High-Fidelity Universal Gate Set for ${}^9$Be${}^{+}$ Ion Qubits

Abstract

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 error per gate of $3.8(1)\times 10^{-5}$. By creating a Bell state with a deterministic two-qubit gate, we deduce a gate error of $8(4)\times 10^{-4}$. 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.