Autonomous stabilization of Gottesman-Kitaev-Preskill states in an LC-circuit strongly driven via a Josephson junction

Gottesman-Kitaev-Preskill (GKP) states encode a logical qubit in a harmonic oscillator in such a way that amplitude and phase errors appear on equal footing [1]. This property allows for efficient error-correction [2].

Here, we show how GKP states can be realized in a simple LC-circuit connected to an AC voltage source via a Josephson junction. The nonlinear Josephson junction converts the voltage oscillations to an effective potential for the LC circuit whose ground states are GKP states. The driven LC circuit relaxes to these GKP ground states when coupled to a thermal bath through a finite-bandwidth filter. This relaxation autonomously corrects phase and amplitude errors, extending the lifetime of the logical qubit through dissipative quantum error correction. We describe gate operations, estimate experimental requirements, and find that the technological requirements for our proposal can be met using demonstrated elements in Al/Al-Ox superconductor heterostructures.



[1] Gottesman, Kitaev, and Preskill, Phys. Rev. A 64, 012310 (2001)

[2] Sivak et al., Nature 616, 50-55 (2023)