An optimal dissipative encoder for the toric code
John Dengis, Robert König, Fernando Pastawski · New Journal of Physics · 2014
We consider the problem of preparing specific encoded resource states for the toric code by local, time-independent interactions with a memoryless environment. We propose the construction of such a dissipative encoder which converts product states to topologically ordered ones while preserving logical information. The corresponding Liouvillian is made up of four local Lindblad operators. For a qubit lattice of size L × L , we show that this process prepares encoded states in time O ( L ), which is optimal. This scaling compares favorably with known local unitary encoders for the toric code which take time of order Ω( L 2 ) and require active time-dependent control.