  Quantum algorithms implemented on near-term devices require qubit mapping due
to noise and limited qubit connectivity. In this paper we propose a strategy
called algorithm-oriented qubit mapping (AOQMAP) that aims to bridge the gap
between exact and scalable mapping methods by utilizing the inherent structure
of algorithms. While exact methods provide optimal solutions, they become
intractable for large circuits. Scalable methods, like SWAP networks, offer
fast solutions but lack optimality. AOQMAP bridges this gap by leveraging
algorithmic features and their association with specific device substructures
to achieve optimal and scalable solutions. The proposed strategy follows a two
stage approach. First, it maps circuits to subtopologies to meet connectivity
constraints. Second, it identifies the optimal qubits for execution using a
cost function. Notably, AOQMAP provides both scalable and optimal solutions for
variational quantum algorithms with fully connected two qubit interactions on
common subtopologies including linear, T-, and H-shaped, minimizing circuit
depth. Benchmarking experiments conducted on IBM quantum devices demonstrate
significant reductions in gate count and circuit depth compared to Qiskit,
Tket, and SWAP network. Specifically, AOQMAP achieves up to an 82% reduction in
circuit depth and an average 138% increase in success probability. This
scalable and algorithm-specific approach holds the potential to optimize a
wider range of quantum algorithms.
