Algorithm-Oriented Qubit Mapping for Variational Quantum Algorithms

Abstract: 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 depth-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 and performs postselection among execution results across subtopologies. 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.