The Gottesman-Kitaev-Preskill (GKP) code may be used to overcome noise in continuous variable quantum systems. However, preparing GKP states remains experimentally challenging. We propose a method for preparing GKP states by engineering a time-periodic Hamiltonian whose Floquet states are GKP states. This Hamiltonian may be realized in a superconducting circuit comprising a SQUID shunted by a superinductor and a capacitor, with a characteristic impedance twice the resistance quantum. The GKP Floquet states can be prepared by adiabatically tuning the frequency of the external magnetic flux drive. We predict that highly squeezed >11.9 dB (10.8 dB) GKP magic states can be prepared on a microsecond timescale, given a quality factor of 106 (105) and flux noise at typical rates.
@article{arxiv.2303.03541,
title = {Gottesman-Kitaev-Preskill state preparation using periodic driving},
author = {Xanda C. Kolesnikow and Raditya Weda Bomantara and Andrew C. Doherty and Arne L. Grimsmo},
journal= {arXiv preprint arXiv:2303.03541},
year = {2024}
}