collection
Toric code
The square Toric code puts one qubit on every edge of an L-by-L periodic square cellulation. Vertex X stars and face Z plaquettes detect endpoints of open error strings. Contractible closed strings are stabilizers, while the two independent primal cycles and their crossing dual cycles form two logical Pauli pairs. This entry is the static two-dimensional qubit family, not an open Surface patch, a higher-dimensional Toric code, or every model in the same topological phase.
Scoped completion
Completion belongs to an entity, not the whole page
eczoo-entity:toric#collectionT2 — preserved
Researched operational entry
The formal core, operations, and typed relations meet the T2 Corpus boundary; full Reader-Contract pedagogy is not implied.
One orienting visual
Orienting view
Inspect constructor-derived qubits, stabilizers, and logical paths without leaving the entry. Visual instance: L3
↔ top/bottom and ↕ left/right edges are identified with matching color and arrow direction.
At a glance
Executable-target parameters
form: collection formal target: css formal target: topological formal target: hypergraph-product
Constructor variables
L- Integer linear size L >= 2 of the periodic square fundamental domain; there are L^2 vertices, L^2 faces, and 2 L^2 edge qubits.
Reference instances
| Instance | n | k | d |
|---|---|---|---|
| L2 | n=8 verified | k=2 verified | d=2 verified |
| L3 | n=18 verified | k=2 verified | d=3 verified |
Scientific scope
Source, page, and formal object are separate identities
Primary entity: eczoo-entity:toric#collection. Formalization target: eczoo-entity:toric#collection. Legacy vocabulary: exact class projection.
Source/entity binding: clean.