Optimal Control of a SNAIL-resonator

Abstract

In recent experiments done at Chalmers, universal control of a bosonic mode was demonstrated for a superconducting cavity terminated by a Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL), while simultaneously cancelling Kerr effects by applying an external magnetic flux to the SNAIL. The universal control was demonstrated by generating a cubic phase state; however, generating other interesting non-Gaussian states remains a non-trivial issue. The aim of this work is to perform optimal control on the SNAIL-resonator. Due to the large Hilbert space of the system and its fast time dependence, an effective Hamiltonian is derived from the previously known full Hamiltonian in the regime of resonant driving, which significantly speeds up the optimization process. The drives of the system are then optimized to reach a target cubic phase state, both by simply tuning the amplitudes and phases of the pulses used in the Chalmers experiment and by pulse shaping optimization. Then, optimal control is used to generate two-photon cat states. The results are analyzed in terms of the fidelity to target states and its susceptibility to circuit parameter deviations. Finally, the potential for using optimal control to find experimentally viable methods of generating non-Gaussian states is discussed.