Extending the memory times of trapped-ion qubits with error correction and global entangling operations

Abstract

The technical demands to perform quantum error correction are considerable. The task requires the preparation of a many-body entangled state, together with the ability to make parity measurements over subsets of the physical qubits of the system to detect errors. Here we propose two trapped-ion experiments to realise error-correcting codes of variable size to protect a single encoded qubit from dephasing errors. Novel to our schemes is the use of a global entangling phase gate, which could be implemented in both Penning traps and Paul traps. We make use of this entangling operation to significantly reduce the experimental complexity of state preparation and syndrome measurements. We also show, in our second scheme, that storage times can be increased further by repeatedly teleporting the logical information between two codes supported by the same ion Coulomb crystal to learn information about the locations of errors. We estimate that a logical qubit encoded in such a crystal will maintain high coherence for times more than an order of magnitude longer than each physical qubit would.Comment: 18 pages, 8 figures. The authors list has changed since the first version of this draf