Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms

Abstract

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 99.9% in ideal situations. Besides, to address the experimental issue of Rabi frequency fluctuation (Rabi error) in Rydberg atom and ensemble, we apply the dynamical-invariantbased zero systematic-error sensitivity (ZSS) optimal control theory to the proposed scheme. Our numerical simulations show that the average fidelity could be 99.98% for single ensemble qubit gate and 99.94% for two-qubit gate even when the Rabi frequency of the gate laser acquires 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 a new 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.

Creating heralded hyper-entangled photons using Rydberg atoms

“…This inhibits other Rydberg excitations in the atomic cloud within a blockade radius 45 . The dipole–dipole interaction between the Rydberg atoms has been explored to implement fast quantum gates in neutral atom 46 and also to perform quantum information processing based on collective excitations in mesoscopic atomic ensembles 47 – 49 in the blockade region and also in the anti-blockade region 50 – 53 .

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Time-Optimal Two- and Three-Qubit Gates for Rydberg Atoms

“…A variety of error sources limit gate fidelities in experiments, including imperfect Rydberg blockades, decay of the Rydberg state, scattering of an intermediate state in a two photon transition, laser phase noise, variations of the laser intensity with the position of the atom in the trap and Doppler shifts of the laser frequency due to thermal motion of the atoms [22,27,28]. To mitigate the effects of these errors, many different improvements of the original protocol [18] have been proposed based on adiabatic passage [29][30][31][32][33][34], dark state mechanisms [35], Rydberg Antiblockade [34,36,37], and many other approaches [19,[38][39][40][41]. It is increasingly recognized that all these approaches can benefit from quantum optimal control methods to improve both the speed and fidelities of the various quantum gates.…”

Dissipative engineering of a tripartite Greenberger–Horne–Zeilinger state for neutral atoms

“…A prominent example is the Rydberg blockade. Benefitting from the significant suppression of the simultaneous excitation for Rydberg atoms, it serves as the backbone not only for a two‐qubit controlled‐phase gate, 1,11,12 but also for quantum entanglement, 13‐17 quantum computation, 18,19 quantum algorithms, 20 quantum simulators, 4 and quantum repeaters 21 . On the other hands, as an opposite effect, the Rydberg antiblockade 22,23 also sheds new light on fundamental questions about quantum logic gate, 24‐27 quantum entanglement, 28‐32 and directional quantum state transfer 33 .…”