An optimal dissipative encoder for the toric code
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 logic...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/16/1/013023 |
| Summary: | 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. |
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| ISSN: | 1367-2630 |