Parallel algebraic surgery for qLDPC codes with constant shuttling depth
Abstract
Reconfigurable atom arrays provide a promising platform for high-rate quantum low-density parity-check codes, but their computational advantage depends on whether logical operations can be implemented without incurring prohibitive shuttling and space overheads. We introduce algebraic surgery for lifted product codes, co-designing the logical measurements, auxiliary codes, and atom shuttling to enable hardware-efficient Pauli-product measurements. These protocols provide flexible logical addressability subject to the cyclic-symmetry constraint, enabling a broad class of parallel logical measurements, including canonical logical operators with heavily overlapping physical supports and joint measurements within or between code blocks even with different lift sizes, while achieving constant shuttling depth on neutral-atom processors under explicit layout assumptions. In a representative hardware-model benchmark, a cycle supporting 33 parallel canonical logical measurements is about 2× faster than the compared single-observable graph-based surgery schedules, with competitive qubit overhead. These shuttling and circuit-level simulations confirm that the algebraic structure of quantum low-density parity-check codes can be used not only to reduce space overhead, but also to simplify physical implementation and expand the set of efficiently accessible logical operations on neutral-atom processors.
Related
- NeST: ultra-high-rate qLDPC codes with sub-50μs stabiliser cycles via spin shuttling
- 2 Fast 2 Surgery: Fast surgery on QLDPC codes with Õ(n(k + d)) space overhead
- Sipser-Spielman meets Dijkgraaf-Witten: non-Abelian qLDPC codes via twisted sheaf gauge theory and almost-constant-overhead magic state fountain
- Lifted surgery: Fast processing with QLDPC codes
- Individually Addressed Logical Pauli Measurements by QLDPC Surgery on a Trapped Ion Quantum Computer
BibTeX
@misc{zhou2026parallel,
title = {{Parallel algebraic surgery for qLDPC codes with constant shuttling depth}},
author = {Tian-Gang Zhou and Boren Gu and Jens Eisert and Chen Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39874},
eprint = {2609.39874},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39874},
}
RIS
TY - UNPB
TI - Parallel algebraic surgery for qLDPC codes with constant shuttling depth
AU - Tian-Gang Zhou
AU - Boren Gu
AU - Jens Eisert
AU - Chen Zhao
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39874
UR - https://arxiv.org/abs/2609.39874
AB - Reconfigurable atom arrays provide a promising platform for high-rate quantum low-density parity-check codes, but their computational advantage depends on whether logical operations can be implemented without incurring prohibitive shuttling and space overheads. We introduce algebraic surgery for lifted product codes, co-designing the logical measurements, auxiliary codes, and atom shuttling to enable hardware-efficient Pauli-product measurements. These protocols provide flexible logical addressability subject to the cyclic-symmetry constraint, enabling a broad class of parallel logical measurements, including canonical logical operators with heavily overlapping physical supports and joint measurements within or between code blocks even with different lift sizes, while achieving constant shuttling depth on neutral-atom processors under explicit layout assumptions. In a representative hardware-model benchmark, a cycle supporting 33 parallel canonical logical measurements is about 2× faster than the compared single-observable graph-based surgery schedules, with competitive qubit overhead. These shuttling and circuit-level simulations confirm that the algebraic structure of quantum low-density parity-check codes can be used not only to reduce space overhead, but also to simplify physical implementation and expand the set of efficiently accessible logical operations on neutral-atom processors.
ER -