← Two-dimensional dynamic-automorphism color 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.

    • reference-isg-checks derived by constructor._schedule + ISGTracker reference row space v1

      The constructor tracks the sign-free instantaneous stabilizer group and exports its independent Pauli rows at the declared reference round as a symplectic CheckMatrix. This R1 snapshot is executable, but it is not a substitute for the fault distance of the full schedule.

      References: davydova2024dynamic

  2. R2

    Structure

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

    • doubled-patch-stack derived by constructor.SITE_COORDS + layer offsets + docking labels v1

      Put two qubits at every site of a finite triangular color substrate and add color-labelled docking sites where the Y boundary would otherwise require a high-weight coupling. Interlayer V measurements fold the two layers into one effective color-code frame; intralayer E measurements unfold them into two toric sectors. The exported coordinates separate the layers visually but are an incidence layout, not a metric claim.

      References: davydova2024dynamic

  3. R3

    Dynamics

    Ordered measurement schedules and their instantaneous stabilizer groups.

    • padded-schedule-isg canonical

      Read the padded witness from t=0 through t=8. The first return to the vertical-measurement frame occurs only after the startup transient; at that reference round the sign-free ISG has one logical degree of freedom, and the same row space returns at the final displayed round. A four-move condensation motif is therefore not by itself the complete executable witness.

      References: davydova2024dynamic

    • measurement-class-dictionary curated from davydova2024dynamic

      V(P1P2) acts between layers at one site, while E_c(P_l) acts along a color-c edge inside layer l. Boundary singles and mixed interlayer Paulis replace the bulk rule where a logical string must terminate. Keeping site, layer, color, Pauli, and round as separate labels prevents a drawing color from being mistaken for a measurement flavor.

      References: davydova2024dynamic

    • spacetime-detectors curated from davydova2024dynamic

      Error information is a product of measurement outcomes from several rounds. A data or measurement fault flips a pattern of spacetime detectors, and a decoder must compare histories modulo time-dependent gauge relations. Static color-code syndrome lookup and the distance of one exported ISG snapshot are therefore not protocol-level guarantees.

      References: davydova2024dynamic, 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.

    • logical-frame-automorphism curated from davydova2024dynamic

      Stabilizer-row-space recurrence says that the code frame closes; it does not say that logical labels return trivially. The primary construction transports the Pauli-triangle representatives as X_L to Z_L, Z_L to Y_L, and Y_L to X_L, which is the logical SH action. The constructor marks this map curated rather than verified because sign-free ISG rank tracking cannot derive outcome-dependent logical transport.

      References: davydova2024dynamic, aasen2022automorphism

    • unfolded-toric-sectors curated from kubica2015unfolding

      At the intermediate E-measurement frames, the doubled color substrate separates into toric-code sectors joined by the boundary prescription. Unfolding explains why the checks stay low weight and how logical strings survive each transition; it is a frame dictionary, not a claim that the time-dependent family is a static surface code.

      References: kubica2015unfolding, davydova2024dynamic

    • measurement-qca curated from aasen2023mqca

      A measurement quantum cellular automaton treats each round as a local causal update and exposes boundary information flow that an unordered stabilizer list erases. The QCA view is useful for comparing dynamic phases, while the literal Schedule remains the executable source for this entry.

      References: aasen2023mqca