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.
Related
- Emergence of Strategic Equilibria from Transverse Field Ising Hamiltonian Dynamics
- A VQE simulation of the transverse field Ising model
- Preparation of a Bell state in an analogue device hosting the transverse-field Ising model
- Exact solution of a boundary-driven transverse-field Ising model with hidden time-reversal symmetry
- Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain
BibTeX
@misc{djellabi2026expressive,
title = {{On the Expressive Power of the Transverse-Field Ising Model for Graph Learning}},
author = {Mehdi Djellabi and Louis-Paul Henry},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.17750},
eprint = {2608.17750},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17750},
}
RIS
TY - UNPB
TI - On the Expressive Power of the Transverse-Field Ising Model for Graph Learning
AU - Mehdi Djellabi
AU - Louis-Paul Henry
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2608.17750
UR - https://arxiv.org/abs/2608.17750
AB - 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.
ER -