Add new Julia tutorial (continuing work from #5254)

[abbycross]

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One or more of the following people are relevant to this code:

• @nathanearnestnoble

[henryzou50]

Thanks for the updates @haimeng-zhang, overall the tutorial looks great! I do have some minor suggestions:

1. Background text still has the old factor-of-2: the Background cell says each Trotter step applies $R_x(h_i\Delta\tau/2)$, but since $R_x(\theta) = e^{-i\theta X/2}$, the half-step needs $\theta = h_i\Delta\tau$, which is what the corrected code now does. Both mentions should read $R_x(h_i\Delta\tau)$. (The $R_{ZZ}(2J_{ij}\Delta\tau)$ part is correct.)

2. Two saved outputs are stale: the println strings in two cells were edited after the notebook was last run, so the saved outputs still show the old text. To fix, edit the saved output text to match the current code (no re-run needed, since only the print strings changed):

   • In the tensor-network fidelity cell (the loop printing "fidelity at Trotter step $(r) was $(fidelity)"), the saved output still reads fidelity at trotter step ..., capitalize "trotter" -> "Trotter" in the output lines.
   • In the N=60 tensor-network reference cell, the code says println("Tensor-network reference:") but the saved output still reads Converged tensor-network reference: - change the output line to Tensor-network reference:.

3. Small copyedits:

   • Comma splice in Requirements: "developed with Julia 1.11, one can install…" -> "…Julia 1.11; install it with juliaup add 1.11"
   • Doubled # # comment marker in the save_counts cell
   • "Github" -> "GitHub" in Next steps

@abbycross one thing I noticed on the infra side: the two plot images don't show up in the PR preview, the "Output:" blocks for both plot cells render empty. The extracted SVGs are deployed correctly; the problem is in the notebook itself. IJulia/Plots.jl saves each plot output with two representations: a text/html entry (an <img> with a ~50 KB base64 data-URI PNG) alongside the text/plain entry that ./fix rewrites to the <Image src="...svg" /> tag. The site renderer prefers text/html when present, and the data-URI <img> gets sanitized away, so nothing renders. I tried tox -e fix as usual, but it doesn't help as it extracts the SVG and rewrites text/plain but leaves the stale text/html entry in place (Python notebooks never hit this since matplotlib emits image/png/image/svg+xml directly). I think a fix for this PR is to delete the text/html key from the two plot outputs (also shrinks the notebook by ~120 KB). Longer term, we could have the notebook normalizer strip text/html from outputs it extracts images from, since any future Julia notebook will hit the same issue.

[abbycross]

Ah, we need to look more closely at how to handle the toml files, and the additional directory added here. We might need to rethink how to support that content. @kaelynj thoughts?