Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the one-dimensional Majorana chain and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.
Cited by 1
Raditya Weda Bomantara et al., Simulation of Non-Abelian Braiding in Majorana Time Crystals
Phys. Rev. Lett. 120, 230405 (2018) [Crossref]
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- 1 Nicolai Lang,
- 1 Hans Peter Büchler