On the Expressive Power of the Transverse-Field Ising Model for Graph Learning

Abstract:We study the quantum evolution induced by graph-indexed Ising Hamiltonians as a source of structural signal for graph learning. Graph automorphisms preserve symmetries of the Hamiltonian, and these symmetries constrain the quantum evolution in a way that turns time-dependent local measurements into informative probes of graph structure. Leveraging this idea, we introduce QDAGer, a quantum-inspired graph-pair Transformer that injects quantum-dynamical features from time series of node occupations and connected two-point correlators directly into the attention mechanism. We apply QDAGer to learning Graph Edit Distance (GED), an NP-hard similarity measure, using either a direct permutation-invariant embedding discrepancy or an alignment-based surrogate loss. Experiments on multiple GED benchmarks under different edit cost settings show that the proposed dynamical features provide a stronger inductive bias than classical structural alternatives under the same training protocol. In addition, we report ablations where the dynamical signal is replaced by standard random-walk and heat-kernel features while keeping the architecture fixed, highlighting that the gain comes from the injected dynamics rather than model capacity alone.

arXiv:2608.17750 [quant-ph]

(or arXiv:2608.17750v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.17750 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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