



01394nas a2200121   4500008004100000245006200041210006200103260001400165520101400179100002001193700002201213856003701235       2023                        eng d00aPartial Syndrome Measurement for Hypergraph Product Codes0 aPartial Syndrome Measurement for Hypergraph Product Codes  c9/26/20233 a<p>Hypergraph product codes are a promising avenue to achieving fault-tolerant quantum computation with constant overhead. When embedding these and other constant-rate qLDPC codes into 2D, a significant number of nonlocal connections are required, posing difficulties for some quantum computing architectures. In this work, we introduce a fault-tolerance scheme that aims to alleviate the effects of implementing this nonlocality by measuring generators acting on spatially distant qubits less frequently than those which do not. We investigate the performance of a simplified version of this scheme, where the measured generators are randomly selected. When applied to hypergraph product codes and a modified small-set-flip decoding algorithm, we prove that for a sufficiently high percentage of generators being measured, a threshold still exists. We also find numerical evidence that the logical error rate is exponentially suppressed even when a large constant fraction of generators are not measured.</p>1 aBerthusen, Noah1 aGottesman, Daniel  uhttps://arxiv.org/abs/2306.17122