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 constructions that imprint edge symmetries on their Tanner graphs. We show that these symmetries can be exploited to design syndrome-extraction circuits from the underlying components, rather than from the full quantum code. For Lifted Product and Balanced Product codes this approach yields an analytical construction with provably optimal or near-optimal CNOT depth. For Quantum Tanner codes it produces depth-optimal circuits on every instance we test, including codes up to nearly 600 data qubits.