High-rate qLDPC processors
Abstract
Despite significant progress on quantum low-density parity-check (qLDPC) codes, building qLDPC processors that are high-rate, high-throughput, hardware-friendly, and fast-to-decode remains a challenge. We introduce mitten codes, a family of qLDPC processor codes of encoding rate 20% and check weight $9$, based on non-abelian groups. Their non-abelian structure evades distance bounds constraining abelian counterparts, allowing mitten codes to reach distance $18$ and beyond with just a few hundred data qubits. The logical operators of a mitten code are related by the group action, yielding a modular, low-overhead logical toolkit: full Clifford operations follow from bridging two reusable seed surgery gadgets or from a single fixed extractor. Furthermore, qLDPC processors based on mitten codes support high-rate surgery that executes many logical measurements in parallel, and parallel magic-state injection into all logical qubits at once. Under circuit-level noise, with our fast decoder, the [ [300,60,14] ] mitten code achieves, without extrapolation, a block logical error rate of ∼10−11 per round at 0.1% physical error rate (PER), while the [ [ 975,195,≤ 24 ] ] code reaches ∼10−8 at 0.4% PER. Decoding $15$ billion surgery experiments on the [ [540,108,18] ] code at 0.1% PER, we observe only two logical failures, demonstrating a qLDPC processor capable of running ∼1010 logical operations. Our decoder is compatible with sub-millisecond average latency per logical cycle, sufficient for real-time decoding on neutral atom hardware. Discovered by an end-to-end design pipeline built on sQetch, a distance estimator orders of magnitude faster than existing tools, and mapping efficiently onto near-term neutral atom and superconducting hardware, mitten codes open a practical path toward fault-tolerant quantum computation.
Related
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BibTeX
@misc{bhardwaj2026highrate,
title = {{High-rate qLDPC processors}},
author = {Aditya Bhardwaj and Muzhou Ma and Nadine Meister and Robbie King and Dolev Bluvstein and John Preskill and Madelyn Cain and Qian Xu and Hsin-Yuan Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.28795},
eprint = {2607.28795},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.28795},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - High-rate qLDPC processors
AU - Aditya Bhardwaj
AU - Muzhou Ma
AU - Nadine Meister
AU - Robbie King
AU - Dolev Bluvstein
AU - John Preskill
AU - Madelyn Cain
AU - Qian Xu
AU - Hsin-Yuan Huang
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2607.28795
UR - https://arxiv.org/abs/2607.28795
AB - Despite significant progress on quantum low-density parity-check (qLDPC) codes, building qLDPC processors that are high-rate, high-throughput, hardware-friendly, and fast-to-decode remains a challenge. We introduce mitten codes, a family of qLDPC processor codes of encoding rate 20% and check weight $9$, based on non-abelian groups. Their non-abelian structure evades distance bounds constraining abelian counterparts, allowing mitten codes to reach distance $18$ and beyond with just a few hundred data qubits. The logical operators of a mitten code are related by the group action, yielding a modular, low-overhead logical toolkit: full Clifford operations follow from bridging two reusable seed surgery gadgets or from a single fixed extractor. Furthermore, qLDPC processors based on mitten codes support high-rate surgery that executes many logical measurements in parallel, and parallel magic-state injection into all logical qubits at once. Under circuit-level noise, with our fast decoder, the [ [300,60,14] ] mitten code achieves, without extrapolation, a block logical error rate of ∼10^−11 per round at 0.1% physical error rate (PER), while the [ [ 975,195,≤ 24 ] ] code reaches ∼10^−8 at 0.4% PER. Decoding $15$ billion surgery experiments on the [ [540,108,18] ] code at 0.1% PER, we observe only two logical failures, demonstrating a qLDPC processor capable of running ∼10^10 logical operations. Our decoder is compatible with sub-millisecond average latency per logical cycle, sufficient for real-time decoding on neutral atom hardware. Discovered by an end-to-end design pipeline built on sQetch, a distance estimator orders of magnitude faster than existing tools, and mapping efficiently onto near-term neutral atom and superconducting hardware, mitten codes open a practical path toward fault-tolerant quantum computation.
ER -