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.

翻译：中性原子阵列因其可扩展性和操作保真度而在量子计算领域备受关注。现有研究主要聚焦于需要大量SWAP操作来实现长程相互作用的固定原子阵列。本文探索了一种名为现场可编程量子比特阵列的新型架构，该架构独特地允许在电路执行过程中实现相干原子移动，从而显著降低长程相互作用成本。然而，原子移动存在多项硬件约束，使得移动调度极具挑战性。本文提出FPQA-C——一个专为FPQA的量子比特映射、原子移动和门调度定制的编译框架。该框架包含量子比特阵列映射器，通过构建门频率图并利用最大k-割算法确定量子比特到阵列的粗粒度映射，以最小化SWAP开销。随后，量子比特原子映射器确定量子比特到阵列中特定原子的细粒度映射，并考虑负载均衡以避免违反硬件约束。我们进一步提出高并行度路由算法，该算法迭代识别可并行化的双量子比特门，并决策原子移动与门执行顺序，从而提升并行性。此外，针对基于FPQA的容错计算，我们提供了涵盖逻辑错误率、执行时间、物理量子比特需求、码距及带宽的全面仿真评估。我们在20余个多样化基准测试（包括通用电路、QASMBench、SupermarQ、量子模拟及QAOA电路）上严格评估了FPQA-C。相较于IBM超导架构、长程门FAA、矩形拓扑FAA及三角形拓扑FAA，FPQA-C分别实现了5.3倍、3.2倍、3.4倍和2.6倍的双量子比特门减少，以及3.6倍、3.2倍、3.1倍和2.2倍的电路深度降低。