In theory, quantum computers can solve certain problems much more efficiently than classical computers. This has motivated experimental efforts to construct and verify devices that manipulate quantum bits (qubits) in a variety of physical systems. The power of quantum computers depends on the ability to accurately control sensitive superposition amplitudes by means of quantum gates, and errors in these gates are one of the chief obstacles to building quantum computers. Here we establish an error probability per randomized one-qubit gate of 2.0(2)x10^-5, well below the threshold estimate of one in ten thousand commonly considered sufficient for fault-tolerant quantum computing. The qubit is realized with two hyperfine ground states of a 9Be+ ion trapped above a microfabricated surface-electrode ion trap and manipulated with microwaves applied to a trap electrode. This demonstration of errors significantly below the fault-tolerant threshold is an essential step toward construction of a scalable quantum computer.
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