An Efficient Iterative Algorithm for Qubit Mapping via Layer-Weight Assignment and Search Space Reduction

TL;DR

The paper tackles the qubit-mapping problem on near-term quantum devices by minimizing the number of SWAP gates required to satisfy device connectivity. It presents HAIL, an iterative heuristic that combines a layer-weighted, subgraph-isomorphism-based initial mapping with a two-stage SWAP sequence routing and a forward-backward refinement, achieving substantial SWAP reductions (notably $20.62\%$ on IBM Q20 with the $\\mathcal{B}_{23}$ benchmark) compared to state-of-the-art methods. Core contributions include the Layer-Weighted Isomorphism Mapping Algorithm, a Mapping Completion Algorithm, a SWAP Sequence Selection strategy with a post-processing discriminant, and a simplified iterative optimization framework. Empirical results on IBM Q20 and Google Sycamore demonstrate that HAIL and its variant HAIL-imp offer favorable trade-offs between runtime and SWAP-gate reductions across diverse benchmarks and architectures, indicating practical utility for improving near-term quantum circuit performance.

Abstract

Current quantum devices support interactions only between physically adjacent qubits, preventing quantum circuits from being directly executed on these devices. Therefore, SWAP gates are required to remap logical qubits to physical qubits, which in turn increases both quantum resource consumption and error rates. To minimize the insertion of additional SWAP gates, we propose HAIL, an efficient iterative qubit mapping algorithm. Leveraging the inherent parallelism in quantum circuits, a new layer-weight assignment method is integrated with subgraph isomorphism to derive an optimal initial qubit mapping. Moreover, we present a two-stage SWAP sequence search algorithm that effectively identifies the most efficient SWAP sequence by distilling feasible SWAP sequences at different stages. The whole qubit mapping algorithm is then refined through a few iterative bidirectional traversals, further reducing the number of SWAP gates required. Experimental results on the IBM Q20 architecture and various benchmarks show that HAIL-3 reduces the number of additional gates inserted in the $\mathcal{B}_{23}$ by 20.62\% compared to state-of-the-art algorithms. Moreover, we propose a partially extended SWAP sequence strategy combined with HAIL to reduce its time complexity, with experiments on the sparsely connected Google Sycamore architecture demonstrating reductions in both algorithm runtime and additional SWAP gates.

Figures (8)

• Figure 1: Some common basic gates. (a) H gate, (b) Ry($\theta$) gate, (c) CNOT gate, (d) SWAP gate.
• Figure 2: (a) An initial circuit and one of its corresponding mappings to the linear quantum architecture, where the red color indicates that the gates are not executable under the mapping in this architecture, (b) A swap is inserted to enable execution in the linear quantum architecture and mapped accordingly, (c) The qubit interaction graph of the initial circuit.
• Figure 3: The quantum hardware architectures. (a) IBM QX2, (b) IBM QX4, (c) IBM Q20, (d) Google Sycamore.
• Figure 4: Paradigm of initial mapping generation. In Step 1, each gate in the quantum circuit is prioritized based on layer-weight assignment, with the number on the gate representing its weight. In Step 2, for the qubit interaction graph generated by the logical circuit, the weight on each edge is the sum of the weights of the gates acting on the respective qubits. In Step 3, the matching of the subgraph for a specific architecture is completed by gradually adding edges with higher priorities. In Step 4, for the unmapped qubits, their placement locations are determined to complete the mapping.
• Figure 5: Diagram of SWAP sequence insertion. Four CNOT gates cannot be executed in the circuit. After determining the optimal SWAP sequence through a Depth-2 sequence search and the subsequent post-processing stage, the mapping relationship is adjusted to ensure the execution of three CNOT gates.