High-fidelity Rydberg-blockade entangling gate using shaped, analytic pulses

We show that the use of shaped pulses improves the fidelity of a Rydberg-blockade two-qubit entangling gate by several orders of magnitude compared to previous protocols based on square pulses or optimal control pulses. Using analytical derivative removal by adiabatic gate (DRAG) pulses that reduce excitation of primary leakage states and an analytical method of finding the optimal Rydberg blockade, we generate Bell states with a fidelity of $F>0.9999$ in a 300 K environment for a gate time of only $50\mathrm{ns}$, which is an order of magnitude faster than previous protocols. These results establish the potential of neutral atom qubits with Rydberg-blockade gates for scalable quantum computation.

Figure 1

(a) DRAG pulse sequence (blue line) and initial Gaussian waveform (thin black line) to implement a two-qubit entangling gate. Pulse durations are ${\tau }_c,{\tau }_t$ for the control and target atoms. The control amplitudes are shown on the same scale. (b) Level diagram for one-photon Rydberg excitation with laser frequency ${\omega }_d$. (c) Detail of the Rydberg level structure and detunings. (d) Spectrum of pulse on control atom for Gaussian (black) and DRAG (blue) waveforms.

Figure 2

Population error for a two-qubit Rydberg-blockade entangling gate as a function of gate time $t_g={\tau }_t+2{\tau }_c$. Gaussian pulses reduce leakage errors by up to 2.5 orders of magnitude compared to conventional square controls, while additional supplementation with DRAG further improves by another 1.5 orders of magnitude for reasonable gate times. The DRAG pulses are designed to minimize primarily leakage into the $|n^{\prime }\rangle$ subset of the control atom as well as blockade leakage in the target atom. The Rydberg blockades ${\mathsf{B}}_0/2\pi$ are 1.54 and $0.68\mathrm{GHz}$ for S1 and S2, respectively.

Figure 3

Population error for a fixed gate time ${\tau }_t=30\mathrm{ns}$ as a function of the blockade shift ${\mathsf{B}}_0$ in settings S1 and S2. The error is minimized for a value of ${\mathsf{B}}_0/2\pi \sim 0.7\mathrm{GHz}$ in S2. In S1, the population error is optimal for blockade shifts in the range of 0.7–2.7 GHz.

Figure 4

Unitary Bell-state infidelity as a measure for entanglement generated by the pulse sequence in Fig. 1 using square pulses, Gaussians, DRAG, detuned (d) DRAG controls, and detuned DRAG controls with amplitude correction (d/r) for the setting S1 as well as optimized DRAG controls in S2. Detuning DRAG pulses on the target atom accounts for wrong phases and combines less leakage with high degrees of entanglement. The necessary detuning $\mathrm{\Lambda }$ decreases proportionally to $1/{\tau }_t^2$ with a value of $\mathrm{\Lambda }/2\pi =124.07\mathrm{MHz}$ at ${\tau }_t=25\mathrm{ns}$.

Figure 5

Bell-state infidelity including decay from all Rydberg levels for optimized detuned DRAG controls in both settings S1 and S2. Bell states are generated with a fidelity of 0.9999 at a total gate time of only $50\mathrm{ns}$.