FPQA-C: A Compilation Framework for Field Programmable Qubit Array.

The neutral atom array has gained prominence in quantum computing for its scalability and operation fidelity. Previous works focus on \textit{fixed} atom arrays (FAA) that necessitate extensive SWAP operations for long-range interactions. This work explores a novel architecture known as \textit{field programmable qubit array (FPQA)}, which uniquely allows for coherent atom movements during circuit execution and significantly \textit{reduces the cost of long-range interactions}. However, the atom movements have multiple hardware constraints, making movement scheduling very challenging. In this work, we introduce FPQA-C, a compilation framework tailored for qubit mapping, atom movement, and gate scheduling of FPQA. It contains a qubit-array mapper to decide the coarse-grained mapping of qubit 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 high-parallelism router that iteratively identifies parallelizable 2Q gates and decide the atom movements and gate executions, thus improving the parallelism. Besides, for fault-tolerant computing with FPQA, we provide comprehensive simulations evaluating logical error rates, execution times, physical qubit requirements, code distances, and bandwidth. We rigorously assess FPQA-C across 20+ diverse benchmarks, including generic circuits (arbitrary, QASMBench, SupermarQ), Quantum Simulation, and QAOA circuits. FPQA-C consistently outperforms the IBM Superconducting, FAA with long-range gates, FAA with rectangular and triangular topologies, achieving 2Q gate reductions by factors of 5.3x, 3.2x, 3.4x, and 2.6x, and circuit depth reductions by factors of 3.6x, 3.2x, 3.1x, and 2.2x, respectively.