Here is a list of Floquet codes and other related dynamical codes.

Code | Description |
---|---|

Dynamical automorphism (DA) code | Dynamically-generated stabilizer-based code whose (not necessarily periodic) sequence of few-body measurements implements state initialization, logical gates and error detection. |

Floquet color code | Floquet code on a trivalent 2D lattice whose parent topological phase is the \(\mathbb{Z}_2\times\mathbb{Z}_2\) 2D color-code phase and whose measurements cycle logical quantum information between the nine \(\mathbb{Z}_2\) surface-code condensed phases of the parent phase. The code's ISG is the stabilizer group of one of the nine surface codes. |

Fracton Floquet code | Floquet code whose qubits are placed on vertices of a truncated cubic lattice. Its weight-two check operators are placed on edges of each truncated cube, while weight-three check operators are placed on each triangle. Its ISG can be that of the X-cube model code or the checkerboard model code. |

Hastings-Haah Floquet code | DA code whose sequence of check-operator measurements is periodic. |

Honeycomb Floquet code | Floquet code based on the Kitaev honeycomb model [1] whose logical qubits are generated through a particular sequence of measurements. |

Hyperbolic Floquet code | Floquet code whose check-operators correspond to edges of a hyperbolic lattice of degree 3. |

X-cube Floquet code | Floquet code whose qubits are placed on vertices of a truncated cubic lattice. Its weight-two check operators are placed on various edges. Its ISG can be that of the X-cube model code or that of several decoupled surface codes. |

## References

- [1]
- A. Kitaev, “Anyons in an exactly solved model and beyond”, Annals of Physics 321, 2 (2006) arXiv:cond-mat/0506438 DOI