High-Fidelity Two-Qubit Gates Using a Microelectromechanical-System-Based Beam Steering System for Individual Qubit Addressing

In a large scale trapped atomic ion quantum computer, high-fidelity two-qubit gates need to be extended over all qubits with individual control. We realize and characterize high-fidelity two-qubit gates in a system with up to four ions using radial modes. The ions are individually addressed by two tightly focused beams steered using microelectromechanical system mirrors. We deduce a gate fidelity of 99.49(7)% in a two-ion chain and 99.30(6)% in a four-ion chain by applying a sequence of up to 21 two-qubit gates and measuring the final state fidelity. We characterize the residual errors and discuss methods to further improve the gate fidelity towards values that are compatible with fault-tolerant quantum computation.

Figure 1

(a),(b) Schematic representation of the Raman beam optical setup. The two individual addressing beams (purple) are steered by two pairs of mirrors tilting in orthogonal directions on a MEMS device to address any qubit in a chain (steered beam is shown in green). The trap axial axis is rotated by 45° with respect to both tilting axes of the MEMS mirrors to utilize orthogonal tilting mirrors in order to maximize the addressable qubits. The projection and beam combining optics are represented by a black box. (c) Energy level schematic of a ${}^{171}{\mathrm{Yb}}^{+}$ ion. The red and blue lines indicate the two photon Raman transition for qubit operations.

Figure 2

(a) Discrete frequency modulation pulse sequence in the present experiment. The solution consists of 20 symmetric segments. The total gate time is $200\mu \mathrm{s}$. The required sideband Rabi frequencies are 5.55 and 5.47 kHz for FM gates in a two-ion chain and a four-ion chain. (b) Phase-space trajectory of four motional modes. (c) The estimated gross gate error of 1, 5, 13, 21 concatenated gates, given different detuning offsets. The estimation includes errors due to residual entanglement between spin and motion and the variation of the rotation angle. (d) The estimated of final-state error of 21 consecutive gates with $\pm 0.8\%$ deviation of Rabi frequency for the motional sideband transition. The amplitude error due to imperfect laser intensity can be compensated by intentional detuning offset.

Figure 3

Infidelity of the entangled state generated by repeated application of MS gates in a (a) two- and a (b) four-ion chain. The blue diamonds, red squares, and black circles are the population leakage to $|01⟩$ and $|10⟩$ space, the loss of parity contrast, and the infidelity of the final state, respectively.