Suppressing crosstalk for Rydberg quantum gates

Abstract

We present a method to suppress crosstalk from implementing controlled-Z gates via local addressing in neutral atom quantum computers. In these systems, a fraction of the laser light that is applied locally to implement gates typically leaks to other atoms. We analyze the resulting crosstalk in a setup of two gate atoms and one neighboring third atom. We then perturbatively derive a spin-echo-inspired gate protocol that suppresses the leading order of the amplitude error, which dominates the crosstalk. Numerical simulations demonstrate that our gate protocol improves the fidelity by two orders of magnitude across a broad range of experimentally relevant parameters. To further reduce the infidelity, we develop a circuit to cancel remaining phase errors. Our results pave the way for using local addressing for high-fidelity quantum gates on Rydberg-based quantum computers.

Figures (5)

• Figure 1: Setup for studying the crosstalk of a two-qubit gate (on atoms 1 and 2) affecting a third neighboring atom (atom 3). Each atom is modeled as a three-level system with states $\ket{0}, \ket{1}$, and a Rydberg state $\ket{r}$. A local laser (depicted in yellow) couples $\ket{1}$ to $\ket{r}$ with Rabi frequency $\Omega(t)$ and detuning $\Delta(t)$. We assume that the third atom is affected by a small fraction $\sqrt{\epsilon}\Omega(t)$ of the Rabi frequency. Atoms in the Rydberg state interact via van der Waals interaction $V_{ ij}$ (green arrows).
• Figure 2: Comparison of the single- and double-pulse protocol. (a) The controlled-Z gate can be realized by a single pulse with a Gaussian detuning sweep $\Delta(t)$ and a smoothly turned on and off Rabi frequency $\Omega(t)$pagano_2022. (b) The green line shows the evolution of the state of the third atom on the Bloch sphere during the single-pulse protocol if initialized in $\ket{1}$. After the pulse, the probability of being in the Rydberg state $\ket{r}$ remains finite. (c) To suppress the crosstalk, we introduce the double-pulse protocol. The gate is split into two controlled-$\pi/2$ gates, realizing a controlled-Z gate on the gate atoms. Between the gate pulses, the phase of the excitation laser is changed so that on the third atom, the second pulse brings the Rydberg population back to $\ket{1}$ (d).
• Figure 3: Comparison of the infidelity $1-\mathcal{F}$ of the effective three-qubit gate after the single- and double-pulse protocols for the equilateral setup with $V_{ 13}/\hbar\Omega_{ 0} = V_{ 23}/\hbar\Omega_{ 0} = V_{ 12}/\hbar\Omega_{ 0} = 21.1$pagano_2022. Infidelity when the gate atoms were initialized in states (a) $\ket{00}$, (b) $\ket{10}$, and (c) $\ket{11}$, and the third atom in $1/\sqrt{2}\left(\ket{0}+\ket{1}\right)$. For $\ket{00}$, the numerical data for the double-pulse protocol (blue crosses) agrees very well with the predicted $\epsilon^2$-increase (orange line). The linear dependence on $\epsilon$ (red line) of the single-pulse protocol (green crosses) is removed. For $\ket{10}$ and $\ket{11}$, the infidelities are small for both protocols. (d) Infidelity $1-\mathcal{F}$ if all atoms are initialized in $1/\sqrt{2}\left(\ket{0}+\ket{1}\right)$. For the double-pulse protocol, the infidelity is reduced by about two orders of magnitude and increases only quadratically in $\epsilon$. For the single-pulse protocol, we observe a linear increase.
• Figure 4: Dependence of the infidelity $1-\mathcal{F}$ on the van der Waals interaction strength between the third atom and the gate atoms. (a) Infidelity for different interaction strengths $V_{ i3}$ for $\epsilon = 0.008$. (b) Infidelity along the dashed line in (a) for $V_{ 13} = V_{ 23}$ and different $\epsilon$-values, when applying the double-pulse protocol. For comparison, the infidelity is plotted for the single-pulse protocol (dotted lines) for the same $\epsilon$-values. The infidelity exhibits the same behavior for all $\epsilon$-values.
• Figure 5: Reducing the infidelity by canceling remaining phase errors. (a) Quantum circuit for canceling the phase errors. (b) By applying the circuit after the double-pulse protocol, the infidelity $1-\mathcal{F}$ is reduced by almost an additional order of magnitude.