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

Matteo Marinelli, Vlad Negnevitsky, Karan Mehta, Hsiang-Yu Lo, Christa Flühmann, Jonathan Home   
Institute for Quantum Electronics,, ETH Zurich, Switzerland

Quantum error correction involves repeated rounds of error detection and recovery, involving multi-qubit non-demolition measurements along with conditional feedback. This requires the use of systems in which, measurement and decision times are short compared to relevant decoherence timescales, and in which the act of measurement does not destroy subspace coherence or disrupt future operations. Using a mixed-species ion chain, we demonstrate up to 50 sequential measurements of correlation between two beryllium ion qubits coupled to a co-trapped calcium ion. State readout of the calcium ancilla has no direct effect on the internal states of beryllium.Using the ability to rapidly make in-sequence processing in our classical computer control, we perform feedback on the beryllium qubits conditioned on the ancilla readout, which we use to prepare and stabilize Bell states and parity subspaces. The methods demonstrated here could be applied to quantum error correcting codes as well as quantum metrology and are key ingredients for realizing a hybrid universal quantum computer based on trapped ions.