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 7 qubits onto a 16 qubit platform, which could not be handled before by exact methods.

翻译：在布局综合中，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，同时考虑物理量子比特间的连接性。这涉及在对远程量子比特执行操作前插入SWAP门。对于当前易出错的硬件平台，最优布局综合对实用量子计算至关重要：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，已有多种方法被提出以最小化所需SWAP插入次数。现有精确方法仅能扩展到少量量子比特场景。证明SWAP插入次数的最优性远比生成近优映射更为困难。本文提出两种将最优布局综合编码为经典规划问题的方法，并采用最优经典规划器对标准基准测试集进行最优布局综合。实验结果表明，与先前领先方法相比，本方法具有可扩展性优势。我们首次实现了将含7个量子比特的电路最优映射至16量子比特平台，这是此前精确方法无法处理的情形。