Algorithm-oriented qubit mapping for variational quantum algorithms

Optimizing qubit mapping is critical for the successful implementation of algorithms on near-term quantum devices. In this paper we present an algorithm-oriented qubit mapping (AOQMAP) that capitalizes on the inherent regular substructures within quantum algorithms. While exact methods provide optimal solutions, their exponential scaling renders them impractical. AOQMAP addresses this challenge through a strategic two-step approach. First, it adapts circuits onto subtopologies of the target quantum device to satisfy connectivity constraints. Optimal and scalable solutions with minimum circuit depth are provided for variational quantum algorithms with all-to-all connected interactions on linear, T-shaped, and H-shaped subtopologies. Second, it identifies the optimal mapping scheme by using a cost function based on current device noise. Demonstrations on various IBM quantum devices indicate that AOQMAP significantly reduces both gate count and circuit depth compared to traditional mapping approaches, consequently enhancing performance. Specifically, AOQMAP achieves up to 82.1% depth reduction and a 138% average increase in success probability compared to Qiskit, Tket, and SWAP network. This specialized and scalable mapping paradigm can potentially optimize broader quantum algorithm classes. Tailoring qubit mapping to leverage algorithmic features holds the promise of maximizing the performance of near-term quantum algorithms.