Add quickstart page on mid-circuit measurements

[dwierichs]

Context:
The PennyLane documentation has a quickstart page on measurements, which includes a large section about mid-circuit measurements.
With the focus on dynamic circuits and mid-circuit measurements more generally, we would like to make the content on MCMs more visible.

Description of the Change:
Extracts the MCM part of the measurements quickstart and adds it as its own quickstart page.
Adds some details on simulation techniques and polishes the content.

Benefits:
Visibility, documentation extent for MCMs

Possible Drawbacks:

Related GitHub Issues:

[sc-65318]

[github-actions]

Hello. You may have forgotten to update the changelog!
Please edit doc/releases/changelog-dev.md with:

• A one-to-two sentence description of the change. You may include a small working example for new features.
• A link back to this PR.
• Your name (or GitHub username) in the contributors section.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.66%. Comparing base (14a0b63) to head (f28f967).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5870      +/-   ##
==========================================
- Coverage   99.67%   99.66%   -0.01%     
==========================================
  Files         422      422              
  Lines       40658    40362     -296     
==========================================
- Hits        40525    40228     -297     
- Misses        133      134       +1     

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

[vincentmr]

Some suggestions, but otherwise looks good to me. Thanks @dwierichs .

[mudit2812]

Thanks a lot @dwierichs . I'm quite happy with this overall. I left a bunch of suggestions. One thought I had while reviewing this is to potentially reorganize the sections. The first 4 sections are really about "what features are available and how to use them", and the next 4 sections are about "simulating MCMs", and maybe it's worth organizing the doc as such. Example hierarchy below

Mid-circuit measurements in PennyLane: info about `qml.measure`
- Qubit reuse/reset
- Conditional operations
- Postselection
- Collecting MCM statistics

Simulation of MCMs: mostly the same as this section is currently
- deferred measurements
- one-shot
- tree traversal

Configuring MCMs: as it is currently

Another suggestion (though I would really like @trbromley 's input here) is to avoid applying the transforms themselves to the qnodes in the examples, as I believe we want to start using mcm_method. We can probably still say that the transforms are available to apply directly to tapes, but that qnodes should request specific configurations using mcm_method rather than decorators.

[dwierichs]

Thanks @mudit2812 for the detailed feedback! 🚀
Regarding the structure, I went for your suggestion, except for the last part (configuring MCMs) being part of the "Simulating MCMs" section.

Regarding applying transforms vs QNode config, I would suggest that for now we do not explicitly discourage users from using the transforms, but we do so implicitly by advertising the config path in the examples.

[mudit2812]

Couple of weird things are happening:

• The panel on the left side is showing a "Simulation of MCMs" page, but it just links to the "Simulation of MCMs" section inside the MCMs doc.
  

• The contents table for the MCMs doc (right side of the page) doesn't show the "Simulation of MCMs" section.
  

[trbromley]

Thanks @dwierichs, this is looking great! I've left a few comments.

[mudit2812]

Thanks @dwierichs . Once again this looks really good. I'm quite happy with the content of the doc, and am happy to approve once the remaining (small) comments are resolved, with the only blocking comment being the note about defer_measurements differentiability 😄

[mudit2812]

Looks good. Mostly non-blocking comments. Happy to approve :)