  The neutral atom array has gained prominence in quantum computing for its
scalability and operation fidelity. Previous works focus on fixed atom arrays
(FAAs) that require extensive SWAP operations for long-range interactions. This
work explores a novel architecture reconfigurable atom arrays (RAAs), also
known as field programmable qubit arrays (FPQAs), which allows for coherent
atom movements during circuit execution under some constraints. Such atom
movements, which are unique to this architecture, could reduce the cost of
long-range interactions significantly if the atom movements could be scheduled
strategically.
  In this work, we introduce Atomique, a compilation framework designed for
qubit mapping, atom movement, and gate scheduling for RAA. Atomique contains a
qubit-array mapper to decide the coarse-grained mapping of the qubits to
arrays, leveraging MAX k-Cut on a constructed gate frequency graph to minimize
SWAP overhead. Subsequently, a qubit-atom mapper determines the fine-grained
mapping of qubits to specific atoms in the array and considers load balance to
prevent hardware constraint violations. We further propose a router that
identifies parallel gates, schedules them simultaneously, and reduces depth. We
evaluate Atomique across 20+ diverse benchmarks, including generic circuits
(arbitrary, QASMBench, SupermarQ), quantum simulation, and QAOA circuits.
Atomique consistently outperforms IBM Superconducting, FAA with long-range
gates, and FAA with rectangular and triangular topologies, achieving
significant reductions in depth and the number of two-qubit gates.
