High-Fidelity Universal Gate Set for

We report high-fidelity laser-beam-induced quantum logic gates on magnetic-field-insensitive qubits comprised of hyperfine states in ^{9}Be^{+} ions with a memory coherence time of more than 1 s. We demonstrate single-qubit gates with an error per gate of 3.8(1)×10^{-5}. By creating a Bell state with a deterministic two-qubit gate, we deduce a gate error of 8(4)×10^{-4}. We characterize the errors in our implementation and discuss methods to further reduce imperfections towards values that are compatible with fault-tolerant processing at realistic overhead.