  Qubit Mapping is a critical aspect of implementing quantum circuits on real
hardware devices. Currently, the existing algorithms for qubit mapping
encounter difficulties when dealing with larger circuit sizes involving
hundreds of qubits. In this paper, we introduce an innovative qubit mapping
algorithm, Duostra, tailored to address the challenge of implementing
large-scale quantum circuits on real hardware devices with limited
connectivity. Duostra operates by efficiently determining optimal paths for
double-qubit gates and inserting SWAP gates accordingly to implement the
double-qubit operations on real devices. Together with two heuristic scheduling
algorithms, the Limitedly-Exhausitive (LE) Search and the Shortest-Path (SP)
Estimation, it yields results of good quality within a reasonable runtime,
thereby striving toward achieving quantum advantage. Experimental results
showcase our algorithm's superiority, especially for large circuits beyond the
NISQ era. For example, on large circuits with more than 50 qubits, we can
reduce the mapping cost on an average 21.75% over the virtual best results
among QMAP, t|ket>, Qiskit and SABRE. Besides, for mid-size circuits such as
the SABRE-large benchmark, we improve the mapping costs by 4.5%, 5.2%, 16.3%,
20.7%, and 25.7%, when compared to QMAP, TOQM, t|ket>, Qiskit, and SABRE,
respectively.
