Large-scale error-correction protocols using global operations in ion traps
Yannick Seis, Joseph F. Goodwin, Benjamin J. Brown, Terry Rudolph · arXiv (Cornell University) · 2016
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 arbitrary size to defend a single encoded qubit from dephasing errors. Novel to both of our schemes, which are achievable using both Penning traps and Paul traps, is the use of a global entangling phase gate. 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 ionic crystal to learn information about the locations of errors. We estimate that a qubit encoded in such a crystal will remain a high fidelity state for a time that is an order of magnitude longer than a qubit written to a single confined ion.