Renormalization for Robust Memory without Synchronization
Abstract
Local error correction can preserve classical information against noise, but protection under synchronized updates need not survive when sites evolve at independent random times. Establishing stability is particularly challenging when protection relies on the collective action of competing local rules. Here we develop a spacetime renormalization framework that reveals how independently acting local updates can collectively stabilize memory. We identify sufficient conditions under which the geometry of stable interfaces and suppression of defect propagation produce reliable erosion at large scales. Applying this framework, we prove stability of the asynchronous \textsf{R} squeezing code and introduce robust processes in two and three dimensions. In these systems, both encoded phases persist under sufficiently weak noise, even when the noise favors one phase. Our results provide a criterion for designing autonomous memories sustained by competing local stochastic dynamics.
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BibTeX
@misc{chakraborty2026renormalization,
title = {{Renormalization for Robust Memory without Synchronization}},
author = {Shashwat Chakraborty and Jong Yeon Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40651},
eprint = {2610.40651},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40651},
}
RIS
TY - UNPB
TI - Renormalization for Robust Memory without Synchronization
AU - Shashwat Chakraborty
AU - Jong Yeon Lee
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40651
UR - https://arxiv.org/abs/2610.40651
AB - Local error correction can preserve classical information against noise, but protection under synchronized updates need not survive when sites evolve at independent random times. Establishing stability is particularly challenging when protection relies on the collective action of competing local rules. Here we develop a spacetime renormalization framework that reveals how independently acting local updates can collectively stabilize memory. We identify sufficient conditions under which the geometry of stable interfaces and suppression of defect propagation produce reliable erosion at large scales. Applying this framework, we prove stability of the asynchronous \textsf{R} squeezing code and introduce robust processes in two and three dimensions. In these systems, both encoded phases persist under sufficiently weak noise, even when the noise favors one phase. Our results provide a criterion for designing autonomous memories sustained by competing local stochastic dynamics.
ER -