Fast native three-qubit gates and fault-tolerant quantum error correction with trapped Rydberg ions

Quantum Science and Technology, vol. 11, pp. 035021

Abstract

Abstract Trapped ions are one of the most promising quantum-information-processing platforms, yet conventional entangling gates mediated by collective motion remain slow and difficult to scale. Exciting trapped ions to high-lying electronic Rydberg states provides a promising route to overcome these limitations by enabling strong, long-range dipole–dipole interactions that support much faster multi-qubit operations. Here, we introduce the first scheme for implementing a native controlled–controlled-Z gate with microwave-dressed Rydberg ions by optimizing a single-pulse protocol that accounts for the finite Rydberg-state lifetime. Under realistic conditions, the resulting gate achieves fidelities above 97 % with execution times of about 2 μ s at cryogenic temperatures, making it more than 8 μ s faster than standard decompositions into one- and two-qubit gates. To explore the potential of trapped Rydberg ions for fault-tolerant (FT) quantum error correction (QEC), and to illustrate the utility of three-qubit Rydberg-ion gates in this context, we develop and analyze a proposal for FT, measurement-free QEC using the nine-qubit Bacon–Shor code. Our simulations confirm that QEC can be performed in a fully FT manner on a linear Rydberg-ion chain despite its limited qubit connectivity. These results establish native multi-qubit Rydberg-ion gates as a valuable resource for fast, high-fidelity quantum computing and highlight their potential for FT QEC.

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