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 multiqudit 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 ( C Z ) 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 C Z 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.
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 multiqudit 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 ( C Z ) 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 C Z 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.
We study the generation of two-qudit entangling quantum logic gates using two techniques in quantum optimal control.We take advantage of both continuous, Lie algebraic control and digital, Lie group control.In both cases, the key is access to a time-dependent Hamiltonian, which can generate an arbitrary unitary matrix in the group SU(d 2 ).We find efficient protocols for creating high-fidelity entangling gates.As a test of our theory, we study the case of qudits robustly encoded in nuclear spins of alkaline earth atoms and manipulated with magnetic and optical fields, with entangling interactions arising from the wellknown Rydberg blockade.We applied this in a case study based on a d = 10 dimensional qudit encoded in the I = 9/2 nuclear spin in 87 Sr, controlled through a combination of nuclear spin resonance, a tensor ac-Stark shift, and Rydberg dressing, which allows us to generate an arbitrary symmetric entangling twoqudit gate, such as CPhase.Our techniques can be used to implement qudit entangling gates for any 2 ≤ d ≤ 10 encoded in the nuclear spin.We also studied how decoherence due to the finite lifetime of the Rydberg states affects the creation of the CPhase gate and found, through numerical optimization, a fidelity of 0.9985, 0.9980, 0.9942, and 0.9800 for d = 2, d = 3, d = 5, and d = 7, respectively.This provides a powerful platform to explore the various applications of quantum information processing of qudits, including metrological enhancement with qudits, quantum simulation, universal quantum computation, and quantum error correction.
We propose a protocol to realize arbitrary state synthesis and unitary operations on a qudit encoded in the collective dressed states of a Rydberg-blockaded array of three-level atoms. This system is isomorphic to the Jaynes-Cummings model and acts as a multilevel Rydberg superatom whose nonlinear spectrum can be precisely controlled through the parameters of the laser driving the intermediate-to-Rydberg transition. Control of the qudit state is possible through pulse sequences of the laser driving the ground-to-intermediate transition. The dimension of the qudit Hilbert space is scalable by adjusting the number of atoms involved in the Rydberg-blockaded array. We estimate the fidelity of our protocol for realizing arbitrary unitaries and discuss the influence of the finite lifetime of the Rydberg state. Our work paves the way for processing quantum information with Rydberg blockaded arrays of atoms as an alternative to atom qubit arrays.
Quantum holonomic gates hold built-in resilience to local noises and provide a promising approach for implementing fault-tolerant quantum computation. We propose to realize high-fidelity holonomic (N+1)-qubit controlled gates using Rydberg atoms confined in optical arrays or superconducting circuits. We identify the scheme, deduce the effective multibody Hamiltonian, and determine the working condition of the multiqubit gate. Uniquely, the multiqubit gate is immune to systematic errors, i.e., laser parameter fluctuations and motional dephasing, as the N control atoms largely remain in the very stable qubit space during the operation. We show that CN-not gates can reach the same level of fidelity at a given gate time for $N\ensuremath{\le}5$ under a suitable choice of parameters, and the gate tolerance against errors in systematic parameters can be further enhanced through optimal pulse engineering. In the case of Rydberg atoms, the proposed protocol is intrinsically different from typical schemes based on Rydberg blockade or antiblockade. Our study paves an alternative way to build robust multiqubit gates with Rydberg atoms trapped in optical arrays or with superconducting circuits. It contributes to current efforts to develop scalable quantum computation with trapped atoms and fabricable superconducting devices.
The neutral atom platform has become an attractive choice to study the science of quantum information and quantum simulation, where intense efforts have been devoted to the entangling processes between individual atoms. A two-qubit controlled-phase gate via Rydberg blockade is one of the most essential elements. Recent theoretical studies have suggested the advantages of introducing nontrivial waveform modulation into the gate protocol, which is anticipated to improve its performance towards the next stage. We report our recent experimental results in realizing the two-qubit controlled-phase (CZ) gate via single-modulated-pulse off-resonant modulated driving embedded in a two-photon transition for Rb atoms. It relies on a global driving laser pulse with a carefully calculated smooth waveform to gain the appropriate phase accumulations required by CZ gate. Combining this CZ gate with global microwave pulses, two-atom entanglement is generated with the raw fidelity of 0.945(6). After accounting for state preparation and measurement errors, we extract the entanglement operation fidelity to be 0.980(7). Our work features completing the CZ gate operation within a single pulse to avoid shelved population in the Rydberg levels, thus demonstrating another promising route for realizing a high-fidelity two-qubit gate for the neutral atom platform.
Abstract The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing 1 . Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits 2,3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture 4 . The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions 5 . Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction 6,7 . Our method uses fast, single-pulse gates based on optimal control 8 , atomic dark states to reduce scattering 9 and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications 10,11 , characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates 12,13 . By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms 14 , error-corrected circuits 7 and digital simulations 15 .
Arrays of optically trapped neutral atoms are an emerging platform for scalable quantum computing, where achieving high-fidelity entangling gates remains a central challenge. We present a systematic analysis of the two-qubit controlled-Z (cz) gate under finite Rydberg blockade, paying particular attention to the influence of near-degenerate Rydberg pair states and resonant dipole-dipole interactions. Using the global two-pulse excitation protocol, we model the full gate dynamics, explicitly capturing population leakage into noncomputational states. By analyzing the interplay between the control parameters such as Rabi frequency, detuning, the F\"orster defect, and interaction strength, we identify conditions that enable fast, high-fidelity gate operation while minimizing leakage. We also quantify the impact of finite Rydberg-state lifetimes on gate error and further demonstrate that the optimal parameter regimes identified here are accessible in current rubidium-based tweezer experiments. These results provide practical guidance for optimizing two-qubit gate protocols in neutral-atom quantum processors with experimentally accessible conditions.