add neutron scattering tutorial

[kevinsung]

corresponding paper: https://arxiv.org/abs/2603.15608

produced with assistance from Claude

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[henryzou50]

Thanks for the changes, this tutorial looks great!

I pushed a commit with some small copyedits (root-relative Next steps links, trimming unused words from the cspell ignore list, a TUT_SNS job tag, and a few wording fixes in line with earlier review comments), so the checks should pass now. None of it touches code that affects results.

Beyond that, here are a few things I noted that could be changed or adjusted, let me know what you think.

Commentary/results

• The intro's caveat only covers the AQC fidelity, but the printed ground-state ansatz fidelity also drops sharply (0.984 at 10 qubits → 0.646 at 50) with no explanation, so readers might think their ground-state prep failed. Suggest adding a sentence to the large-scale intro noting the ~0.65 fidelity is expected, and that increasing gs_n_layers or maxiter improves it at additional classical cost.
• The text says the two-layer ansatz is used "where higher fidelity is needed," yet its printed fidelities (k=7–10: 0.67–0.77) are lower than the one-layer ones (k=1–6: 0.81–1.0). That's expected, as later time steps are just harder to compress, but a short sentence saying so would keep it from reading as a regression.
• The large-scale section ends at the plots with no discussion. One or two closing sentences pointing out the continuum boundaries and the intensity at q = π would be nice here

Step 2c runtime for k > 6

When I ran the notebook, Step 2c only completed overnight, which matches the committed outputs: the one-layer stage (k=1–6) takes ~28 minutes, but the two-layer stage (k=7–10) takes ~5.3 hours (k=7 alone is ~3 hours, maybe because the stage boundary resets to fresh initial parameters and it runs all ~100 L-BFGS-B iterations on the 3412-parameter ansatz). That puts Step 2c at ~6 hours end to end.

Is there a way to shorten this, or should we expect it to always take this long to get good results?

Index placement (question for @abbycross)

The new entry is inserted at the top of the Observable estimation section in both _toc.json and index.mdx, whereas #5280 appended its tutorial at the end of the section. Which placement do we want?

[henryzou50]

Since Kevin is away, I applied the following commentary revisions as I mentioned before:

• Explained in the large-scale intro that the lower fidelities at 50 qubits (~0.65 ground state, ~0.7 AQC) are expected, and which knobs improve them.
• Clarified that the two-layer AQC fidelities being lower than the one-layer ones is not a regression (later steps are harder to compress).
• Added a short closing discussion after the hardware plots tying the measured DSF back to the two-spinon continuum.

This tutorial LGTM! Let me know if you want to do a quick pass on this @nathanearnestnoble

[henryzou50]

@abbycross This is approved by me and @nathanearnestnoble, if you'd like to take a final quick pass before merge, now's a great time. Since your review, the main updates are commentary revisions on the 50-qubit results, a Step 2c runtime note, and copyedits.

Also, whenever you get a chance, could you weigh in on the index placement question above? This entry currently sits at the top of the Observable estimation section in _toc.json and index.mdx, while #5280 appended its tutorial at the end. Happy to adjust to whichever convention you'd like.

[abbycross]

@abbycross This is approved by me and @nathanearnestnoble, if you'd like to take a final quick pass before merge, now's a great time. Since your review, the main updates are commentary revisions on the 50-qubit results, a Step 2c runtime note, and copyedits.

Also, whenever you get a chance, could you weigh in on the index placement question above? This entry currently sits at the top of the Observable estimation section in _toc.json and index.mdx, while #5280 appended its tutorial at the end. Happy to adjust to whichever convention you'd like.

Hi and apologies for the delay in response - I'm still sorting through notifications after being OOO! The index placement is totally whatever you and Nate think makes sense. I normally add new tutorials at the end of the index/toc sections, but only because I haven't been asked to make a title more prominent or place in a specific order. Feel free to keep it where you think it makes most sense!

I will take a final look through. Thanks for pinging me.

[abbycross]

Thanks! 👍

[henryzou50]

Thanks @abbycross and no worries! Appreciate your reviews and suggestions! Having this one at top of the index is fine for me as it is a tutorial that we want to promote.