977

[HuangJunye]

Correct QVFitter confidence level threshold to 0.977 corresponding to z = 2 as defined by the QV paper Algorithm 1

Summary

Fixes #473 and #481 :

1. Added new methods calc_z_value and calc_confidence_level.
2. Correct the confidence level threshold to calc_confidence_level(z_value=2).
3. Store confidence level even when hmean < 2/3.
4. Raises a warning if sigma=0 in calc_z_value
5. Added explanations for how to calculate statistics based on binomial distribution in calc_statistics()

Details and comments

[HuangJunye]

Suggest reviewers @dcmckayibm @levbishop. CC: @oliverdial.

[ShellyGarion]

Hi @HuangJunye - thank you for your contribution. Please note that if you would like your code to get merged, then you should fix the minor travis errors. Thanks!

[HuangJunye]

@ShellyGarion Sorry about that. This is the first time I am making a real PR haha. I removed the trailing white spaces which I think are the reasons for Travis errors. Still waiting for the build to finish but the build that failed has passed now.

Shall I add add anything to release note?

[HuangJunye]

Made a minor change to store confidence level even when hmean < 2/3 based on the comment from @oliverdial #483

[HuangJunye]

I realise what I did is not what @oliverdial asked for. He wants to store the confidence interval not confidence level. The QVFitter doesn’t calculate or store confidence interval. It calculate the confidence level for hmean > 2/3. I think it doesn’t harm to store confidence level for hmean < 2/3, but adding a feature To calculate confidence interval is probably another PR.

[oliverdial]

Actually, I misread the code -- I thought in some cases sigma was not stored, but it always is (with this the CI is easy to calculate). But saving the confidence level as well is still nice -- thanks!

[ShellyGarion]

Shall I add add anything to release note?

After you verify that this PR is correct and fits the theory of the QV paper, then you may also add release notes as you suggested.

[HuangJunye]

I tested with the quantum volume tutorial and textbook chapter. It behaves exactly as before the changes. I think it’s correct but the best would be getting @dcmckayibm or @levbishop to review the PR.

[HuangJunye]

Raises ValueError when sigma = 0 and added explanations for how to calculate statistics based on binomial distribution in calc_statistics() (addresses #481).

[HuangJunye]

@dcmckayibm I have added the error if, can you please review the code? Thank you.

[HuangJunye]

Thanks @dcmckayibm for your approval!

[ShellyGarion]

Thanks @HuangJunye for your contribution!

[HuangJunye]

Thank you @ShellyGarion. I am really excited to contribute my first ever PR to Qiskit!

[lazyoracle]

[HuangJunye]

@chriseclectic Thanks for merging the PR!!!