Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Djellabi, Mehdi, Henry, Louis-Paul
Institution: Pasqal (France)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203775983