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Unlike the surface code, quantum low-density parity-check (QLDPC) codes canhave a finite encoding rate, potentially lowering the error correctionoverhead. However, finite-rate QLDPC codes have nonlocal stabilizers, making itdifficult to design stabilizer measurement circuits that are low-depth and donot decrease the effective distance. Here, we demonstrate that a popular familyof finite-rate QLDPC codes, hypergraph product codes, has the convenientproperty of distance-robustness: any stabilizer measurement circuit preservesthe effective distance. In particular, we prove the depth-optimal circuit in[Tremblay et al, PRL 129, 050504 (2022)] is also optimal in terms of effectivedistance.

Distance-preserving stabilizer measurements in hypergraph product codes