Robust Control and Entanglement of Qudits in Neutral Atom Arrays

TL;DR

The paper tackles the challenge of universal, high-fidelity multi-qudit control in neutral-atom arrays by introducing a universal scheme that combines multi-tone addressing for single-qudit gates with Rydberg-mediated, globally driven entangling pulses. It provides explicit qutrit gate constructions (X, Hadamard, and CZ) optimized via GRAPE to be time-efficient and robust to noise, and proves a no-go result for CZ using a single Rydberg transition when d>3, motivating a two-tone (or more) approach. A general CZ construction for any dimension d is given, along with a practical experimental path using $^{171}$Yb, including mitigation of Rydberg-tone crosstalk and detailed noise analysis demonstrating fidelities around 0.994 for qutrit CZs under realistic conditions. The work positions native qudit control in neutral-atom platforms as a practical route to qudit-based quantum computation, error correction, and complex quantum simulations, potentially outperforming qubit-based encodings in terms of resource efficiency and scalability.

Abstract

Quantum devices comprised of elementary components with more than two stable levels - so-called qudits - enrich the accessible Hilbert space, enabling applications ranging from fault-tolerant quantum computing to simulating complex many-body models. While several quantum platforms are built from local elements that are equipped with a rich spectrum of stable energy levels, schemes for the efficient control and entanglement of qudits are scarce. Importantly, no experimental demonstration of multi-qudit control has been achieved to date in neutral atom arrays. Here, we propose a general scheme for controlling and entangling qudits and perform a full analysis for the case of qutrits, encoded in ground and metastable states of alkaline earth atoms. We find an efficient implementation of single-qudit gates via the simultaneous driving of multiple transition frequencies. For entangling operations, we provide a concrete and intuitive recipe for the controlled-Z (CZ) gate for any local dimension d, realized through alternating single qudit and entangling pulses that simultaneously drive up to two Rydberg transitions. We further prove that two simultaneous Rydberg tones are, in general, the minimum necessary for implementing the CZ gate with a global drive. The pulses we use are optimally-controlled, smooth, and robust to realistic experimental imperfections, as we demonstrate using extensive noise simulations. This amounts to a minimal, resource-efficient, and practical protocol for realizing a universal set of gates. Our scheme for the native control of qudits in a neutral atom array provides a high-fidelity route toward qudit-based quantum computation, ready for implementation on near-term devices.

Figures (7)

• Figure 1: Robust qudit control in neutral atoms. (a) Level structure for qudit encoding, as can be found e.g. in $^{171}{\rm Yb}$; our scheme requires $d-1$ laser tones for universal single-qudit rotations and two Rydberg tones for global entangling gates (the example shown is for $d=3$). (b) Robust pulse scheme for realizing the two-qudit $\mathrm{C}\mathcal{Z}$ gate, which requires $\frac{d(d-1)}{2}$ entangling pulses interspersed with single-qudit rotations.
• Figure 2: Single-qutrit gates. Optimal-time pulse shapes implementing the $\mathcal{X}$ and $\mathcal{H}$ single-qutrit gates. The lasers operate at maximal intensity $\overline{\Omega}$ (top row), and the gates are implemented by the modulation of the phase (middle row). Note that the apparent discontinuity of the phase of $\Omega_{1,2}$ in $\mathcal{H}$ is simply a $2\pi$ phase wrap. The bottom row shows the population evolution, starting from $\psi(0)=\ket{0}$.
• Figure 3: Composite qutrit $\mathrm{C}\mathcal{Z}$ gate.(a) Implementation using a single Rydberg state (i.e., only $\Omega_2^{(\mathrm{r})}$) and single-qudit permutations, following Eq. \ref{['eq:CZ_qutrit_single_ryd']}, showing the evolution of the input state under the applied pulses. (b) Amplitude and phase of the optimal-time pulse shape $\Omega_{\mathrm{C}\mathcal{R}}^{(\mathrm{r})}$ implementing the $\mathrm{C}\mathcal{R}\left(\frac{4\pi}{3}\right)$ gates. (c) Implementation using two available Rydberg states, following Eq. \ref{['eq:CZ_general_qutrit']}. The first pulse has $\Omega_1^{(\mathrm{r})} = \Omega_{\mathrm{C}\mathcal{R}}^{(\mathrm{r})}$ and $\Omega_2^{(\mathrm{r})} = 0$, the second pulse has $\Omega_1^{(\mathrm{r})} = 0$ and $\Omega_2^{(\mathrm{r})} = \Omega_{\mathrm{C}\mathcal{R}}^{(\mathrm{r})}$, and the third pulse activates both lasers simultaneously.
• Figure 4: Predicted infidelity for the qudit $\mathrm{C}\mathcal{Z}$ gate from Rydberg decay. We assume a Rydberg lifetime of $60~\mu\textrm{sec}$ and a Rabi frequency of $\overline{\Omega}=2\pi\times 5~\textrm{MHz}$. The dotted black line shows the predicted scaling of the infidelity with the qudit dimension, given by Eq. \ref{['eq:infid_scaling']}. The yellow square marks the infidelity of the qutrit $\mathrm{C}\mathcal{Z}$ gate obtained from the noise simulation, accounting also for shot-to-shot noise and a finite Rydberg blockade. The inset shows the average $\mathrm{C}\mathcal{R}$ pulse duration for each $d$ and the weighted number of non-trivial $\mathrm{C}\mathcal{R}$ pulses (i.e., with $\theta \neq 0$), where each two-tone pulse is counted as two pulses.
• Figure 5: Pulse shapes implementing the qutrit $\mathrm{C}\mathcal{Z}$ gate, obtained from GRAPE optimization in Fourier space. The apparent phase discontinuities are $2\pi$ phase wraps.