Timo Hillmann

Gottesman–Kitaev–Preskill (GKP) codes provide a family of promising schemes for encoding discrete quantum information (qudits) into infinite-dimensional bosonic modes based on mathematical lattices. While such codes, when concatenated with discrete-variable codes, are relatively well studied, the decoding problem of native GKP codes has largely remained open due to the computationally hard problems encountered. To address this challenge, we advocate a strategy of co-designing the decoder and the quantum error-correcting code itself by constructing lattices for which decoding is feasible and does not reduce to hard instances. This construction is built on classical low-density lattice codes (LDLCs), a lattice analogue of low-density parity-check codes, here lifted to families of GKP codes. Concretely, we introduce quantum versions of classical LDLCs and study the performance of message-passing decoders—originally developed for LDLCs—when applied to GKP codes with sparse stabilizer generators. We hope that the tools we introduce, along with their analysis, will facilitate future research on the structure and performance of general GKP codes. In this spirit, the source code used to reproduce all results presented here is released as an open-source Julia package.