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arXiv:2608.19917

Disassembling qLDPC codes for depth-optimal parity-check circuits

Minh T. P. Nguyen, Maximilian Rimbach-Russ, Stefano Bosco

quant-phSubmitted Aug 20, 2026• Announced Aug 21, 2026• 0 citations• Revised Oct 4, 2026 (v2)
v1 · Aug 20, 2026v2 · Oct 4, 2026
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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.

Comments
20 pages, 5 figures, 2 Tables. Supplementary Material and GitHub updated

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