An Optimal Dissipative Encoder for the Toric Code
Journal Article - Open Access
WATERLOO UNIV (ONTARIO) WATERLOO Canada
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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 x L, we show that this process prepares encoded states in time OL, which is optimal. This scaling compares favorably with known local unitary encoders for the toric code which take time of order Omega L2 and require active time-dependent control.
- Quantum Theory and Relativity