Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes
Abstract
We construct the first fully spatially local fault-tolerant quantum computer based on topological codes in fewer than four spatial dimensions. Our construction is a two-dimensional architecture that uses only geometrically local quantum and classical operations, bounded-speed classical communication and computation, and a constant density of quantum and classical resources. The core component is a new time-translation-invariant cellular-automaton decoder for the surface code. This decoder preserves logical information for a time stretched-exponential in the code distance and operates continuously during state injection, stabilizer-state preparation, lattice surgery, and transversal readout. We also prove that every translation-invariant topological Pauli stabilizer code is locally decodable under phenomenological noise.
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BibTeX
@misc{selub2026local,
title = {{Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes}},
author = {Nathaniel Selub and Aditya Bhardwaj and Ethan Lake},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.11457},
eprint = {2609.11457},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11457},
}
RIS
TY - UNPB
TI - Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes
AU - Nathaniel Selub
AU - Aditya Bhardwaj
AU - Ethan Lake
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.11457
UR - https://arxiv.org/abs/2609.11457
AB - We construct the first fully spatially local fault-tolerant quantum computer based on topological codes in fewer than four spatial dimensions. Our construction is a two-dimensional architecture that uses only geometrically local quantum and classical operations, bounded-speed classical communication and computation, and a constant density of quantum and classical resources. The core component is a new time-translation-invariant cellular-automaton decoder for the surface code. This decoder preserves logical information for a time stretched-exponential in the code distance and operates continuously during state injection, stabilizer-state preparation, lattice surgery, and transversal readout. We also prove that every translation-invariant topological Pauli stabilizer code is locally decodable under phenomenological noise.
ER -