Neutral-atom quantum processors are a promising platform for large-scale quantum computing. Integrating them with optical cavities enables fast nondestructive qubit readout and access to fast remote entanglement generation for quantum networking. In this work, we introduce a platform for coupling single atoms in optical tweezers to a Fabry-Perot fiber cavity. Leveraging the strong atom-cavity coupling, we demonstrated fast qubit-state readout with [Formula: see text] fidelity and two methods for cavity-mediated entanglement generation with integrated error detection. First, we used cavity-carving to generate a Bell state with 91(4)% fidelity and a 32(1)% success rate (the number in parentheses is the standard deviation). Second, we performed a cavity-mediated gate with a deterministic entanglement fidelity of 52.5(18)%, increased to 76(2)% with error detection. Our approach provides a route toward modular quantum computing and networking.
High-fidelity two-qubit gates in neutral-atom arrays rely on the Rydberg blockade, which is intrinsically short ranged and requires long range connectivity to be achieved through atom shuttling. We propose a four level architecture, where the typical ground state qubit can be leveraged for its long lifetime and the Rydberg states couple to a microwave cavity, allowing for long range cavity mediated gates. We first find the thermal dependence of two established protocols, the dispersive iSWAP native to the Tavis-Cummings model and the Controlled phase gate generated from driving the cavity. We simulate them under the presence of Rydberg decay, thermal photons, finite cavity linewidth and find fidelities which accompany closed form bounds. We then introduce the bichromatic Raman gate, which only virtually populates the Rydberg states and cancels dispersive shifts to mitigate both atomic and cavity decay, achieving a fidelity of
F=0.997. Finally, we consider a full optical tweezer array in a microwave cavity, and show that using a cavity mediated gate to close the periodic boundaries of the toric code shortens an error correction round by a factor of 2.3 for realistic array sizes. This was then applied to the wider family of Bivariate bicycle codes, and we find that it shortens a round of the gross code by a factor of 4.8.