Hybrid Circuit Mapping: Leveraging the Full Spectrum of Computational Capabilities of Neutral Atom Quantum Computers.

Quantum computing based on Neutral Atoms (NAs) provides a wide range of computational capabilities, encompassing high-fidelity long-range interactions with native multi-qubit gates, and the ability to shuttle arrays of qubits. While previously these capabilities have been studied individually, we propose the first approach of a fast hybrid compiler to perform circuit mapping and routing based on both high-fidelity gate interactions and qubit shuttling. We delve into the intricacies of the compilation process when combining multiple capabilities and present effective solutions to address resulting challenges. The final compilation strategy is then showcased across various hardware settings, revealing its versatility, and highlighting potential fidelity enhancements achieved through the strategic utilization of combined gate- and shuttling-based routing. With the additional multi-qubit gate support for both routing capabilities, the proposed approach is able to take advantage of the full spectrum of computational capabilities offered by NAs.