Experimental repetitive quantum error correction

The computational power of a quantum processor can only be unleashed if errors during a quantum computation can be controlled and corrected for. Quantum error correction works if imperfections of quantum gate operations and measurements are below a certain threshold and corrections can be applied repeatedly. We have realized the first implementation of multiple quantum error correction steps for phase-flip errors on qubits encoded with trapped ions. Errors are corrected without measurement by a quantum feedback algorithm employing high-fidelity gate operations and a reset technique for the auxiliary qubits. Up to three consecutive consecutive correction steps are realized and the behavior of the algorithm for different noise environments is analyzed.