Deterministic Universal Logical Gates for Finite-Energy GKP Qubits in Trapped Neutral Atoms

Abstract:We present a universal logical gate set for finite-energy Gottesman-Kitaev-Preskill (GKP) qubits encoded in the harmonic motional states of trapped neutral atoms. Internal electronic states serve as ancilla for implementing state-dependent conditional displacements in phase space, enabling arbitrary single-qubit phase gates. A Transient Rydberg excitation-mediated atomic dipole-dipole interaction enables a controlled-Z gate without invoking the blockade mechanism. The gates operate under magic-trapping conditions, allowing continuous trapping throughout the gate sequence, thereby preserving the motional encoding without intermediate measurement or feedforward. We assess the experimental feasibility of the proposed protocols using neutral $^{88}\mathrm{Sr}$ atoms and obtain average gate fidelities of $0.986$ for single-qubit phase gates and $0.985$ for the controlled-Z gate at a finite squeezing parameter of $\Delta=0.25$ (12 dB of squeezing), increasing to $0.997$ and $0.995$ respectively as $\Delta$ reaches $0.1$. These results provide a route toward universal, measurement-free logical control of motional GKP qubits in neutral-atom architectures.

arXiv:2608.30631 [quant-ph]

(or arXiv:2608.30631v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.30631 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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