Stable measurement-induced Floquet enriched topological order

Understand

The Floquet code utilizes a periodic sequence of two-qubit measurements to realize the topological order.

• After each measurement round, the instantaneous stabilizer group can be mapped to a honeycomb toric code, explaining the topological feature.
• The code also possesses a time-crystal order - the $e-m$ transmutation after every cycle, breaking the Floquet symmetry of the measurement schedule.
• This behavior is distinct from the stationary topological order realized in either random circuits or time-independent Hamiltonian.