arXiv:2606. 26873v1 Announce Type: cross Abstract: Graphs provide a natural language for relational data in chemistry, biology and optimisation.
By Snehal Raj, Brian Coyle, L\'eo Monbroussou, Andr\'e J. Ferreira-Martins, Renato M. S. Farias, Elham Kashefi
The paper introduces a quantum method for extracting spectral features from the density of states (DOS) of a problem-dependent Hamiltonian, applied to signed graphs represented as Ising models. Using standardized moments of the Ising DOS as features, the authors demonstrate that these moments count signed closed walks, are switching‑invariant, and size‑free. On a benchmark of 140,000 labeled graphs, the exact DOS predicts the frustration index exactly, while five moments achieve a mean error of 0.4, and a new DOS‑QPE protocol offers efficient sampling with far fewer shots than classical trace‑sampling methods.
By Stefano Scali, Oleksandr Kyriienko
arXiv:2607. 00063v1 Announce Type: cross Abstract: This paper studies how spectral geometry emerges in quantum learning models and how it can be diagnosed with physically grounded probes.
By Santanu Ganguly, Xing Liang, Dimitrios Makris
arXiv:2608.20660v1 Announce Type: cross
Abstract: Simulating a continuous-time quantum walk (CTQW) on a graph in the circuit model of quantum computing requires decomposing its Hamiltonian into terms...
By Mostafa Atallah, Rebekah Herrman, Zain H. Saleem
The paper presents a reinforcement‑learning approach to schedule link‑level entanglement in quantum networks, using a Markov Decision Process and double deep Q‑networks with message‑passing neural networks. The resulting policies achieve 100% success rates even when the link activation probability is reduced by up to 71% compared to baseline heuristics, and maintain at least 80% success when task placements are hardware‑restricted. The authors also develop metrics to interpret the learned policy and employ a large language model to generate a heuristic that matches the DQN performance, suggesting a scalable method for extracting interpretable strategies in large quantum networks.
By Leon Rode, Sumeet Khatri, Supartha Podder
The paper introduces CTQW-GNN, a graph neural network that uses Continuous‑Time Quantum Walks (CTQW) to address two common GNN problems: low‑pass bias on heterophilic graphs and over‑smoothing with deep layers. By exploiting the unitary nature of the CTQW propagator, the model preserves high‑frequency signals and maintains feature norms across layers. Three aggregation modules—CTQW‑based, CTQW‑attention, and a low‑pass GAT branch—combine to handle both heterophilic and homophilic graph structures, supported by spectral‑gap analysis and a Lieb–Robinson‑type bound for walk‑time selection.
By Yuliang Zhan, Zefeng Gao, Jian Li, Yang Liu, Hao sun