  With a 9Be+ trapped-ion hyperfine-states qubit, we demonstrate an error
probability per randomized single-qubit gate of 2.0(2) x 10^-5, below the
threshold estimate of 10^-4 commonly considered sufficient for fault-tolerant
quantum computing. The 9Be+ ion is trapped above a microfabricated
surface-electrode ion trap and is manipulated with microwaves applied to a trap
electrode. The achievement of low single-qubit-gate errors is an essential step
toward the construction of a scalable quantum computer.
