Error correction of a logical grid state qubit by dissipative pumping

Abstract

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. Physical systems with continuous degrees of freedom can be used to implement quantum error correction codes. An autonomous correction protocol has now been used to extend the lifetime of a qubit encoded in the motion of a trapped ion.