← Binary quantum Hamming CSS 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.

    • hamming-css-matrix canonical

      Columns are ordered by increasing nonzero binary value. The resulting matrix is duplicated into pure-X and pure-Z sectors; the orienting scene shows exact stabilizer incidence and makes no spatial-locality claim.

      References: steane1996simple

  2. R2

    Structure

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

    No representation at this rung is recorded for this entry.

  3. R3

    Dynamics

    Ordered measurement schedules and their instantaneous stabilizer groups.

    No representation at this rung is recorded for this entry.

  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.

    No representation at this rung is recorded for this entry.