Quick fix: Fix typo and headings in classical shadows tutorial

[JMuff22]

Description

I noticed some typos and an unrendered heading in the classical shadows documentation. These are fixed here.

Additionally, if you (the maintainers) think it useful I think it would be good to highlight Remark 1 from the paper (https://arxiv.org/abs/2002.08953)

Remark 1 (Constants in Theorem 1). The numerical constants featuring in N and K result from a conservative
(worst case) argument that is designed to be simple, not tight. We expect that the actual constants are much
smaller in practice.

In the shadows_tutorial for equation (10). I think the sudden appearance of 34 is confusing in the guide.

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License

• I license this contribution under the terms of the GNU GPL, version 3 and grant Unitary Fund the right to provide additional permissions as described in section 7 of the GNU GPL, version 3.

Before opening the PR, please ensure you have completed the following where appropriate.

• I added unit tests for new code.
• I used type hints in function signatures.
• I used Google-style docstrings for functions.
• I updated the documentation where relevant.
• Added myself / the copyright holder to the AUTHORS file

[github-actions]

Hello @JMuff22, thank you for submitting a PR to Mitiq! We will respond as soon as possible, and if you have any questions in the meantime, you can ask us on the Unitary Fund Discord.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.72%. Comparing base (9561b9f) to head (80067a2).
Report is 3 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2574   +/-   ##
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  Coverage   98.72%   98.72%           
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  Files          92       92           
  Lines        4168     4168           
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  Hits         4115     4115           
  Misses         53       53           

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[purva-thakre]

Hi @JMuff22, thank you for your correction! Cleaning up this tutorial is on our list of todos #2110

Additionally, if you (the maintainers) think it useful I think it would be good to highlight Remark 1 from the paper

I have a very high-level understanding of how this technique works. Is there a particular spot where this remark might be useful?

In the shadows_tutorial for equation (10). I think the sudden appearance of 34 is confusing in the guide.

I think this equation is directly taken from the paper. See eq S13 in the supplementary info.

[JMuff22]

I think this equation is directly taken from the paper. See eq S13 in the supplementary info.

Yes S13 without remark 1 is confusing in my opinion.

[natestemen]

Good catch! Thanks for the patch.

I agree the remark would be helpful here. Is that something you'd like to add to this PR?

[JMuff22]

By the way, is there a quicker way of building the documentation for quick fixes? I noticed that make docs builds and executes all the jupyter notebooks which is not ideal for testing how a small change like this would look when rendered.

[JMuff22]

Good catch! Thanks for the patch.

I agree the remark would be helpful here. Is that something you'd like to add to this PR?

Added my suggested fix.

[natestemen]

Thanks Jake! BTW are you using the mitiq.shadows module in practice? Would love to get your thoughts/opinions on how it's going if so.

[natestemen]

By the way, is there a quicker way of building the documentation for quick fixes? I noticed that make docs builds and executes all the jupyter notebooks which is not ideal for testing how a small change like this would look when rendered.

make docs will cache the results from notebooks, so if it doesn't change it won't rerun. There's no caching on CI, but locally it should speed up after the first build. I think @cosenal had a command to run a single file, but I cannot find it now.

[JMuff22]

Thanks Jake! BTW are you using the mitiq.shadows module in practice? Would love to get your thoughts/opinions on how it's going if so.

I am not really using it in practice. Maybe in the future. I was more using it to learn the protocol and apply it myself.