feat: plot the pulse with Piccolo plot_pulse (not hand-rolled Makie)

[Rchari1]

Swaps the Run Inspector's per-iteration plot from hand-rolled CairoMakie to Piccolo's canonical plot_pulse. Stacked on #13 (inspector aesthetics); base rchari/inspector-aesthetics.

Why

The template's save_control_plot hand-rolled a Makie figure of prob.trajectory[:u] (raw control amplitudes vs timestep index) with one lines! per drive. Piccolo ships plot_pulse for exactly this — proper stacked per-drive panels, math-font labels, physical time axis, and optional drive-bound shading.

Change

solve_template.jl save_control_plot(k) becomes:

fig = plot_pulse(qcp; bounds = true, title = @sprintf("iter %d", k))
CairoMakie.save(@sprintf("iter_%04d.png", k), fig)

• plot_pulse(qcp::QuantumControlProblem) reads the current optimizer iterate (kept in sync by callback_update_trajectory_factory), so frames stay live.
• bounds=true shades the per-drive bounds.
• Still cheap — no rollout, so the per-iter cadence (PLOT_EVERY) and the live solve speed are unchanged.
• No new dependency: plot_pulse is in Piccolo, rendered via its Makie extension; CairoMakie (already a dep) stays the savefig backend. Net −5 lines.

Verification

Vetted end-to-end through amico-run on ~/.amico/julia (Piccolo 1.19):

• X gate → F = 0.9997, 60 iters, status=completed, exit 0.
• 7 of 7 frames distinct (md5) — confirms plot_pulse(qcp) tracks the live iterate, not a static initial pulse.
• Extension build + 37 tests green (template is a bundled asset; no TS impact).

Pairs with #13: the inspector's branded "converged" panel now shows a canonical Piccolo pulse plot instead of raw line plots.

🤖 Generated with Claude Code

[jack-champagne]

Gave it a look — clean one-file swap to Piccolo's plot_pulse(qcp; bounds=true), no new dep (Makie ext), CI green. Correct as-is, nothing blocking.

Taste / non-blocking

• Heads-up: the Phase 0′ callback work (#19/#21) replaces this per-iter plotting with AbstractIntermediateCallback/LivePulsePlotCallback, so this polish lands on a scaffold we're about to swap. Fine to take now — just flagging so we don't double-invest.

[jack-champagne]

LGTM. Clean swap to Piccolo's plot_pulse, net-negative LOC, and — the thing that could have broken the inspector — the iter_<N>.png filename, write location, per-iter callback, and PLOT_EVERY cadence are all preserved, so the watcher's frame discovery is unaffected. Frames stay live (plot_pulse reads qcp.prob.trajectory, the object the callback mutates).

Two minors, neither blocking: the body calls plot_pulse a "Makie extension" — it's a normal Visualizations submodule (works because using CairoMakie is already loaded), so the "no new dep" rationale is slightly off. And bounds=true adds a path that, under the bare try/catch, would swallow into zero frames if a future system's drive_bounds shape mismatches — consider a narrower catch or a bounds=false fallback.

[jack-champagne]

Approving — clean swap, and the iter_*.png frame contract is preserved. Two non-blocking minors above.