← Honeycomb Floquet code

Entry facet

Representation ladder

R1 checks through R5 cross-model views, with canonicality and provenance.

  1. R1

    Checks

    Sparse Pauli generators in symplectic form, including stabilizer and gauge rows.

    • steady-isg-checks derived by honeycomb.build Schedule -> ISGTracker steady snapshot v1

      After the declared startup, the constructor exports independent sign-free Pauli generators for one instantaneous stabilizer group as a symplectic CheckMatrix. This is the universal R1 snapshot for rank and commutation; it does not determine the protocol's spacetime distance.

      References: hastings2021dynamically

  2. R2

    Structure

    CSS pairs, chain complexes, lattices, and other structure behind the checks.

    • instantaneous-toric curated from hastings2021dynamically

      Contract every edge measured in the latest round into an effective qubit. The resulting instantaneous stabilizer group is locally Clifford-equivalent to a toric code, which explains the two logical qubits without identifying the full spacetime protocol with a static toric memory.

      References: hastings2021dynamically

  3. R3

    Dynamics

    Ordered measurement schedules and their instantaneous stabilizer groups.

    • schedule-isg canonical

      The executable object is a three-round Schedule. An incoming matching replaces anticommuting generators in the instantaneous stabilizer group while preserving a rank-eight plaquette backbone; this view distinguishes the dynamical code from a frozen check matrix.

      References: hastings2021dynamically

    • spacetime-detector curated from blackwell2025distance

      Plaquette information is assembled from measurement outcomes at different times. Faults are classified by the detector events they create and by whether an undetectable spacetime history is benign, so circuit fault distance cannot be read from one instantaneous snapshot.

      References: gidney2021fault, blackwell2025distance

  4. R4

    Circuit & detectors

    Named syndrome-extraction circuits and detector error models.

    No representation at this rung is recorded for this entry.

  5. R5

    Cross-model views

    Executable or illuminating algebraic, ZX, fermionic, tensor, and statistical dictionaries.

    • fermionic — parton curated from kitaev2006anyons

      Kitaev's four-Majorana representation factors each directional Pauli edge into a Z2 gauge variable and a matter-fermion pairing. The measurement cycle then becomes a rotating pairing pattern whose gauge-invariant products are the plaquette fluxes.

      References: kitaev2006anyons, zhu2023majoranaliquid

      Open machine-derivation problem →

    • anyon-automorphism curated from aasen2022automorphism

      One full code period transports the instantaneous toric order through a protected cycle and exchanges electric and magnetic anyon labels. This separates preservation of a logical subspace from the nontrivial logical frame motion performed by the memory schedule itself.

      References: hastings2021dynamically, aasen2022automorphism

    • measurement-qca curated from aasen2023mqca

      Treating the periodic measurements as a measurement quantum cellular automaton exposes information flow along boundaries and anomalies that are invisible in the bulk stabilizer rank.

      References: aasen2023mqca

    • zx-spacetime curated from bombin2024zx

      A ZX diagram represents the whole measurement history as a spacetime tensor network. Different circuit, fusion, and Floquet descriptions can be related by local rewrites without pretending that their hardware noise models are identical.

      References: bombin2024zx