Parallel Transport Quantum Logic Gates with Trapped Ions

We demonstrate single-qubit operations by transporting a beryllium ion with a controlled velocity through a stationary laser beam. We use these to perform coherent sequences of quantum operations, and to perform parallel quantum logic gates on two ions in different processing zones of a multiplexed ion trap chip using a single recycled laser beam. For the latter, we demonstrate individually addressed single-qubit gates by local control of the speed of each ion. The fidelities we observe are consistent with operations performed using standard methods involving static ions and pulsed laser fields. This work therefore provides a path to scalable ion trap quantum computing with reduced requirements on the optical control complexity.

Figure 1

(a) Image of the different trap zones along the transport axis $z$. (b) The Rabi oscillation experiment is carried out using operations occurring in numerical order from (i) to (v). The use of the two coherent transfer pulses (labeled as ${\pi }_{\mathrm{FDQ}}$ and ${\pi }_{\mathrm{FIS}}$) is described in the text. (c) The pulse sequence used to probe Rabi oscillations. The qubit beam is rapidly switched off at a time $t_{\text{off}}$ during the transport in order to probe the dynamics of the spin. (d) Rabi oscillations as a function of $t_{\text{off}}$ for an ion transported through a two-frequency Raman laser beam pair. The fitted curve follows the theoretical prediction from Eq. (1), which assumes a Gaussian beam profile. Each data point represents the average of 350 repeats of the experimental sequence. Here and in the rest of the Letter, error bars are estimated assuming quantum projection noise.

Figure 2

(a) The Ramsey sequence involves steps (i) to (vii). (b) The pulse sequence used for the Ramsey experiment. We concatenate two transport $\pi /2$ gates in which the phase of the laser during the second gate is shifted by $\varphi$ relative to the first. In this case, the qubit beams remain on until the ion has passed through to zone $E$. (c) Experimental results for a Ramsey experiment. The phase $\varphi$ is scanned using a shift in the relative phase of the two Raman beams applied with an acousto-optic modulator. The contrast of the oscillations obtained from the fit is $0.985\pm 0.004$. For comparison, the plotted horizontal dashed lines indicate the maximum and minimum of Rabi oscillations performed using standard static-ion gates. Each data point is the average of 600 repeats of the experimental sequence.

Figure 3

For work on parallel gates, the steps (i) through to (xiii) are carried out sequentially. Optical pumping to $|F=2,m_F=2⟩$ and state detection are performed in the experimental zone using pulsed operations, which are also used for coherent transfer pulses (${\pi }_{\mathrm{FDQ}}$ and ${\pi }_{\mathrm{FIS}}$) in the separated zones. The transport gates are applied simultaneously, by passing the ions through qubit beams located at $\pm 600\mu \mathrm{m}$ from the trap center.

Figure 4

(a),(b) Time scans for the simultaneous rotation of ion 1 (blue) and ion 2 (red) with two different velocities for ion 2 resulting in a rotation $\widehat{R}(\pi )$ in (a) and $\widehat{R}(\pi /2)$ in (b), respectively. The dashed horizontal lines indicate the maximum and minimum of Rabi oscillations performed using static-ion gates. Corresponding scans of the difference frequency of the Raman lasers with $t_{\text{off}}>150\mu \mathrm{s}$ are shown in (c),(d), which we fit with Gaussian functions. Vertical dashed lines indicate the center of the fit to the blue data points. Each data point is the average of 250 repeats of the experimental sequence.