Generation of Gottesman-Kitaev-Preskill codes in a periodically driven quantum system

The Gottesman-Kitaev-Preskill (GKP) code is one of the most promising bosonic error correction codes, with good protection against natural noise and a relatively easy gate set. However, preparing high quality codewords is challenging. In this talk we present a relatively simple periodically driven quantum system whose Floquet eigenstates are approximate Gottesman-Kitaev-Preskill codewords. The system may be realized in a superconducting circuit consisting of an LC circuit shunted by a switchable Josephson junction. We show that high quality GKP codewords can be prepared, given a sufficiently fast on-off switching of the Josephson junction, and that environmental noise is highly suppressed in this regime.