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arXiv:1109.5009 · Physical Review A

Geometric manipulation of ensembles of atoms on an atom chip for quantum computation

Yi-Cong Zheng, Todd A. Brun

Published Sep 18, 2012• 13 citations
arXivHTMLPDF

Abstract

We propose a feasible scheme to achieve quantum computation based on geometric manipulation of ensembles of atoms and analyze it for neutral rubidium atoms magnetically trapped in planoconcave microcavities on an atom chip. The geometric operations are accomplished by optical excitation of a single atom into a Rydberg state in a constant electric field. Strong dipole-dipole interactions and incident lasers drive the dark state of the atom ensembles to undergo cyclic evolutions that realize a universal set of quantum gates. Such geometric manipulation turns out naturally to protect the qubits from the errors induced by nonuniform laser illumination as well as cavity loss. The gate performance and decoherence processes are assessed by numerical simulation.

DOI
10.1103/physreva.86.032323

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We propose a feasible scheme to achieve quantum computation based on geometric manipulation of ensembles of atoms and analyze it for neutral rubidium atoms magnetically trapped in planoconcave microcavities on an atom chip. The geometric operations are accomplished by optical excitation of a single atom into a Rydberg state in a constant electric field. Strong dipole-dipole interactions and incident lasers drive the dark state of the atom ensembles to undergo cyclic evolutions that realize a universal set of quantum gates. Such geometric manipulation turns out naturally to protect the qubits from the errors induced by nonuniform laser illumination as well as cavity loss. The gate performance and decoherence processes are assessed by numerical simulation.
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.
Summary form only given. Optical lattices provide new opportunities to create entangled states of neutral atoms for quantum information processing. Such systems have some attractive features: decoherence is suppressed because neutrals couple weakly to the environment, and operations can be performed in parallel on a large ensemble of trapped atoms, thus offering avenues for scaling to many qubits. The main source of decoherence is spontaneous emission, but this can be negligible if all manipulations are performed rapidly compared to the photon scattering rate. We consider here the possibility of using resonantly induced electric dipole-dipole interactions to engineer two-qubit operations such as the swap gate and the controlled-phase which, together with single qubit operations, can perform arbitrary quantum computations.
We consider an ensemble of atoms with $\mathrm{\ensuremath{\Lambda}}$-type level structure trapped in a single-mode cavity, and propose a geometric scheme of coherent manipulation of quantum states on the subspace of zero-energy states within the quantum Zeno subspace of the system. We find that the particular subspace inherits the decoherence-free nature of the quantum Zeno subspace and features a symmetry-protected degeneracy, fulfilling all the conditions for a universal scheme of arbitrary unitary operations on it.
Neutral atom quantum computing utilizes laser-trapped neutral atoms as qubits and realizes quantum logic gate operations through Rydberg-state interactions. In recent years, it has become one of the most vibrant directions in quantum computing hardware. This paper systematically reviews the working principles of neutral-atom quantum computers, including qubit encoding, atom trapping and manipulation, Rydberg states and interactions, the Rydberg blockade quantum gate mechanism, and atom rearrangement with reconfigurable architectures. The mainstream technical routes are surveyed, represented by optical tweezer arrays combined with Rydberg interactions, optical lattice schemes, and dipole trap arrays. A panoramic review is provided of domestic and international research progress from theoretical foundations in 2000 to the latest achievements in 2026, including thousand-qubit-scale systems, logical qubits, and quantum error correction experiments. Key breakthroughs are highlighted, such as the 6100-atom qubit array, continuous operation of a 3000-qubit system, quantum simulation of the Kitaev honeycomb model, toric code error correction demonstrations, encoding rates exceeding 1/2, and fault-tolerant architectures. The core bottlenecks are analyzed in depth, including the scalability--fidelity trade-off, engineering implementation of quantum error correction, atom loss and mid-circuit replenishment, laser system industrialization, control electronics scalability, and long-distance quantum interconnection. This paper aims to provide a systematic reference for academic research and technological development in this field.
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 an experimentally feasible scheme to achieve quantum computation based solely on geometric manipulations of a quantum system. The desired geometric operations are obtained by driving the quantum system to undergo appropriate adiabatic cyclic evolutions. Our implementation of the all-geometric quantum computation is based on laser manipulation of a set of trapped ions. An all-geometric approach, apart from its fundamental interest, offers a possible method for robust quantum computation.