  Neutral atom arrays have become a promising platform for quantum computing,
especially the field programmable qubit array (FPQA) endowed with the unique
capability of atom movement. This feature allows dynamic alterations in qubit
connectivity during runtime, which can reduce the cost of executing long-range
gates and improve parallelism. However, this added flexibility introduces new
challenges in circuit compilation. Inspired by the placement and routing
strategies for FPGAs, we propose to map all data qubits to fixed atoms while
utilizing movable atoms to route for 2-qubit gates between data qubits. Coined
flying ancillas, these mobile atoms function as ancilla qubits, dynamically
generated and recycled during execution. We present Q-Pilot, a scalable
compiler for FPQA employing flying ancillas to maximize circuit parallelism.
For two important quantum applications, quantum simulation and the Quantum
Approximate Optimization Algorithm (QAOA), we devise domain-specific routing
strategies. In comparison to alternative technologies such as superconducting
devices or fixed atom arrays, Q-Pilot effectively harnesses the flexibility of
FPQA, achieving reductions of 1.4x, 27.7x, and 6.3x in circuit depth for
100-qubit random, quantum simulation, and QAOA circuits, respectively.
