Add tile codes and barbell codes (open-boundary qLDPC codes on a 2D lattice)

[TomaszAnd]

Two new related code entries: tile codes and barbell codes (a special case of
tile codes). Both are nested under the existing qubit QLDPC code, with barbell
codes as a child of the new tile code entry.

New Codes:

• Tile code (tile): 2D-local CSS QLDPC codes on a planar lattice with open
  boundaries, generalizing the surface code by allowing higher-weight checks
  confined to a fixed-size box. Covers the construction, the k = 2D^2 logical
  dimension, the [[288,8,12]] / [[288,8,14]] / [[512,18,19]] examples,
  the cellular-automaton logical basis, the Koszul-complex framework on
  P^1 x P^1, and derived automorphisms. Refs: arXiv:2504.09171, 2504.08887,
  2511.14589.
• Barbell code (barbell): tile codes tailored to a fixed-connectivity
  superconducting "six-qubit star lattice plus near-local coupler" architecture,
  with superdense syndrome extraction. Covers the example code families, the
  C_hw ≈ 1.65 hardware-complexity figure, the teraquop result, and Relay-BP
  decoding. Ref: arXiv:2606.06062.

Parents/cousins link to surface, rotated surface, bivariate bicycle,
hypergraph product, La-Cross, 2D lattice stabilizer, and 2D color codes.

I have added myself (TomaszAndrzejewski) to users/users_db.yml.

Checklist:

I remembered to:

• Include relevant citations I could think of (with \cite{...})
• Create links to the other referenced codes (with \hyperref[code:...]{...})
• Update the relevant meta changelog fields with my user_id