Repeated multi-qubit readout and feedback with a mixed-species trapped-ion register.

Quantum error correction is essential for realizing the full potential of large-scale quantum information processing devices. Fundamental to its experimental realization is the repetitive detection of errors via projective measurements of quantum correlations among qubits, as well as corrections using conditional feedback. Repetitive application of such tasks requires that they neither induce unwanted crosstalk nor impede further control operations, which is challenging owing to the need to dissipatively couple qubits to the classical world for detection and reinitialization. For trapped ions, state readout involves scattering large numbers of resonant photons, which increases the probability of stray light causing errors on nearby qubits and leads to undesirable recoil heating of the ion motion. Here we demonstrate up to 50 sequential measurements of correlations between two beryllium ion microwave qubits using an ancillary optical qubit in a calcium ion, and implement feedback that allows us to stabilize two-qubit subspaces as well as Bell states, a class of maximally entangled states. Multi-qubit mixed-species gates are used to transfer information within the register from the qubit to the ancilla, enabling readout with negligible crosstalk to the data qubits. Heating of the ion motion during detection is mitigated by recooling all three ions using light that interacts with only the calcium ion, known as sympathetic cooling. A key element of our experimental setup is a powerful classical control system that features flexible in-sequence processing for feedback control. The methods employed here provide essential tools for scaling trapped-ion quantum computing, quantum-state control and entanglement-enhanced quantum metrology.