High-Fidelity Trapped-Ion Quantum Logic Using Near-Field Microwaves

We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated surface ion trap. We introduce a dynamically decoupled gate method, which stabilizes the qubits against fluctuating energy shifts and avoids the need to null the microwave field. We use the gate to produce a Bell state with fidelity 99.7(1)%, after accounting for state preparation and measurement errors. The gate is applied directly to ${}^{43}{\mathrm{Ca}}^{+}$ hyperfine “atomic clock” qubits (coherence time $T_2^{*}\approx 50\mathrm{s}$) using the oscillating magnetic field gradient produced by an integrated microwave electrode.

Figure 1

Part of the ground-level hyperfine structure of ${}^{43}{\mathrm{Ca}}^{+}$ at 14.6 mT, showing the clock-qubit states ($|\downarrow ⟩$, $|\uparrow ⟩$), and other states (grey) connected to them by spectator transitions. The blue and red sideband fields (BSB, RSB) have frequencies $({\omega }_0+\mathrm{\Delta })\pm ({\omega }_{\mathrm{r}}+\delta )$, where ${\omega }_0$ is the unperturbed qubit frequency, ${\omega }_{\mathrm{r}}$ the motional mode frequency, $\delta$ the gate detuning, and $\mathrm{\Delta }={\mathrm{\Delta }}_{\uparrow }-{\mathrm{\Delta }}_{\downarrow }$ the differential a.c. Zeeman shift produced by the (strong) sidebands. The (weak) carrier used for dynamical decoupling is resonant with the shifted qubit transition at $({\omega }_0+\mathrm{\Delta })$. Dashed lines indicate unshifted qubit states.

Figure 2

Experimental demonstration of a four-loop DDMS gate. (a) State populations $P$ as a function of detuning $\delta$, where the dashed line indicates the detuning used in (b). Solid lines show a numerical simulation, starting from a ground-state cooled motional mode. (b) Measurement of the parity ($P_{\uparrow \uparrow }+P_{\downarrow \downarrow }-P_{\uparrow \downarrow }-P_{\downarrow \uparrow }$), used to determine the fidelity of the Bell state $|\mathrm{\Psi }⟩=|\uparrow \uparrow ⟩+i|\downarrow \downarrow ⟩$ produced by the gate. The data consist of five separate experimental runs, which were interleaved with measurements of the SPAM error and Bell state populations. A maximum-likelihood fit (solid line), assuming binomial statistics [24], gives a parity amplitude of 0.9953(23). The phase offset is determined from an independent calibration and is not floated in the fit. Error bars represent 68% confidence intervals. Weighted residuals $[(\text{data}-\text{fit}\text{)}\text{/}\text{error]}$ are plotted. All data have been corrected for SPAM errors (see text).

Figure 3

Single-ion Ramsey experiment used to measure a.c. Zeeman shift fluctuations, with (blue circles) and without (red squares) the carrier drive and refocusing $\pi [y]$ pulse. (a) We scan the Ramsey phase $\varphi$ to obtain a fringe. Lines show maximum-likelihood fits to the data, giving fringe contrasts of 0.998(5) and 0.924(6). (b) We set $\varphi$ to the fringe’s peak and monitor fluctuations in $P_{\uparrow }$ over time. The average of the blue data points gives $P_{\uparrow }=0.9994(4)$, indicating that the gate fields induce $\lesssim 0.1\%$ loss of qubit coherence. The right-hand ordinate gives, for the red points, the simulated MS gate error for a given fringe contrast, assuming normally distributed shot-to-shot a.c. Zeeman shift fluctuations. All data have been corrected for SPAM errors.