Distance-preserving stabilizer measurements in Hypergraph Product Codes*

Quantum Low-Density Parity-Check (qLDPC) codes are stabilizer codes with a bounded number of qubits per check and checks per qubit. QLDPC codes can surpass the number of encoded qubits and distance of the surface code with the use of non-local stabilizers. However, the non-locality of the stabilizers makes them hard to measure with low-depth circuits, and such circuits can potentially propagate errors and significantly reduce the effective distance. In this work, we study Hypergraph Product (HPG) Codes, a popular family of such qLDPC codes. We show that HPG codes have the useful and surprising property of distance-robustness; any stabilizer measurement circuit will preserve the code distance. We motivate this result visually and prove it mathematically. Our work implies that all previous constructions of HPG stabilizer measurement circuits, such as the ones in  [Tremblay et al, PRL 129, 050504 (2022)], preserve the code distance. This property makes HPG codes a very attractive choice for experimental applications.