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Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata
by Nicolai Lang, Hans Peter Büchler
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Nicolai Lang |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1711.08196v2 (pdf) |
| Date accepted: | 2018-01-21 |
| Date submitted: | 2018-01-15 01:00 |
| Submitted by: | Lang, Nicolai |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
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.
Author comments upon resubmission
List of changes
- Added Eq. (39) to derive the validity of Eq. (40)
- Added a preliminary statement on p. 17 before the proof to allow readers to skip the latter without loosing the guiding thread of the paper.
- Added a preliminary note on p. 33 at the beginning of section 5.2 to highlight the proof-of-concept character of our proposed setup.
Published as SciPost Phys. 4, 007 (2018)