Gottesman-Kitaev-Preskill State Preparation Using Periodic Driving

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 $>11.9\mathrm{dB}$ (10.8 dB) GKP magic states can be prepared on a microsecond timescale, given a quality factor of ${\mathrm{10⁶}}^{}$ (${\mathrm{10⁵}}^{}$) and flux noise at typical rates.

The supplemental material provides supporting analytical derivations and numerical results for the main text, as well as details of the simulation methods used to generate the numerical results. The SM has 11 sections, which are:
1. Floquet analysis of the harmonic driving scheme
2. Subsystem decomposition decoder
3. Circuit QED implementation
4. Adiabatic state preparation
5. Arbitrary logical state preparation
6. Fidelity of prepared state with Floquet state
7. Numerical simulation of photon loss
8. Flux noise
9. Lifetime of the GKP Floquet states
10. Quasienergies
11. Comparison to Conrad, J. (2021)