Error correction of a logical grid state qubit by dissipative pumping

Stabilization of encoded logical qubits using quantum error correction is key to the realization of reliable quantum computers. GKP states are a powerful encoding for oscillators, which allow small displacement errors to be corrected. I will present theory and implementation of a dissipative map designed for physically realistic finite GKP codes which performs quantum error correction of a logical qubit implemented in the motion of a single trapped ion. The correction cycle involves mapping the finite GKP code stabilizer information onto an internal electronic state ancilla qubit, and then applying coherent feedback and ancilla repumping. We demonstrate the extension of logical coherence using both square and hexagonal GKP codes, achieving an increase in logical lifetime of a factor of three. The simple dissipative map used for the correction can be viewed as a type of reservoir engineering, which pumps into the highly non-classical GKP qubit manifold. These techniques open new possibilities for quantum state control alongside their application to scaling quantum computing.

Reference:
B. de Neeve, T.-L. Nguyen, T. Behrle, and J. Home, "Error correction of a logical grid state qubit by dissipative pumping", arXiv:2010.09681 [quant-ph] (2020).