Distance-preserving stabilizer measurements in hypergraph product codes

Abstract

Unlike the surface code, quantum low-density parity-check (QLDPC) codes can have a finite encoding rate, offering potentially lower overhead. However, finite-rate QLDPC codes have nonlocal stabilizers, making it difficult to design stabilizer measurement circuits that are low-depth and preserve the effective distance. Here, we demonstrate that a popular construction of finite-rate QLDPC codes, the hypergraph product, has the convenient property of distance-robustness: any stabilizer measurement circuit preserves the effective distance. In particular, we prove a previously proposed depth-optimal circuit is also optimal in terms of effective distance.