Refresh the documentation website with figures, rebuilt examples, and cool animations - #23

Summary

Figures, structure, and consistency

• Rewrite the theory path so tensor networks lead into process tensors, and replace the diagram placeholders with TikZ figures for vectorisation, MPS/MPO vocabulary, channels, process-tensor anatomy, and contractions.
• Those figures follow the documentation theme: each diagram has a light and a dark SVG, and the page shows the one that matches the active theme.
• Split the process-tensor tutorials into construction and instruments, and shorten the unitary and dissipative TEBD/TDVP tutorials.
• Tighten the examples around one stated observable, the executable run versus the companion figure, and named-tuple diagnostics. This covers the dissipative spin, driven Bose–Hubbard, laser-driven, two-time, Ramsey, noisy-circuit, thermal, and central-spin pages.
• Drop the boundary-driven XXZ and closed-system TEBD/TDVP example pages. Point installation at the current release versus main.

Scripts rebuilt on current main

• Rebase onto the ACE and chronological-bond fixes. :zipup is gone. Central spin, e tester, and Ramsey use explicit :zipup_cpp. The thermal example stays on :canonzip.
• Bump the process-tensor caches to format 2 so cores built before that constructor change are not reused.
• Regenerate the Dense and ACE figures: single-mode and multimode spin baths, two-time correlations, central spin, thermal spin-boson, the noisy-circuit tester, and Ramsey.
• Raise the Ramsey bond cap to 512 so the record probabilities stay normalised. The central-spin lower panel is the error against the exact finite-bath formula.
• Shorten the companion scripts and drop the tester coherence panel. julia --project=. -t auto is the run command in the script headers.

Cool animations in homepage and README

• Add three Manim clips: ACE compression of bath modes into a process tensor, an instrument tape that fills empty slots with identity, and one process tensor contracted either to an open reduced state or to a closed scalar.
• Each clip has a light and a dark GIF, plus a static poster. The homepage plays the GIF for the active theme and shows the poster when the browser requests reduced motion.
• The same clips are on the README.

Test plan

• Confirm CI passes

• Confirm the documentation build completes.

• docs: add new Ramsey POVM example

• feat: add thermal_mode for bath Gibbs states

• docs: use thermal_mode in thermal bath examples

• docs: update landing page, install notes, and Liouville/PT examples

• docs: better landing page

• docs: split process-tensor tutorials into construction and instruments

• docs: rewrite tensor-network theory as a path to process tensors

• docs: polished liouville space theory

• docs: more precise statements in pt theory

• chore: remove boundary-driven spin and tebd/tdvp examples

• docs: shorten unitary and dissipative TEBD/TDVP tutorials

• docs: concise pt-mpo construction in example

• add: support to do + in tester sequences

• docs: detailed explanation of theory vs results

• docs: more concise example in rabi oscillations

• docs: reduce the length of content

• docs: better figure for noisy qubit tester

• docs: better placement of the model equations

• docs: improve ramsey povm discussion

• docs: tighten example physics and match executable runs

• scripts: shorten ACE companion scripts and drop the tester coherence panel

• docs: pin ACE compression and invalidate process-tensor caches

• test: capture the empty-Hamiltonian warning with test_logs

• docs: regenerate process-tensor figures on the corrected constructors

• docs: replace theory diagram placeholders with TikZ figures

• cool feat: switch theory figures with the documentation theme

• docs: minor corrections in indices and instruments

• manim: animate ACE compression of bath modes into a process tensor

• manim: animate an instrument tape filling empty slots with identity

• manim: animate contracting one process tensor to a state or a scalar

• docs: play the three homepage clips in the active documentation theme

• manim: safer theme-specific gif rendering

• fix: bad figures of povm and histogram fixed

• add cool gifs to README