In Layout Synthesis, the logical qubits of a quantum circuit are mapped to the physical qubits of a given quantum hardware platform, taking into account the connectivity of physical qubits. This involves inserting SWAP gates before an operation is applied on distant qubits. Optimal Layout Synthesis is crucial for practical Quantum Computing on current error-prone hardware: Minimizing the number of SWAP gates directly mitigates the error rates when running quantum circuits. In recent years, several approaches have been proposed for minimizing the required SWAP insertions. The proposed exact approaches can only scale to a small number of qubits. Proving that a number of swap insertions is optimal is much harder than producing near optimal mappings. In this paper, we provide two encodings for Optimal Layout Synthesis as a classical planning problem. We use optimal classical planners to synthesize the optimal layout for a standard set of benchmarks. Our results show the scalability of our approach compared to previous leading approaches. We can optimally map circuits with 9 qubits onto a 14 qubit platform, which could not be handled before by exact methods.

翻译：在布局合成中，量子电路的逻辑量子比特被映射到给定量子硬件平台的物理量子比特上，同时需考虑物理量子比特间的连接性。这要求在远距离量子比特上执行操作前插入SWAP门。对于当前易出错的硬件，量子电路的实际应用而言，最优布局合成至关重要：最小化SWAP门数量可直接降低运行量子电路时的错误率。近年来，研究者提出了多种最小化所需SWAP插入次数的方法。现有精确方法仅能扩展至少量量子比特。证明SWAP插入次数的最优性远比生成近似最优映射困难。本文提出两种将最优布局合成编码为经典规划问题的方法。我们使用最优经典规划器对一组标准基准测试进行最优布局合成。实验结果表明，相较于先前领先方法，我们的方法具有可扩展性。我们首次实现了将含9个量子比特的电路最优映射至14量子比特平台，这是此前精确方法无法处理的规模。