Fast GKP state preparation using periodic driving

The Gottesman-Kitaev-Preskill (GKP) code may be used to overcome noise in superconducting qubits. However, preparing GKP states remains experimentally challenging. Here, we propose a novel method for preparing GKP states by engineering a time-periodic Hamiltonian whose Floquet states are GKP states. This Hamiltonian may be realised in a superconducting circuit by coupling an LC oscillator to a SQUID. The GKP Floquet states can be prepared by adiabatically evolving the low-energy harmonic oscillator eigenstates. We show that with typical photon loss rates and flux noise in superconducting circuits, GKP states with squeezings > 11.5 dB may be prepared with infidelities < 10^-2 in less than a microsecond. This represents a promising alternative to current dissipative state-preparation methods.