Robust entanglement by continuous dynamical decoupling of the J-coupling interaction

We propose a σz ⊗ laser-free entangling gate which uses the intrinsic J-coupling of ions in static magnetic gradient. Dephasing interaction is suppressed by means continuous dynamical decoupling using pairs microwave fields. The virtually insensitive to common amplitude noise fields and enables high fidelities despite qubit frequency fluctuations, while interaction's inherent robustness motional decoherence retained. Errors far below fault-tolerant threshold can be achieved at initial temperatures, negating requirement sideband cooling Doppler temperature. By adjusting powers fields, tuned used implement parallel gates within an ion chain.