Disassembling qLDPC codes for depth-optimal parity-check circuits
Abstract
Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computing, but their practical implementation requires efficient circuits for syndrome extraction. Many qLDPC families are assembled from a small set of components through explicit operations that imprint edge symmetries on their Tanner graphs. We show that disassembling the code by quotienting its symmetries one at a time, reduces parity-check circuit design to a much smaller problem acting only on the underlying components. Solutions to the reduced problem can then be lifted to the full code, yielding circuit constructions that apply to entire families of codes built from the same components. For lifted-product codes, our approach provides an optimal analytical construction for parity-check circuits achieving the lower bound on CNOT depth. We obtain analogous constructions for balanced-product codes and quantum--classical homological product codes. For quantum Tanner codes, the reduced problem is small enough to solve numerically, reaching the CNOT-depth lower bound for nearly all instance tested, including codes with up to 576 data qubits.
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BibTeX
@misc{nguyen2026disassembling,
title = {{Disassembling qLDPC codes for depth-optimal parity-check circuits}},
author = {Minh T. P. Nguyen and Maximilian Rimbach-Russ and Stefano Bosco},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.19917},
eprint = {2608.19917},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.19917},
}
RIS
TY - UNPB
TI - Disassembling qLDPC codes for depth-optimal parity-check circuits
AU - Minh T. P. Nguyen
AU - Maximilian Rimbach-Russ
AU - Stefano Bosco
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2608.19917
UR - https://arxiv.org/abs/2608.19917
AB - Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computing, but their practical implementation requires efficient circuits for syndrome extraction. Many qLDPC families are assembled from a small set of components through explicit operations that imprint edge symmetries on their Tanner graphs. We show that disassembling the code by quotienting its symmetries one at a time, reduces parity-check circuit design to a much smaller problem acting only on the underlying components. Solutions to the reduced problem can then be lifted to the full code, yielding circuit constructions that apply to entire families of codes built from the same components. For lifted-product codes, our approach provides an optimal analytical construction for parity-check circuits achieving the lower bound on CNOT depth. We obtain analogous constructions for balanced-product codes and quantum--classical homological product codes. For quantum Tanner codes, the reduced problem is small enough to solve numerically, reaching the CNOT-depth lower bound for nearly all instance tested, including codes with up to 576 data qubits.
ER -