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

2025-02-11

AI Summary

To address the problem of excessive SWAP gate insertion—necessitated by limited hardware connectivity in quantum devices—which increases circuit depth and error rates during logical-to-physical qubit mapping, this paper proposes HAIL, an efficient iterative mapping algorithm. Methodologically, HAIL introduces three key innovations: (1) a layer-weighted subgraph isomorphism initialization to enhance initial mapping quality; (2) a bidirectional iterative refinement framework that jointly optimizes qubit mapping and SWAP insertion sequences; and (3) a search-space compression strategy tailored for sparse architectures, complemented by a post-processing heuristic search. Evaluated on IBM Q20 (B23 benchmark), HAIL reduces extraneous SWAP gates by 20.62% over state-of-the-art methods. On Google Sycamore, it simultaneously lowers SWAP overhead and runtime, significantly improving mapping efficiency and circuit executability.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Current quantum devices only support interactions between physical qubits and a limited number of neighboring qubits, preventing quantum circuits from being executed directly on the devices. To execute the circuit, SWAP gates must be inserted to adjust the mapping relationships between qubits, which consequently increases runtime and error rates in quantum circuits. To address these challenges, this paper proposes HAIL, an efficient iterative qubit mapping algorithm to minimize additional SWAP gates. First, a layer-weight assignment method integrated with the subgraph isomorphism algorithm is introduced to establish an initial mapping. Next, we propose a SWAP sequence search combined with the post-processing function to identify the optimal SWAP sequences. Finally, the qubit mapping algorithm is refined through iterative forward and backward traversals to further reduce the number of SWAP gates. Experimental results on the IBM Q20 architecture and various benchmarks demonstrate 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. Additionally, we present a partially extended strategy based on HAIL to reduce the sequence search space, with experiments on the sparsely connected Google Sycamore architecture showing a reduction in both algorithm runtime and additional SWAP gates.

Problem

• Optimizes qubit mapping to minimize SWAP gates
• Reduces quantum circuit runtime and error rates
• Enhances efficiency on sparse quantum architectures

Innovation

• Layer-weight assignment method
• SWAP sequence search optimization
• Iterative qubit mapping refinement