Full Extractors for Logical Processing in Hypergraph Product Codes
Abstract
Quantum low-density parity-check (QLDPC) codes are promising candidates for practical low-overhead quantum memories. For large-scale fault-tolerant quantum computation, we further need logical processing methods for QLDPC codes. In this work, we construct full extractors---surgery systems capable of measuring arbitrary logical Pauli operators on a code block---for several hypergraph product (HGP) codes. These extractors enable logical processing via Pauli-based computation (PBC) without the compilation overhead observed in prior works. Moreover, our extractors have sizes between 47% and 80% of the base HGP codes, and the extractor-augmented codes can be supported on fixed-connectivity hardware with maximum qubit degree ten. Our approach involves assembling many partial extractors with verifiable fault tolerance into a single full extractor. For a distance $10$ HGP code, circuit-level noise simulations yield logical measurement error rates of approximately 10−6 at a physical error rate of 0.1%. These results demonstrate that extractor architectures, when designed in the fixed-connectivity setting, can achieve the space efficiency of QLDPC codes without introducing compilation overhead compared to surface-code PBC architectures.
Related
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BibTeX
@misc{blue2026full,
title = {{Full Extractors for Logical Processing in Hypergraph Product Codes}},
author = {John Blue and Zhiyang He and Hengyun Zhou and Isaac L. Chuang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.03507},
eprint = {2606.03507},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.03507},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Full Extractors for Logical Processing in Hypergraph Product Codes
AU - John Blue
AU - Zhiyang He
AU - Hengyun Zhou
AU - Isaac L. Chuang
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2606.03507
UR - https://arxiv.org/abs/2606.03507
AB - Quantum low-density parity-check (QLDPC) codes are promising candidates for practical low-overhead quantum memories. For large-scale fault-tolerant quantum computation, we further need logical processing methods for QLDPC codes. In this work, we construct full extractors---surgery systems capable of measuring arbitrary logical Pauli operators on a code block---for several hypergraph product (HGP) codes. These extractors enable logical processing via Pauli-based computation (PBC) without the compilation overhead observed in prior works. Moreover, our extractors have sizes between 47% and 80% of the base HGP codes, and the extractor-augmented codes can be supported on fixed-connectivity hardware with maximum qubit degree ten. Our approach involves assembling many partial extractors with verifiable fault tolerance into a single full extractor. For a distance $10$ HGP code, circuit-level noise simulations yield logical measurement error rates of approximately 10^−6 at a physical error rate of 0.1%. These results demonstrate that extractor architectures, when designed in the fixed-connectivity setting, can achieve the space efficiency of QLDPC codes without introducing compilation overhead compared to surface-code PBC architectures.
ER -