Because of the fragile nature of quantum states, error correction will likely become a fundamental feature of any fully functional quantum computer. Quantum error correction studies ways to robustly encode information in suitable larger systems. Bosonic codes in particular embed finite systems (such as qubits) into infinite-dimensional ones. So-called Gottesman-Kitaev-Preskill (GKP) codes, named after their inventors, belong to this family. They rely on discrete translation symmetries in the phase space of an ensemble of harmonic oscillators to identify suitable encoded states. Such symmetries are mathematically represented by lattices, which are objects studied in many branches of pure and applied mathematics and (classical) coding theory.

In this talk, after introducing GKP codes and explaining their connection to lattices, I will show with a few examples that methods borrowed from lattice theory can be fruitfully put to use to analyze these codes and improve on some practical aspects related to their implementation.

The talk will be based on the paper with the same title published on Quantum 6, 648 (2022), which was a joint work with Jonathan Conrad and Jens Eisert.