Quantum circuit mapping is a crucial process in the quantum circuit compilation pipeline, facilitating the transformation of a logical quantum circuit into a list of instructions directly executable on a target quantum system. Recent research has introduced a post-compilation step known as remapping, which seeks to reconfigure the initial circuit mapping to mitigate quantum circuit errors arising from system variability. As quantum processors continue to scale in size, the efficiency of quantum circuit mapping and the overall compilation process has become of paramount importance. In this work, we introduce a quantum circuit remapping algorithm that leverages the intrinsic symmetries in quantum processors, making it well-suited for large-scale quantum systems. This algorithm identifies all topologically equivalent circuit mappings by constraining the search space using symmetries and accelerates the scoring of each mapping using vector computation. Notably, this symmetry-based circuit remapping algorithm exhibits linear scaling with the number of qubits in the target quantum hardware and is proven to be optimal in terms of its time complexity. Moreover, we conduct a comparative analysis against existing methods in the literature, demonstrating the superior performance of our symmetry-based method on state-of-the-art quantum hardware architectures and highlighting the practical utility of our algorithm, particularly for quantum processors with millions of qubits.

翻译：量子电路映射是量子电路编译流程中的关键步骤，它将逻辑量子电路转化为可直接在目标量子系统上执行的指令列表。近期研究引入了一种称为重映射的后编译步骤，旨在通过重新配置初始电路映射来缓解由系统差异性引起的量子电路错误。随着量子处理器规模的不断扩展，量子电路映射及整体编译过程的效率变得至关重要。在本工作中，我们提出了一种利用量子处理器固有对称性的量子电路重映射算法，使其特别适用于大规模量子系统。该算法通过对称性约束搜索空间，识别所有拓扑等价的电路映射，并利用向量计算加速每个映射的评分过程。值得注意的是，这种基于对称性的电路重映射算法随目标量子硬件中量子比特数量呈线性扩展，且已被证明在时间复杂度上达到最优。此外，我们与文献中现有方法进行了对比分析，证明我们的基于对称性的方法在最新量子硬件架构上具有优越性能，并凸显了该算法（特别是在拥有百万量子比特的量子处理器上）的实际应用价值。