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<p>The qubit mapping problem (QMP) addresses the routing of qubits in quantum circuits to comply with the limited connectivity of near-term quantum hardware. Solving QMP is a key step in quantum circuit compilation and is known to be NP-complete. This paper proposes a novel approach called adaptive divide-and-conquer (ADAC), which uses subgraph isomorphism check to partition the circuit and construct the initial mapping and employs a heuristic search strategy for efficient qubit routing. Extensive experiments on various NISQ architectures demonstrate that ADAC significantly outperforms state-of-the-art methods. For example, on IBM Tokyo, it achieves over 50% SWAP gate reduction on realistic benchmarks from RevLib and Qiskit. Although ADAC incurs additional runtime and memory usage due to its quality-focused design, these overheads remain well within practical limits, especially for near-term quantum circuits with moderate gate counts. Crucially, the resource cost scales more with gate count than with qubit count, making ADAC both efficient and scalable for small- to medium-sized circuits. Its high mapping quality and consistent performance render it particularly suitable for offline compilation workflows, benchmarking, and fidelity-sensitive quantum applications. Overall, ADAC represents a robust and scalable framework for structure-aware quantum circuit transformation.</p>

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Qubit mapping: the adaptive divide-and-conquer approach

  • 期刊论文

  • 发表日期：

    2025年7月2日

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  • Yunqi Huang,
  • Xiangzhen Zhou,
  • Fanxu Meng,
  • Sanjiang Li

摘要

The qubit mapping problem (QMP) addresses the routing of qubits in quantum circuits to comply with the limited connectivity of near-term quantum hardware. Solving QMP is a key step in quantum circuit compilation and is known to be NP-complete. This paper proposes a novel approach called adaptive divide-and-conquer (ADAC), which uses subgraph isomorphism check to partition the circuit and construct the initial mapping and employs a heuristic search strategy for efficient qubit routing. Extensive experiments on various NISQ architectures demonstrate that ADAC significantly outperforms state-of-the-art methods. For example, on IBM Tokyo, it achieves over 50% SWAP gate reduction on realistic benchmarks from RevLib and Qiskit. Although ADAC incurs additional runtime and memory usage due to its quality-focused design, these overheads remain well within practical limits, especially for near-term quantum circuits with moderate gate counts. Crucially, the resource cost scales more with gate count than with qubit count, making ADAC both efficient and scalable for small- to medium-sized circuits. Its high mapping quality and consistent performance render it particularly suitable for offline compilation workflows, benchmarking, and fidelity-sensitive quantum applications. Overall, ADAC represents a robust and scalable framework for structure-aware quantum circuit transformation.