  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.
