Optimized ancillary drive for fast Rydberg entangling gates

Abstract

Reaching fast and robust two-qubit gates with low infidelities has been an outstanding challenge for the long-term goal of useful quantum computers. Typically, optimizing the pulse shapes can minimize the gate infidelity and improve its robustness to certain types of errors; yet it remains incapable of speeding up the gate execution time which is fundamentally restricted by the attainable Rabi frequency in a realistic setup. In this work, we develop a fast implementation of two-qubit CZ gates using optimized ancillary drive to enhance the two-photon Rabi frequency between the ground and Rydberg states.This ancillary drive can work in an error-robustness framework without increasing the original gate infidelity in the absence of the drive. Considering the experimentally feasible parameters for $^{87}$Rb atoms, we demonstrate that the execution time required for such CZ gates can be shortened by more than 30$\%$ as compared to standard two-photon protocols arising the gate fidelity above 0.9954 by taking account of all relevant error sources. Our results reduce the high-power laser requirement and unlock the potential toward fast, high-fidelity quantum operations for large-scale quantum computation with neutral atoms.

Figures (7)

• Figure 1: Acceleration mechanism. (a) Schematic representation of a general atomic qubit defined in a five-level space $\{|0\rangle$, $|1\rangle$, $|e\rangle$, $|r\rangle$, $|a\rangle$$\}$ where $|0\rangle$ is idle. $|a\rangle$ serves an ancillary state individually coupling the intermediate state $|e\rangle$, which provides an efficient control for accelerating the standard two-photon Rabi oscillations between the ground $|1\rangle$ and the Rydberg $|r\rangle$ states. (b) The original qubit system can be mapped into an effective two-level model $\{|1\rangle,|r\rangle \}$ with Rabi frequency $\Omega_{eff}$ and detuning $\Delta_{eff}$, in the limit of large intermediate detuning conditions.
• Figure 2: Numerical verification of the ancillary-field acceleration scheme. Time-dependent population dynamics in two periods on state $|1\rangle$ are comparably shown, resolved from the exact Hamiltonian (\ref{['Hamn']}) with ancillary-field, the effective Hamiltonian (\ref{['ef']}) and the exact dynamics without ancillary-field. We set $\alpha=(0.9,0.95,0.98)$ for panels (a)-(c). Common parameters are $\Delta/2\pi=500$ MHz, $\Omega_1=\Omega_2=0.1\Delta$, $\Omega_c=0.2\Delta$, $\Delta_c = –\alpha \Delta$ and $\delta=0$. Panel (d) separately shows the case of weak ancillary drive where $\Omega_c=0.01\Delta, \alpha=0.98$ and others are same as in (a)-(c).
• Figure 3: Fast and high-fidelity CZ gates with Rydberg atomic qubits. Schematic diagram and atomic level structure utilized in this work. The qubit state $|1\rangle$ couples to the Rydberg state $|r\rangle$ via a native two-photon transition mediated by state $|e\rangle$, with respective Rabi frequencies $\Omega_1,\Omega_2$ and detunings $\Delta,\delta_{opt}$. Specifically, another ancillary field near-resonantly couples the intermediate state $|e\rangle$ to another hyperfine (stable) ground state $|a\rangle$ with detuning $\Delta+\Delta_c\approx 0$ due to $\Delta\Delta_c<0$ and Rabi frequency $\Omega_c$, which can serve as a robust control knob for gate acceleration. Time-dependent pulse shaping is carried out via optimal control over two laser amplitudes $\Omega_1(t)$ and $\Omega_c(t)$ while $\Omega_2$ is kept fixed. A natural vdWs interaction with strength $V$ is assumed between atoms in double excited state $|rr\rangle$ implementing the Rydberg blockade effect Gaetan2009PhysRevLett.119.160502.
• Figure 4: (a) Upper panels: Optimized pulse amplitudes as a function of time for $\Omega_1(t)$ of the SA gates and $(\Omega_1^\prime(t),\Omega_c(t))$ of the ASA gates, corresponding to Cases I-III in Table I. Note that $\Omega_1^\prime(t)$ takes a same shape as $\Omega_1(t)$ except for a reduced gate time. Lower panels: Resolved time-dependent population on the intermediate $|e\rangle$ (dashed, $\bar{n}_e$ and $\bar{n}_e^\prime$), the Rydberg $|r\rangle$ (solid, $\bar{n}_r$ and $\bar{n}_r^\prime$) and the auxiliary $|a\rangle$ (dotted, $\bar{n}_a^\prime$) states during the pulse duration. Clearly, using the ASA gate strategy we can implement the gates with faster execution of laser pulses while keeping the intrinsic decay errors at a same level. (b) Same parameters resolved for two LIM Cases in which the pulse durations $T_0$ and $T$ are fixed to be $0.1$$\mu$s.
• Figure 5: The gate fidelity $F$ with the shortest gate time $T_0=T=0.1\mu$s for (a) the SA gate and (b) the ASA gate, depending on 100 independent optimization runs. Each point represents the realistic gate fidelity of single optimization run. The dashed line and the shaded region denote the average number and the standard deviation, respectively. The red dots represent the LIM case specified in Table I.