Error correction of a logical GKP qubit using engineered dissipation

Quantum error correction is expected to play an important role in the realization of large-scale quantum computers. At the lowest level, it takes advantage of embedding qubits in a larger Hilbert space, giving redundancy which allows measurements which preserve logical information while revealing the presence of errors. While many codes rely on multiple physical systems, Bosonic codes make use of the higher dimensional Hilbert space of a single harmonic oscillator mode. A powerful Bosonic code is the GKP code proposed in 2001, which uses non-local "grid" states to protect information from small displacements of an oscillator. I will describe experiments in which we encode, measure and perform quantum error correction on an encoded logical GKP qubit, using the motion of a trapped ion coupled by laser light to an electronic ancilla qubit. We introduce a measurement approach for the finite-energy GKP code which can realize high fidelity qubit readout, and use this to construct a dissipative map which performs error correction, achieving an extension of logical coherence across all logical axes of more than three. I will also show how these techniques are related laser cooling, offering a particularly efficient means of entropy extraction from the oscillator via a single spin.