  Dynamically field-programmable qubit arrays based on neutral atoms have high
fidelity and highly parallel gates for quantum computing. However, it is
challenging for compilers to fully leverage the novel flexibility offered by
such hardware while respecting its various constraints. In this study, we break
down the compilation for this architecture into three tasks: scheduling,
placement, and routing. We formulate these three problems and present efficient
solutions to them. Notably, our scheduling based on graph edge coloring is
provably near-optimal in terms of two-qubit gate stage count (at most one more
than the optimum), the fidelity bottleneck of this platform. As a result, our
compiler, Enola, produces higher fidelity results compared to existing works,
e.g., 3.7X stage reduction and 5.9X fidelity improvement on the benchmark set
used by OLSQ-DPQA, the current state of the art. Additionally, Enola is highly
scalable, e.g., within 30 minutes, it can compile circuits with 10,000 qubits,
a scale sufficient for the current era of quantum computing. Enola is open
source at https://github.com/UCLA-VAST/Enola
