docs: tutorial reproducing Fig. 4a - codes under global rotations (closes #119)

[Ronit-Raj9]

Summary

Adds docs/demos/global_rotations.ipynb, a tutorial that reproduces Fig. 4a of the linked Nature paper (Bluvstein et al., Nature 649, 39, 2026) using tsim, and wires it into the Tutorials nav.

A logical qubit is prepared in |+_L>, every physical qubit is rotated by the same R_Z(φ), and we track the logical-X projection and the X-stabilizer revival versus φ, for all four configurations of the figure:

• 2D colour code [[7,1,3]] (Steane) - decoded logical Clifford plateaus at multiples of 90° (S, S†, Z).
• 3D colour code [[15,1,3]] (Reed-Muller) - an additional plateau at multiples of 45° (T, T†, TS, (TS)†), the signature of its transversal non-Clifford T gate, with the stabilizers reviving there too.
• Unentangled - 15 bare qubits in |+>^15 read out with the same Reed-Muller operators: <X_L> = cos^15(φ) collapses away from 0°/±180° and the stabilizers revive only at multiples of 180°.
• 3D negative stabilizer - the Reed-Muller code with the four tetrahedron corners flipped (the paper's "incorrect stabilizer signs"): the curve falls onto the unentangled one, showing that the 45° plateau needs the correctly signed, genuinely entangled code state.

Reproduced figure

Following the paper's analysis: the encoded curves show the decoded (syndrome-postselected) logical projection, the two control curves are raw, and the bottom panel is the raw stabilizer revival - so the panels reproduce the published figure point for point (plateau positions, stabilizer revivals, and the green/grey controls hugging each other).

What's inside

• Literal hypercube encoder (Ext. Data Fig. 10a / ref. 128). The notebook builds the actual encoding circuit - the transversal CNOT network E = ((1,0),(1,1))^⊗m with the quantum-Reed-Muller input pattern (|+> on low-weight rows, |0> on high-weight rows), punctured at the 0…0 corner - and verifies by statevector overlap (= 1.000000) that it prepares the same |+_L> as the stabilizer-defined encoder, for both [[7,1,3]] (3-cube) and [[15,1,3]] (4-cube). [[16,6,4]] is the same circuit without puncturing.
• Encoders verified with stim.Circuit.flow_generators(), as the issue suggests.
• tsim is the workhorse. A generic global rotation on the 15-qubit code is 15 non-Clifford rotations at once - tcount() and a ZX timeline diagram make that explicit, and tsim's stabilizer-rank sampler produces the data points on the decoded curves (open markers), including the ±45° transversal-T angles. A dense 2^15 statevector of the rotated diagram is out of reach, so an exact Clifford-statevector reference (stim + analytic diagonal rotation) cross-checks every curve, with a φ = 0 assertion guarding correctness.
• Postselection / acceptance fraction. Implements the paper's stabilizer postselection, reports acceptance fractions, and uses it to recover the decoded staircase from the oscillating raw expectation - with a markdown explanation of why the raw and decoded curves differ.
• Physics-as-tutorial markdown throughout: global rotations as transversal gates, triorthogonality and why only the 3D code has a T plateau, Eastin-Knill and how logical measurement circumvents it, and why logical magic requires in-block entanglement (CHSH 1.99(3)×√2 in the paper).

Tests & CI

• Adds test/unit/demos/test_global_rotations.py (7 tests): encoder flow_generators, the hypercube ↔ stabilizer-encoder equivalence, the φ = 0 state, the Reed-Muller transversal-T plateau (and its absence for Steane), the negative-stabilizer control, and a tsim-sampler-vs-exact check on the 15-qubit code.
• Verified locally: ruff, black, isort, pyright (0 errors) and pytest (7 passed) all green, and the notebook builds clean under mkdocs-jupyter (execute: true, allow_errors: false) in ~6 min on CPU, so CI re-executes and guards it.

Notes for review

• Self-contained single notebook; no changes to src/.
• Outputs are stripped to match the existing demos.
• 3D Tsim markers are sampled at the Clifford / T angles (cheap even at 15 qubits); SAMPLE_SHOTS and the marker grids are exposed for heavier runs.

Closes #119.