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Physical Review Applied

Error-resilient geometric entangling gates in Rydberg atoms

Yan Liang, Xue-Dong Tian, Li‐Na Ji, Zheng‐Yuan Xue

Published Aug 21, 2025• 2 citations
Publisher

Abstract

Quantum computation holds great potential in revolutionizing information processing, with high-fidelity quantum gates serving as the cornerstone for realizing fault-tolerant quantum architectures. Here, we present a robust protocol for implementing high-fidelity entangling gates in Rydberg atomic systems via unconventional geometric quantum control strategies. By removing the stringent zero-dynamical-phase constraint inherent to conventional nonadiabatic geometric quantum computation, our scheme achieves high flexibility in designing driving fields while simultaneously enhancing gate fidelity and resilience against various errors. Notably, our protocol enables direct extension to multiqubit controlled-phase gate construction, with the gate duration remaining independent of the number of qubits involved. The results establish a practical and scalable framework for error-resilient quantum operations in Rydberg platforms, with broad implications for both fault-tolerant quantum computing and the quantum simulation of complex many-body systems.

DOI
10.1103/dq7w-7hnl

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Quantum computation holds great potential in revolutionizing information processing, with high-fidelity quantum gates serving as the cornerstone for realizing fault-tolerant quantum architectures. Here, we present a robust protocol for implementing high-fidelity entangling gates in Rydberg atomic systems via unconventional geometric quantum control strategies. By removing the stringent zero-dynamical-phase constraint inherent to conventional nonadiabatic geometric quantum computation, our scheme achieves high flexibility in designing driving fields while simultaneously enhancing gate fidelity and resilience against various errors. Notably, our protocol enables direct extension to multiqubit controlled-phase gate construction, with the gate duration remaining independent of the number of qubits involved. The results establish a practical and scalable framework for error-resilient quantum operations in Rydberg platforms, with broad implications for both fault-tolerant quantum computing and the quantum simulation of complex many-body systems.
Recently, nonadiabatic geometric quantum computation has been received great attentions, due to its fast operation and intrinsic error resilience. However, compared with the corresponding dynamical gates, the robustness of implemented nonadiabatic geometric gates based on the conventional single-loop geometric scheme still has the same order of magnitude due to the requirement of strict multi-segment geometric controls, and the inherent geometric fault-tolerance characteristic is not fully explored. Here, we present an effective geometric scheme combined with a general dynamical-corrected technique, with which the super-robust nonadiabatic geometric quantum gates can be constructed over the conventional single-loop geometric and two-loop composite-pulse geometric strategies, in terms of resisting the systematic error, i.e., σx error. In addition, combined with the decoherence-free subspace (DFS) coding, the resulting geometric gates can also effectively suppress the σz error caused by the collective dephasing. Notably, our protocol is a general one with simple experimental setups, which can be potentially implemented in different quantum systems, such as Rydberg atoms, trapped ions and superconducting qubits. These results indicate that our scheme represents a promising way to explore large-scale fault-tolerant quantum computation.
Quantum computation has demonstrated advantages over classical computation for special hard problems, where a set of universal quantum gates is essential. Geometric phases, which have built-in resilience to local noise, have been used to construct quantum gates with excellent performance. However, this advantage has been smeared in previous schemes. Here, we propose a state-independent nonadiabatic geometric quantum-gate scheme that is able to realize a more fully geometric gate than previous approaches, allowing for the cancelation of dynamical phases accumulated by an arbitrary state. Numerical simulations demonstrate that our scheme has significantly stronger gate robustness than the previous geometric and dynamical ones. Meanwhile, we give a detailed physical implementation of our scheme with the Rydberg atom system based on the Rydberg blockade effect, specifically for multiqubit control-phase gates, which exceeds the fault-tolerance threshold of multiqubit quantum gates within the considered error range. Therefore, our scheme provides a promising way for fault-tolerant quantum computation in atomic systems.
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)(N+1)(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 NNN control atoms largely remain in the very stable qubit space during the operation. We show that CN{C}_{N}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.
Fault-tolerant implementation of quantum gates is one of preconditions for realizing quantum computation. The platform of Rydberg atoms is one of the most promising candidates for achieving quantum computation. We propose to implement a controlled-ZZZ gate on Rydberg atoms where an amplitude-modulated field is employed to induce Rydberg antiblockade. Gate robustness against the fluctuations in the Rydberg-Rydberg interaction can be largely enhanced by adjusting amplitude-modulated field. Furthermore, we introduce a Landau-Zener-St\"uckelberg transition on the target atom so as to improve the gate resilience to the deviation in the gate time and the drift in the pulse amplitude. With feasible experimental parameters, one can achieve the gate with low fidelity errors caused by atomic decay, interatomic dipole-dipole force, and Doppler effects. Finally, we generalize the gate scheme into multiqubit cases, where resilient multiqubit phase gates can be obtained in one step with an unchanged gate time as the number of qubits increases.
While geometric quantum gates are often theorized to possess intrinsic resilience to control errors by exploiting the global properties of evolution paths, this promise has not consistently translated into practical robustness. We present a streamlined framework for nonadiabatic geometric quantum gates (NGQGs) that incorporates additional auxiliary constraints to suppress dynamical contamination and achieve super-robust performance. Within this framework, we also design NGQGs using noncyclic paths, offering enhanced design flexibility. Implemented on superconducting transmon qubits, our scheme realizes high-fidelity single-qubit gates that are robust against Rabi amplitude error εεε, with infidelity scaling as O(ε4)\mathcal{O}(ε^4)O(ε4), in contrast to the O(ε2)\mathcal{O}(ε^2)O(ε2) behavior of conventional dynamical gates. We further analyze two-qubit NGQGs under parametric driving. Our results identify subtle limitations that compromise performance in two-qubit scenarios, underscoring the importance of phase compensation and waveform calibration. The demonstrated simplicity and generality of our super-robust NGQG scheme make it applicable across diverse quantum platforms.
Geometric quantum computation offers a potential route to fault-tolerant quantum information processing by exploiting the global nature of geometric phases. However, achieving controlled high-order suppression of multiple error sources remains a long-standing limitation, particularly in realistic large-scale circuits with complex noise environments. This limitation is largely due to the absence of a general framework that directly characterizes error accumulation and enables systematic improvement. Here we establish such a framework for universal doubly geometric gates by embedding target operations into a hierarchy of level-n identity constructions. This approach enables direct quantification of error accumulation while removing structural constraints inherent in previous schemes. We analytically show that the defining conditions lead to simultaneous fourth-order suppression of control errors, with a systematic extension to sixth-order suppression via higher-level constructions. Our results establish doubly geometric control as a general and scalable route toward high-order robust quantum gates, with potential implications for fault-tolerant quantum information processing.