Abstract

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 & times; 5-seed & times; 30-endpoint-pair & times; 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 rho approximate to+0.70) and anti-correlates with overlap-cluster metrics (rho approximate to-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.