With a
9Be+ trapped-ion hyperfine-state qubit, we demonstrate an error probability per randomized single-qubit gate of $2.0(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, below the threshold estimate of ${10}^{\ensuremath{-}4}$ 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.
The trapped atomic ion qubits feature desirable properties for use in a quantum computer such as long coherence times, high qubit readout fidelity, and universal logic gates. While these essential properties have been demonstrated, the ability to scale a trapped ion quantum system has not yet been shown. The challenge of scaling the system calls for methods to realize high-fidelity logic gates in scalable trap structures. Surface electrode ion traps, that are microfabricated from a silicon substrate, provide a scalable platform for trapping ion qubits only if high-fidelity operations are achievable in these structures. Here, we present a system for trapping and manipulating ions in a scalable surface trap. Trapping times exceeding 20 minutes without laser cooling, and heating rates as low as 0.8 quanta/ms indicate stable trapping conditions in these microtraps. Coherence times of more than one second verify adequate qubit and control field stability. We demonstrate low-error single-qubit gates performed using stimulated Raman transitions driven by lasers that are tightly focused on the ion qubit. Digital feedback loops are implemented to control the driving field's amplitude and frequency. Gate errors are measured using a randomized benchmarking protocol for single qubit gates, where residual amplitude error in the control beam is compensated using various pulse sequence techniques. Using pulse compensation, we demonstrate single qubit gates with an average error per randomized Clifford group gate of
3.6(3)times10−4, which is below the fault-tolerant threshold for some error-correction schemes.
This study presents single qubit gates with trapped ions that are robust against experimental imperfections over a wide range of parameters. In particular it is shown that errors caused by an inaccurate setting of either frequency, amplitude, or duration of the driving field, or of a combination of these errors are tolerable when a suitable sequence of radiation pulses, or a shaped pulse is applied instead of, for instance, a single rectangular pi-pulse. Thus an essential prerequisite for scalable quantum computation with trapped ions is demonstrated.