Quantum error correction of a qubit encoded in grid states of an oscillator*

In 2001, Gottesman, Kitaev and Preskill (GKP) proposed to encode a fully correctable logical qubit in grid states of a single harmonic oscillator. Although this code was originally designed to correct against shift errors, GKP qubits are robust against virtually all realistic error channels. Since this proposal, other bosonic codes have been extensively investigated, but only recently were the exotic GKP states experimentally synthesized and stabilized. These experiments relied on stroboscopic interactions between a target oscillator and an ancillary two-level system to measure non-destructively the GKP code error syndromes.
In this talk, I will review the fascinating properties of the GKP code and the conceptual and experimental tools developed for trapped ions and superconducting circuits, which enabled quantum error correction of a logical GKP qubit encoded in a microwave cavity. I will describe ongoing efforts to suppress further logical errors, and in particular to avoid the apparition of uncorrectable errors stemming from the noisy ancilla involved in error syndrome detection.