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arXiv:2405.00471 · Physica Scripta

Floquet geometric entangling gates in ground-state manifolds of Rydberg atoms

Hao-Wen Sun, Jin-Lei Wu, Shi‐Lei Su

Published Jul 15, 2024• 4 citations
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Abstract

Abstract We propose new applications of Floquet theory in Rydberg atoms for constructing quantum entangling gates in atomic ground-state manifolds. By dynamically periodically modulating the Rabi frequencies of transitions between ground and Rydberg states of atoms, error-resilient two-qubit entangling gates can be implemented in the regime of Rydberg blockade. According to different degrees of Floquet theory utilization, the fidelity of the resulting controlled gates surpasses that of the original reference, and it exhibits high robustness against Rabi error in two qubits and detuning error in the control qubit. Our method only uses encoding in the ground states, and compared to the original scheme using Rydberg state for encoding, it is less susceptible to environmental interference, making it more practical to implement. Therefore, our approach may have broader applications or potential for further expansion of geometric quantum computation with neutral atoms.

DOI
10.1088/1402-4896/ad635b

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Abstract We propose new applications of Floquet theory in Rydberg atoms for constructing quantum entangling gates in atomic ground-state manifolds. By dynamically periodically modulating the Rabi frequencies of transitions between ground and Rydberg states of atoms, error-resilient two-qubit entangling gates can be implemented in the regime of Rydberg blockade. According to different degrees of Floquet theory utilization, the fidelity of the resulting controlled gates surpasses that of the original reference, and it exhibits high robustness against Rabi error in two qubits and detuning error in the control qubit. Our method only uses encoding in the ground states, and compared to the original scheme using Rydberg state for encoding, it is less susceptible to environmental interference, making it more practical to implement. Therefore, our approach may have broader applications or potential for further expansion of geometric quantum computation with neutral atoms.
We propose a nontrivial two-qubit gate scheme in which Rydberg atoms are subject to designed pulses resulting from geometric evolution processes. By utilizing hybrid robust nonadiabatic and adiabatic geometric operations on the control atom and target atom, respectively, we improve the robustness of the two-qubit Rydberg gate against Rabi control errors as well as blockade errors in comparison with the conventional two-qubit blockade gate. Numerical results with the current state-of-the-art experimental parameters corroborates the above mentioned robustness. We also evaluate the influence induced by the motion-induced dephasing and the dipole-dipole interaction and imperfection-excitation-induced leakage errors, which both could decrease the gate fidelity. Our scheme provides a promising route towards systematic control error (Rabi error) as well as blockade-error-resilient geometric quantum computation on neutral atom system.
We propose a geometric quantum computation (GQC) scheme, called Floquet GQC (FGQC), where error-resilient geometric gates based on periodically driven two-level systems can be constructed via a non-Abelian geometric phase proposed in a recent study [V. Novi\ifmmode \check{c}\else \v{c}\fi{}enko and G. Juzeli\ifmmode \bar{u}\else \={u}\fi{}nas, Phys. Rev. A 100, 012127 (2019)]. Based on Rydberg atoms, we give possible implementations of universal FGQC single-qubit gates and a nontrivial FGQC two-qubit gate. By using numerical simulation, we evaluate the performance of the FGQC Z and X gates in the presence of both decoherence and a certain kind of systematic control error. For the currently available coherence time of the Rydberg state, ${T}_{2}\ensuremath{\approx}32\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$, the numerical results show that the X and Z gate fidelities are about 0.9000.9000.900 and 0.8990.8990.899, respectively. In addition, we find that FGQC is robust against global control error; both analytical demonstration and numerical evidence are given. As the coherence time of various qubits grows, FGQC may provide a promising error-resilient quantum computation scheme in the future.
We achieve the robust nonadiabatic holonomic two-qubit controlled gate in one step based on the ground-state blockade mechanism between two Rydberg atoms. By using the Rydberg-blockade effect and the Raman transition mechanism, we can produce the blockade effect of double occupation of the corresponding ground state, i.e., ground-state blockade, to encode the computational subspace into the ground state, thus effectively avoiding the spontaneous emission of the excited Rydberg state. On the other hand, the feature of geometric quantum computation independent of the evolutionary details makes the scheme robust to control errors. In this way, the controlled quantum gate constructed by our scheme not only greatly reduces the gate infidelity caused by spontaneous emission but is also robust to control errors.
Neutral atom systems are promising platforms for quantum simulation and computation, owing to their long coherence times. However, their intrinsically weak ground-state interactions pose a major limitation to the advancement of scalable quantum simulation and computation. To address this challenge, we propose an approach to enhancing the ground-state interaction strength of neutral atoms via Floquet modulation of a Rydberg atomic ensemble. Each Floquet period consists of ground-state coupling followed by a pulse driving the transition from the ground state to the Rydberg state. Theoretical analysis and numerical simulations demonstrate that after a defined evolution time, neutral atoms within Rydberg ensembles can collectively form a WWW state in the ground-state manifold. Even when the Rydberg interaction strength is far below the blockade regime, the fidelity remains remarkably high. Finally, we analyze the application of this scheme in the preparation of single-photon sources. In general, our proposed mechanism offers an efficient and highly controllable method for quantum state preparation within the Rydberg atomic ensembles, significantly enhancing the accuracy and stability of quantum state engineering while providing a well-controlled quantum environment for single-photon generation.
We propose a nonadiabatic non-Abelian geometric quantum operation scheme to realize universal quantum computation with mesoscopic Rydberg atoms. A single control atom entangles a mesoscopic ensemble of target atoms through long-range interactions between Rydberg states. We demonstrate theoretically that both the single-qubit and two-qubit quantum gates can achieve high fidelities around or above 99.999.9%99.9 in ideal situations. Besides, to address the experimental issue of Rabi frequency fluctuation (Rabi error) in Rydberg atom and ensemble, we apply the dynamical-invariant-based zero systematic-error sensitivity (ZSS) optimal control theory to the proposed scheme. Our numerical simulations show that the average fidelity could be 99.9899.98%99.98 for single ensemble qubit gate and 99.9499.94%99.94 for two-qubit gate even when the Rabi frequency of the gate laser acquires 1010%10 fluctuations. We also find that the optimized scheme can also reduce errors caused by higher order perturbation terms in deriving the Hamiltonian of the ensemble atoms. To address the experimental issue of decoherence error between the ground state and Rydberg levels in Rydberg ensemble, we introduce a dispersive coupling regime between Rydberg and ground levels, based on which the Rydberg state is adiabatically discarded. The numerical simulation demonstrate that the quantum gate is enhanced. By combining strong Rydberg atom interactions, nonadiabatic geometric quantum computation, dynamical invariant and optimal control theory together, our scheme shows another route to construct fast and robust quantum gates with mesoscopic atomic ensembles. Our study contributes to the ongoing effort in developing quantum information processing with Rydberg atoms trapped in optical lattices or tweezer arrays.
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.