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Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata

by Nicolai Lang, Hans Peter Büchler

Submission summary

As Contributors: Nicolai Lang
Arxiv 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
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Quantum Physics
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.

Ontology / Topics

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Cellular automata Majorana fermions One-dimensional systems Quantum error correction Qubits Topological codes Topological quantum computation

Published as SciPost Phys. 4, 007 (2018)



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.

Submission & Refereeing History

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Resubmission 1711.08196v2 on 15 January 2018

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