Autonomous quantum error correction of a grid state qubit*

Title: Quantum error correction with motional states of trapped ions”

Abstract: I will describe experimental progress aimed at realizing error-corrected quantum computing systems in the motional degree of freedom of trapped-atomic ions. We have realized many rounds of quantum error correction in GKP-encoded logical qubits, extending the logical qubit lifetime by more than a factor of 3 [1,2]. Critical to these experiments was the implementation of measurement and correction suited to experimentally accessible finite-energy states. I will present theoretical and experimental progress towards implementing multi-qubit gates on GKP qubits in a radio-frequency trap, and also describe new methods for stabilizing rotation symmetric subspaces using the non-linear ion-light interaction, which are closely related to cat qubits demonstrated previously.