Ultra-high-distance quantum memories from amplified qLDPC codes
Abstract
A large code distance does not by itself guarantee a well-protected quantum memory, as faults during syndrome extraction can propagate into correlated data errors. Certifying circuit distance becomes demanding as circuits grow. In this work, we introduce distance amplifiers, a modular approach to increasing both code distance and certified circuit-level protection in quantum low-density parity-check codes. The construction tensors a base code with an amplifier, adapting their syndrome-extraction circuits to the amplified code. To certify the resulting memory, we develop a fault-response certificate that yields rigorous lower bounds on circuit distance. Suitable gate ordering and flag qubits control correlated errors, allowing us to establish explicit conditions under which the amplified circuit distance equals the product of the constituent circuit distances. We prove this multiplicative relation for three types of amplifiers: the flagged $[[4,2,2]]$, hypergraph-product, and rotated surface codes. The certificate extends recursively, so the circuit distance multiplies exactly at every amplification step. For example, four successive applications of the flagged $[[4,2,2]]$ amplifier to a $[[18,4,4]]$ seed yield a $[[13320,64,64]]$ code with the circuit distance dcirc ≥ 48 and check weights w ≤ 14. We further show how individual logical qubits can be tracked explicitly through amplification. By enabling high-distance quantum memories to be built and certified from smaller building blocks, our framework offers a systematic route toward scalable fault-tolerant quantum computing.
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BibTeX
@misc{liang2026ultrahighdistance,
title = {{Ultra-high-distance quantum memories from amplified qLDPC codes}},
author = {Zijian Liang and Boren Gu and Yu-An Chen and Jens Eisert and Zongyuan Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37231},
eprint = {2609.37231},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37231},
}
RIS
TY - UNPB
TI - Ultra-high-distance quantum memories from amplified qLDPC codes
AU - Zijian Liang
AU - Boren Gu
AU - Yu-An Chen
AU - Jens Eisert
AU - Zongyuan Wang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37231
UR - https://arxiv.org/abs/2609.37231
AB - A large code distance does not by itself guarantee a well-protected quantum memory, as faults during syndrome extraction can propagate into correlated data errors. Certifying circuit distance becomes demanding as circuits grow. In this work, we introduce distance amplifiers, a modular approach to increasing both code distance and certified circuit-level protection in quantum low-density parity-check codes. The construction tensors a base code with an amplifier, adapting their syndrome-extraction circuits to the amplified code. To certify the resulting memory, we develop a fault-response certificate that yields rigorous lower bounds on circuit distance. Suitable gate ordering and flag qubits control correlated errors, allowing us to establish explicit conditions under which the amplified circuit distance equals the product of the constituent circuit distances. We prove this multiplicative relation for three types of amplifiers: the flagged $[[4,2,2]]$, hypergraph-product, and rotated surface codes. The certificate extends recursively, so the circuit distance multiplies exactly at every amplification step. For example, four successive applications of the flagged $[[4,2,2]]$ amplifier to a $[[18,4,4]]$ seed yield a $[[13320,64,64]]$ code with the circuit distance d_circ ≥ 48 and check weights w ≤ 14. We further show how individual logical qubits can be tracked explicitly through amplification. By enabling high-distance quantum memories to be built and certified from smaller building blocks, our framework offers a systematic route toward scalable fault-tolerant quantum computing.
ER -