PHoTE: Photonic Quantum-Walk Encodings for Temporal Link Prediction

Jointly learning graph structure and temporal dependencies can make temporal link prediction computationally expensive. Precomputed features avoid structural-encoder optimization, yet their usefulness depends on which information they retain. We introduce PHoTE, a photonic framework combining non-trainable continuous-time quantum-walk encodings with a learned temporal predictor. One- and two-photon statistics at multiple evolution times are projected into identity-sensitive features or reduced to role summaries, yielding four encodings. Features are precomputed per snapshot; only a recurrent readout shared across nodes and a link scorer are trained. We evaluate PHoTE against nine temporal baselines, two classical positional encodings, and two heuristics on nine real networks and 53 synthetic settings from T-GRAB. The two-photon encoding achieves higher mean test average precision than the evaluated temporal baselines and classical encodings on eight of nine real networks. Across its four variants, PHoTE attains or ties the highest mean $F_1$ in five of seven synthetic task–metric comparisons. The identity-sensitive encodings also approach the optimal expected-count $F_1$ reference for stochastic periodicity. After feature precomputation, training takes $0.1$–$9.6$ seconds per epoch, compared with $1.0$–$783.3$ seconds for baselines on the same task families. One-photon measurements from a 24-mode processor yield AP comparable to that obtained with analytic features on the full test snapshots of a 13-node Guinea baboon contact network. Results support non-trainable photonic encodings for temporal prediction and demonstrate small-scale hardware feasibility. Although the present encodings are classically simulable, these results motivate exploring richer encodings on future multiphoton quantum processors.