Error correction of a logical grid state qubit by dissipative pumping

Stabilization of encoded logical qubits using quantum error correction is crucial for the realization of reliable quantum computers. Although error-correcting codes implemented using individual physical qubits require many separate systems to be controlled, codes constructed using a quantum oscillator offer the possibility to perform error correction with a single physical entity. One powerful encoding approach for oscillators is the grid state or Gottesman–Kitaev–Preskill (GKP) encoding, which allows small displacement errors to be corrected. Here we introduce and implement a dissipative map designed for physically realistic finite GKP codes, which performs quantum error correction of a logical qubit encoded in the motion of a single trapped ion. The correction cycle involves two rounds, which correct small displacements in position and momentum. We demonstrate an extension in coherence time of logical states by a factor of three using both square and hexagonal GKP codes. The simple dissipative map used for this correction can be viewed as a type of reservoir engineering, which pumps into the manifold of highly non-classical GKP qubit states.