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Journal of the Optical Society of America B

Influence of the interaction geometry on the fidelity of the two-qubit Rydberg blockade gate

Ivan Vybornyi, L. V. Gerasimov, Dmitriy V. Kupriyanov, Stanislav S. Straupe, K. S. Tikhonov

Published Nov 20, 2023• 2 citations
Publisher

Abstract

We present a comparative analysis of physical constraints limiting the quality of spin entanglement created using the Rydberg blockade technique in an ensemble of trapped neutral 87 Rb atoms. Based on the approach developed earlier in Phys. Rev. A 106 , 042410 ( 2022 ) PLRAAN 1050-2947 10.1103/PhysRevA.106.042410 , we consider the complete multilevel Zeeman structure of the interacting atoms and apply our simulations to two excitation geometries featured by different transition types, both feasible for experimental verification. We demonstrate that the blockade shift strongly depends not only on the interatomic separation but also on the angular position of the atom pair with respect to the quantization axis determined by polarization of the driving fields. As an example, we have estimated fidelity for a promising design of a CZ gate, recently proposed by Levine et al . [ Phys. Rev. Lett. 123 , 230501 ( 2019 ) PRLTAO 0031-9007 10.1103/PhysRevLett.123.230501 ] for various possible experimental geometries. Anisotropic effects in entangling gates considered here are important for the optimal choice of proper geometry for quantum computing in two- and three-dimensional arrays of atomic qubits and are of considerable interest for quantum simulators, especially those that are designed for anisotropic physical models.

DOI
10.1364/josab.504629

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Physical Review A•Oct 7, 2022•7 citations
We present a comparative analysis of physical constraints limiting the quality of spin entanglement created using the Rydberg blockade technique in an ensemble of trapped neutral 87 Rb atoms. Based on the approach developed earlier in Phys. Rev. A 106 , 042410 ( 2022 ) PLRAAN 1050-2947 10.1103/PhysRevA.106.042410 , we consider the complete multilevel Zeeman structure of the interacting atoms and apply our simulations to two excitation geometries featured by different transition types, both feasible for experimental verification. We demonstrate that the blockade shift strongly depends not only on the interatomic separation but also on the angular position of the atom pair with respect to the quantization axis determined by polarization of the driving fields. As an example, we have estimated fidelity for a promising design of a CZ gate, recently proposed by Levine et al . [ Phys. Rev. Lett. 123 , 230501 ( 2019 ) PRLTAO 0031-9007 10.1103/PhysRevLett.123.230501 ] for various possible experimental geometries. Anisotropic effects in entangling gates considered here are important for the optimal choice of proper geometry for quantum computing in two- and three-dimensional arrays of atomic qubits and are of considerable interest for quantum simulators, especially those that are designed for anisotropic physical models.
We study the spatial performance of the entangling gate proposed by H. Levine et al. (Phys. Rev. Lett. 123, 170503 (2019)). This gate is based on a Rydberg blockade technique and consists of just two global laser pulses which drive nearby atoms. We analyze the multilevel Zeeman structure of interacting 87^{87}87Rb Rydberg atoms and model two experimentally available excitation schemes using specific driving beams geometry and polarization. In particular, we estimate the blockade shift dependence on inter-atomic distance and angle with respect to the quantization axis. In addition, we show that using Rydberg ddd-states, in contrast to sss-states, leads to a pronounced angular dependence of the blockade shift and gate fidelity.
Arrays of qubits encoded in the ground-state manifold of neutral atoms trapped in optical (or magnetic) lattices appear to be a promising platform for the realization of a scalable quantum computer. Two-qubit conditional gates between nearest-neighbor qubits in the array can be implemented by exploiting the Rydberg blockade mechanism, as was shown by D. Jaksch et al. [Phys. Rev. Lett. 85, 2208 (2000)]. However, the energy shift due to dipole-dipole interactions causing the blockade falls off rapidly with the interatomic distance, and protocols based on direct Rydberg blockade typically fail to operate between atoms separated by more than one lattice site. In this work, we propose an extension of the protocol of Jaksch et al. for controlled-ZZZ and controlled-not gates which works in the general case where the qubits are not nearest neighbors in the array. Our proposal relies on the Rydberg excitation hopping along a chain of ancilla noncoding atoms connecting the qubits on which the gate is to be applied. The dependence of the gate fidelity on the number of ancilla atoms, the blockade strength, and the decay rates of the Rydberg states is investigated. A comparison between our implementation of a distant controlled-not gate and one based on a sequence of nearest-neighbor two-qubit gates is also provided.
A neutral-atom system serves as a promising platform for realizing gate-based quantum computing because of its capability to trap and control several atomic qubits in different geometries and the ability to perform strong, long-range interactions between qubits; however, the two-qubit entangling gate fidelity lags behind competing platforms such as superconducting systems and trapped ions. The aim of our work is to design a fast, robust, high-fidelity controlled-ZZZ (cz) gate, based on the Rydberg-blockade mechanism, for neutral atoms. We propose a gate procedure that relies on simultaneous and transitionless quantum driving of a pair of atoms using broadband lasers. By simulating a system of two interacting cesium atoms, including spontaneous emission from excited levels and parameter fluctuations, we yield a Rydberg-blockade cz gate with fidelity 0.9985 over an operation time of $0.12\phantom{\rule{3.33333pt}{0ex}}\mathrm{\textmu{}s}$. Our gate procedure delivers cz gates that are superior than the state-of-the-art experimental cz gate and the simulated cz gates based on adiabatic driving of atoms. Our results show that our gate procedure carries significant potential for achieving scalable quantum computing using neutral atoms.
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.
We present experimental results on two-qubit Rydberg-blockade quantum gates and entanglement in a two-dimensional qubit array. Without postselection against atom loss we achieve a Bell state fidelity of $0.73\ifmmode\pm\else\textpm\fi{}0.05$. The experiments are performed in an array of single Cs atom qubits with a site to site spacing of $3.8\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$. Using the standard protocol for a Rydberg-blockade CZ{C}_{Z}CZ​ gate together with single qubit operations we create Bell states and measure their fidelity using parity oscillations. We analyze the role of ac Stark shifts that occur when using two-photon Rydberg excitation and show how to tune experimental conditions for optimal gate fidelity.
Single atoms in dipole microtraps or optical tweezers have recently become a promising platform for quantum computing and simulation. Here we report a detailed theoretical analysis of the physics underlying an implementation of a Rydberg two-qubit gate in such a system---a cornerstone protocol in quantum computing with single atoms. We focus on a blockade-type entangling gate and consider various decoherence processes limiting its performance in a real system. We provide numerical estimates for the limits on fidelity of the maximally entangled states and predict the full process matrix corresponding to the noisy two-qubit gate. We consider different excitation geometries and show certain advantages for the gate realization with linearly polarized driving beams. Our methods and results may find implementation in numerical models for simulation and optimization of neutral atom based quantum processors.