SciPost logo

SciPost Submission Page

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
Preprint Link:  (pdf)
Date accepted: 2018-01-21
Date submitted: 2018-01-15 01:00
Submitted by: Lang, Nicolai
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approaches: Theoretical, Computational


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

See our reply to the first referee report for detailed comments.

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)

Login to report or comment