Fast measurements and multiqubit gates in dual species atomic arrays

TL;DR

This work addresses the need for fast, high-fidelity mid-circuit syndrome measurements in neutral-atom quantum processors by proposing a dual-species architecture where Cs ancilla qubits map syndrome information onto multiple Rubidium measuring qubits via Rydberg interactions. The approach realizes a native inter-species ${\sf CNOT}_k$ gate by conditioning Rubidium state transfer on the Cs ancilla being in a Rydberg state, and then reads out the measurement qubits with fluorescence imaging to achieve extremely low infidelity within a few microseconds. Key contributions include a quantitative analysis of the ancilla-measurement dynamics, a detailed cycle-time budget showing potential syndrome-cycle rates approaching tens of kHz, and a validated multiqubit gate where fidelities of $\mathcal{F} \ge 0.98$ are possible for up to $k=4$ targets, with clear paths to higher fidelity via higher Rydberg states or Raman transitions. The proposed scheme promises scalable, low-crosstalk syndrome extraction for surface-code like architectures, enabling fast quantum error correction in large neutral-atom qubit arrays.

Abstract

We propose and analyze an approach for fast syndrome measurements in an array of rubidium and cesium atomic qubits. The scheme works by implementing an inter-species $\textsf{CNOT}_k$ gate, entangling one cesium ancilla qubit with $k\geq 1$ rubidium qubits which are then used for state measurement. Utilizing Rydberg states with different inter- and intra-species interaction strengths, the proposal provides a syndrome measurement fidelity of $\mathcal{F}>0.9999$ in less than 5 $μ$s of integration time.

Figures (8)

• Figure 1: Surface code layout with Cs data and ancilla qubits and Rb measuring atoms. The relative distances are $r_{\rm da}$ - data to ancilla qubits, $r_{\rm am}$ - ancilla to measurement qubits, and $r_{\rm mm}$ - measurement to measurement qubits.
• Figure 2: Level scheme and couplings of the Cs ancilla qubit and Rb measuring atoms. Conditional upon the state of the ancilla qubit $\ket{0,1}_{\mathrm{a}}$, the Rb atoms are transferred to state $\ket{1}_{\mathrm{m}}$ and then interrogated by a laser on the cycling transition to state $\ket{f}_\mathrm{m}$ providing a fluorescence signal for measurement.
• Figure 3: Transition probability $\braket{\sigma_{11}(t=\tau)}$ from state $\ket{0}$ to state $\ket{1}$ for a two-level atom driven by a square $\pi$-pulse $\Omega(t)=\Omega_\mathrm{max} \Theta(t) \Theta(\tau-t)$ of duration $\tau = \pi/\Omega_\mathrm{max}$ (dotted brown line), and a smooth $\pi$-pulse $\Omega(t)=\Omega_\mathrm{max} \sin^2(\pi t/\tau)$ of duration $\tau = 2\pi/\Omega_\mathrm{max}$ (solid red line), vs the detuning $\delta=\delta_0$. Inset shows the pulse amplitudes $\Omega(t)$ with $\Omega_\mathrm{max}=2\pi\times 0.2\;$MHz.
• Figure 4: Dynamics of populations $\braket{\sigma_{11}^{(j)}}$ of state $\ket{1}_{\rm m}$ of each of the five measuring Rb atoms, initially in state $\ket{0}_{\rm m}$, upon applying a resonant microwave $\pi$-pulse $\Omega(t)=\Omega_\mathrm{max} \sin^2(\pi t/\tau)$ with $\Omega_\mathrm{max}=2\pi\times 0.2\;$MHz. State $\ket{1}_{\rm m}$ is dressed with the Rydberg state $\ket{r}_{\rm m}$ by a laser with the Rabi frequency $\Omega_r/2\pi = 6\;$MHz and detuning $\Delta_r/2\pi = 15\:$MHz. For the Cs atom in Rydberg state $\ket{r}_\mathrm{a}$, the Rb atoms undergo population transfer to state $\ket{1}_{\rm m}$ (solid lines); while for the Cs atom in state $\ket{0}_\mathrm{a}$, the transfer is suppressed (dashed lines). In the simulations, we take the Rydberg state lifetimes $1/\gamma_{r_{\rm m}}= 50, 80, 100\:\mu \mathrm{s}$ for Rb and $1/\gamma_{r_{\rm a}}=55, 90, 110\:\mu \mathrm{s}$ for Cs, assuming the temperatures $T=300,77,4\:$K, respectivelly. For comparison, we also show on the main panel the transfer dynamics for a resonant two-level atom (black dotted line). Inset shows the populations $\braket{\sigma_{11}^{(j)}}$ of the Rb atoms (for $T=300\:$K) on a log scale.
• Figure 5: State measurement infidelity as a function of integration time and the number of measurement atoms. The inset shows the optimal camera count threshold values. Simulation parameters were used corresponding to measurement of Rb atoms at 780 nm with an ORCA-Quest qCMOS camera: $\Omega_d/4\pi=0.14,$$\Delta/\gamma=-1/2,$$I/I_s=5,$$\gamma=2\pi \times 6.06\times 10^6 ~\rm (s^{-1}),$$\eta_{d}=0.54$, $\eta_{\rm loss}=0.9$, $b_0=0.016 ~\rm (s^{-1}/pixel),$$\sigma=4 ~\rm camera~ counts/pixel$ (assuming standard readout mode), $\kappa=1/0.107,$ and $P_{\rm dark}=P_{\rm bright}=1/2.$ With these parameters $q/t_{\rm m}=9.25\times 10^5 ~\rm (s^{-1})/atom$.