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

TL;DR

This paper introduces a strictly local, scalable quantum error decoder for one-dimensional topological codes using cellular automata, significantly improving decoherence times and paving the way for practical quantum memories.

Contribution

It develops a novel local decoder based on cellular automata for 1D topological quantum error correction, demonstrating scalability and exponential decoherence time growth.

Findings

Decoder achieves exponential growth in decoherence times with noise

Numerical and analytical studies validate the decoder's performance

Designs enable scalable, modular quantum memories

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.