ToricCode — model index
The toric code — Kitaev's exactly-solvable stabilizer model, the paradigmatic $\mathbb{Z}_2$ topological order with deconfined anyonic excitations.
\[H = -\sum_v A_v - \sum_p B_p, \qquad A_v = \prod_{i\in v}\sigma^x_i,\ \ B_p = \prod_{i\in p}\sigma^z_i\]
Generated by docs/atlas/generate.jl — a pure VIEW over the *_registry.jl claims + the static test/INVENTORY.jsonl AST scan. No test is executed and no src is run; test/INVENTORY.jsonl is regenerated in-place (idempotently) from that static scan; fetch/@register untouched. Assurance labels are PROVISIONAL: residuals / confidence are not shown yet (RES not wired). Badges reflect the committed test AST, not the latest CI run — a hub can read green while its @test is red between regenerations. @sweep = a graceful regime-resolution gap, not card omission.
All (Quantity, BC) hubs src claims for ToricCode. Cells link to the per-hub card; — = not yet implemented at that BC. The shape of the matrix is the gap visualisation: empty cells are where physics could be added next.
Convention
| Field | Value |
|---|---|
| Hamiltonian | Stabilizer / operator product |
| Observable | Operator-product expectations (Wilson loops, GSD, TEE, S-matrix entries); convention-free |
| Reference | docs/src/conventions.md §Topological / operator-product |
Coverage
| Level | Count |
|---|---|
| 🟣 universality-corroborated | 0 |
| 🟢 corroborated-at-p | 4 |
| 🔵 coherent | 0 |
| ⚪ cited-only | 1 |
| 🟠 uncorroborated-but-feasible | 0 |
| total claimed hubs | 5 |
This model is in ED_INFEASIBLE_MODELS (true 2D / frontier). Its cited-only hubs are the published ceiling, not an actionable gap.
Methods (from @register, derived): analytic
Quantity × BC matrix
| Quantity | PBC | Infinite |
|---|---|---|
AnyonStatistics | — | ⚪ hub |
GroundStateDegeneracy | 🟢 hub | — |
GroundStateEnergyDensity | — | 🟢 hub |
MassGap | — | 🟢 hub |
TopologicalEntanglementEntropy | — | 🟢 hub |
References
Papers cited by this model's @register cards. The full numbered list is on the Reference List.
- [163]
- A. Kitaev. Fault-tolerant quantum computation by anyons. Annals of Physics 303, 2–30 (2003).
- [75]
- A. Kitaev and J. Preskill. Topological Entanglement Entropy. Physical Review Letters 96 (2006).
- [164]
- M. Levin and X.-G. Wen. Detecting Topological Order in a Ground State Wave Function. Physical Review Letters 96 (2006).
- [122]
- C. Nayak, S. H. Simon, A. Stern, M. Freedman and S. Das Sarma. Non-Abelian anyons and topological quantum computation. Reviews of Modern Physics 80, 1083–1159 (2008).