Narrative extraction algorithms construct storylines by finding coherent paths through document collections. The Narrative Trails algorithm frames this as maximum-capacity path optimization, where path quality depends on a coherence function measuring document relationships. We introduce quantum kernels as coherence functions for narrative extraction—to the best of our knowledge, the first systematic characterisation of quantum kernel methods for storyline extraction—and compare them against classical baselines on two corpora using a multi-seed protocol. The sweep covers 93 method evaluations (54 quantum kernels across three encoder families—RY+CNOT-ring, IQP/ZZ-feature-map, and a projected quantum kernel—and 39 classical kernels—cosine, RBF, and the cluster-aware Narrative Trails baseline). On 11,215 human navigation paths from Wikispeedia, evaluation metrics divide into two clusters that disagree with each other: alignment-based metrics (length-normalised DTW and per-step DTW similarity) favour methods that produce long alignment-rich paths, while set-overlap metrics (Jaccard and F1) favour methods that produce shorter paths with higher article overlap. On LLM-judged coherence for Cuban news storylines, evaluated under a 12-method × 5-seed × 30-endpoint-pair × 2-judge design (Claude Sonnet 4.5 and GPT-4o, both at T=0 via structured tool calling), the cluster-aware classical baseline is the top method in terms of mean overall coherence; the 5-method quantum-kernel pool and the 7-method classical-kernel pool on matched projection input show no significant differences after Holm correction. Cross-task analysis reveals that LLM coherence rank correlates with alignment-cluster Wikispeedia metrics (Spearman ρ≈+0.70) and anti-correlates with overlap-cluster metrics (ρ≈−0.62). A closed-form theoretical analysis shows that the depth-1 RY+CNOT-ring kernel reduces to a classical product-of-cosines kernel order equivalent to RBF, explaining the absence of empirical separation at low depth; deeper encoders break the cancellation but exponentially concentrate kernel values, eroding inter-pair distinguishability. Our results characterise quantum coherence kernels as competitive with classical kernels on the same projected input rather than decisively superior, with the cluster-aware classical baseline retaining a modest advantage attributable to its explicit topical structure.
Keith-Norambuena et al. (Mon,) studied this question.