Quantum Kernels for Narrative Coherence: An Application to Path Optimization in Document Graphs for Storyline Extraction
Brian Felipe Keith-Norambuena, Javiera Canales, Maximiliano Araya, Carolina Rojas-Córdova, Claudio Meneses Villegas, Elizabeth Lam-Esquenazi, Angélica Flores-Bustos
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.
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.
Selecting a compact subgraph of a document graph while maximising a learned coherence function, subject to flow conservation and temporal ordering, is important in storyline detection, event threading, and Narrative Map extraction. Existing Narrative Map methods either recover a single optimal path (a Narrative Trail) or solve a linear program with an output size which grows with graph density (Narrative Maps). We propose a hybrid classical–quantum pipeline that casts the problem as a Quadratic Unconstrained Binary Optimisation (QUBO) problem and solves it both with the Quantum Approximate Optimisation Algorithm (QAOA) and with off-the-shelf classical QUBO solvers (simulated annealing, Tabu search) on the same Hamiltonian; this approach uses a classical mean field active space reduction and Matrix Product State tensor network simulation to scale beyond 16 qubits. We evaluate node- and edge-level qubit encodings under a range of QAOA circuit variants (transverse field and XY mixers; classical warm-start deeper circuits) on a 418-document news corpus across four graph densities and ten endpoint pairs, and audit their reproducibility across optimiser seeds. The QUBO formulations—whether solved by QAOA or by classical QUBO solvers on the same Hamiltonian—produce maps averaging 4.7–9.0 nodes versus 26.6 for Narrative Maps (p<10−7) and they are far more focused on their main storyline (main path fraction 0.61–0.99 versus 0.20). The Hamming-weight-preserving XY mixer goes the furthest: the node-level XY mixer variant produces the most compact (4.7 nodes) and most spine-focused (0.99 main path fraction) maps of any method tested, and a multi-seed audit identifies it as the most reproducible of the eight QAOA variants we compared. Main path coherence is on par with Narrative Maps’ and 0.031–0.072 below the bottleneck-optimising baselines—Narrative Trails (0.770) and Iterative Maximin (0.758). These results position QAOA not as a uniformly stronger alternative but as a distinct trade-off region favouring compactness and spine focus over raw bottleneck coherence and corpus topic breadth.
Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive empirical study of quantum kernel support vector machines (QSVMs) across nine binary classification datasets, four quantum feature maps, three classical kernels, and multiple noise models, totalling 970 experiments with strict nested cross-validation.
Our analysis spans four phases: (i) statistical significance testing, revealing that none of 29 pairwise quantum-classical comparisons reach significance at α=0.05; (ii) learning curve analysis over six training fractions, showing steeper quantum slopes on six of eight datasets that nonetheless fail to close the gap to the best classical baseline; (iii) hardware validation on IBM ibm_fez (Heron r2), demonstrating kernel fidelity r≥0.976 across six experiments; and (iv) seed sensitivity analysis confirming reproducibility (mean CV 1.4%).
A Kruskal-Wallis factorial analysis reveals that dataset choice dominates performance variance (ε2=0.73), while kernel type accounts for only 9%. Spectral analysis offers a mechanistic explanation: current quantum feature maps produce eigenspectra that are either too flat or too concentrated, missing the intermediate profile of the best classical kernel, the radial basis function (RBF). Quantum kernel training (QKT) via kernel-target alignment yields the single competitive result -- balanced accuracy 0.968 on breast cancer -- but with ~2,000x computational overhead.
Our findings provide actionable guidelines for quantum kernel research. The complete benchmark suite is publicly available to facilitate reproduction and extension.
Quantum kernel techniques aim to leverage quantum computational capabilities on social data. However, their application to natural language processing tasks faces formidable obstacles, such as extreme dimensionality reduction (D=384→k=8), concentration of measure in quantum feature spaces, and the lack of theoretical understanding of when quantum advantages occur in kernel-based text classification. Filling this gap, we provide a comprehensive study of quantum kernels for text classification that addresses three major challenges in existing studies: general data compression approaches that ignore class structure, the lack of a predictive diagnostic toolkit, and overlooked approaches for handling concentration effects. Our main contributions include a supervised contrastive data compression approach with theoretical guarantees of kernel alignment, a five-diagnostic toolkit connecting theoretical insights with practical performance, the discovery of a small-data regime (n≤200) in which quantum methods perform comparably to classical approaches, and a transparent demonstration that quantum kernels require carefully designed settings to remain competitive with classical counterparts. Across four datasets, evaluated using five random seeds and exact paired statistical testing, we observe that quantum projected kernels achieve an accuracy of 84.5% compared to 85.1% for the classical RBF kernel (p>0.05, not statistically significant) under supervised compression settings. However, quantum methods lag behind by approximately 2%–4% at larger scales due to concentration effects, reflected in reduced off-diagonal kernel variance (0.003 vs. 0.025).
Abstract Quantum kernel approaches have been touted as a possible way to gain representational advantages over classical machine learning techniques however most comparative work only looks at classification accuracy leaving the geometric structure of the kernels unexplored. We carry out a comprehensive kernel-level comparison between classical support vector machines (SVMs) with radial basis function (RBF) kernels and quantum support vector classifiers that use ZZFeatureMap and PauliFeatureMap fidelity kernels, tested on two synthetic and two real-world two-dimensional datasets. After applying centred kernel alignment(CKA), the Hilbert-Schmidt Independence Criterion (HSIC), eigenvalue spectrum analysis, spectral entropy, and effective rank. Firstly, shallow quantum kernels form a moderately aligned band with RBF across all datasets and conditions that is quite stable (CKA : 0.41 → 0.57), whereas going deeper in the circuit to two repetitions largely mismatches both alignment and accuracy with no representational gain (e.g. Iris cross-validation accuracy: 0.920 → 0.670, p = 0.0004). Secondly, depolarising noise surprisingly increases the quantum-classical kernel alignment, which means that near-term hardware kernels are structurally closer to RBF than noiseless simulations suggest. Thirdly, the scenarios that lead to maximum apparent quantum-classical divergence, small sample sizes and low noise, are precisely those most used to benchmark quantum kernel advantage. Kernel-level structural analysis is essential for meaningful evaluation of quantum machine learning methods.
Do quantum kernels improve cross-sectional stock return prediction? We run a controlled horse race on the Chinese A-share market in which a quantum fidelity kernel, a projected quantum kernel, and a classical RBF control share identical training subsamples, solver, and tuning budgets, so that only the kernel is exchanged. On the main evaluation -- a point-in-time universe and 170 walk-forward windows (2012-2025) -- no quantum advantage exists: the fidelity kernel is indistinguishable from its RBF control (ΔIC =+0.005, p=0.42), and a 2×2 design crossing kernel type with training budget (a Nystrom extension to the full ~38,000-observation windows) shows quantum kernels matching, but never beating, equal-budget linear models; after family-wise correction no pairwise difference among eleven models is significant, with point estimates favoring penalized linear regressions throughout. We then document how the opposite conclusion arises: a 60-window evaluation on a universe screened with full-sample information makes the same quantum kernel appear dominant on stability criteria and significantly better than neural baselines. Interaction characteristics from the anomalies literature help nothing, quantum or classical; a widened bandwidth grid reveals an interior optimum rather than the near-classical endpoint a coarse grid suggests; and the geometric difference, while large throughout (g≫1), does not predict out-of-sample gains (ρ=−0.20). We propose protocol standards -- kernel-swap controls, budget-equalized comparisons, point-in-time universes, and multiplicity-robust inference -- for empirical claims of quantum advantage in finance.
We present ThylerSpectral-Audit-Q, a three-layer automated diagnostic framework for quantum kernel pathologies, validated across 124 configurations spanning 7 data domains plus a systematic six-family quantum kernel survey: tabular (digits, diabetes, California housing, covtype), clinical (Iris, Wine, Breast Cancer), quantum-native (V0/V1 ZZFeatureMap, V2 IQPFeatureMap), molecular graph (MUTAG, PTC_FM), industrial (semiconductor proxy, Steel Plates Faults, satellite proxy), time series (AR2, ECG5000 via ZZFeatureMap, QHMM, and TSHK kernels). The kernel survey applies six encoding families (PauliFeatureMap, AngleEncoding, AmplitudeEncoding, EfficientSU2, RandomCircuitKernel, QFTFeatureMap) to three tabular benchmark datasets at n ∈ {4, 6, 8}. Contribution 1 — Diagnostic framework. Three sequential layers — exponential concentration (EC) detection (Shannon effective rank ratio r_eff; five-tier spectral taxonomy), dequantization filter (Tang-Chia eigenvalue truncation), and kernel-target alignment evaluation (centered KTA) — combine into a composite PROCEED/CAUTION/ABORT Spectral Health Card. All four primary datasets (breast cancer, make_moons, Iris, Wine) yield ABORT or CAUTION verdicts under ZZFeatureMap. The framework generalizes: IQPFeatureMap reproduces EC_COLLAPSE at n=8 (r_eff=0.943) without recalibration. A data-kernel structural sensitivity is also detected: the same kernel yields LIKELY_DEQUANTIZABLE on molecular graph data (r_eff=0.153) versus CONFIRMED_DEQUANTIZABLE on tabular data (r_eff=0.095) — a distinction invisible to kernel architecture inspection alone. Contribution 2 — Advantage regime, retired at n_train=150 (v19). At n_train=50, Hamming Quantum Kernel (HQK) on quantum-native data produced the paper's only non-ABORT signal: large effect sizes over SVM-Linear on V2 (IQPFeatureMap) data (d=+0.949–1.015; under the corrected resampled t-test for repeated-CV dependence, p_NB=0.0605 for λ=0.5 and p_NB=0.0485 for λ=0.1 — marginal). Because the pre-registered robustness criterion required corrected significance in both λ configurations, a recovery experiment at n_train=150 was pre-registered (exploracion_010) and has now been executed (S052). Result: every V2 effect size reverses sign — λ=0.5: d=−0.215 (p_NB=0.6375, ns); λ=0.1: d=−1.243 (p_NB=0.0189 — a significant disadvantage, HQK now performing worse than SVM-Linear/RBF) — and the pre-registered effect-size-floor control (d≥0.5 in both λ, designed to distinguish gradual collapse from sign reversal) fails in both configurations. The secondary same-architecture V0/V1 arm also reverses sign (d=+0.27→−0.374 vs Linear, ns). Per the pre-registered decision rule, the cross-architecture advantage claim is retired, not restored. This converges with exploracion_012's finding that V6 — a circuit verified diagonal-unitary by construction but structurally distinct from V0/V1/V2's ZZ/IQP coupling — also shows significant disadvantage at n_train=150 (d=−1.10 to −1.13, p_NB<0.05 in both λ): at the matched n_train=150 standard, no HQK configuration tested in this paper shows a robust advantage over classical baselines. The dual concentration bottleneck — global EC (fidelity collapse) and local EC (Pauli-Z observables ⟨Z_i⟩→0 as n increases) — disables both fidelity kernels and projected quantum kernels simultaneously, and this negative result is now the paper's consistent empirical picture rather than a partial exception to it. A complementary negative structural result: exhaustive hyperparameter optimization over ZZFeatureMap (63 grid configurations: γ × reps × entanglement, plus 100-step continuous variational search) on classical time series data (AR2_n4, r_eff=0.2975) finds zero configurations with Δ_kta > 0 in full audit, confirming that quantum-native data is a necessary but not sufficient structural condition for any advantage signal under the full three-layer audit within the ZZFeatureMap family. The D6 kernel survey further shows that K2 (AngleEncoding) achieves Δ_kta>0 on classical tabular data, but is blocked from PROCEED by the dequantization filter, confirming that Layers 1–2 are essential to prevent false PROCEED verdicts. Contribution 3 — Quantum kernel phase diagram. The 124 audited configurations form a quantum kernel phase diagram in (r_eff × Δ_acc × n_qubits) space with two robustly confirmed empirical phases (ABORT, CAUTION) and measurable phase boundaries, plus a third, provisional phase (PROCEED, 7/124 configs) that has not been re-verified at the n_train=150 standard that retired Contribution 2 above. Seven geometric patterns are observable, including a cross-domain discovery: the STRUCTURED_LOW_RANK regime (0.10 < r_eff ≤ 0.35) appears independently in molecular graph data (r_eff ∈ [0.036, 0.312]) and industrial quality-control data (r_eff=0.22), despite no domain relationship — a finding invisible to kernel architecture inspection alone. Contribution 4 — Domain-agnostic spectral classification. A k-nearest-neighbor classifier trained exclusively on spectral audit features achieves F1-macro=1.000 and MCC=1.000 on an external test set of 20 configurations from three entirely unseen domains: molecular graphs, industrial QC, and time series. Random Forest feature importance reveals dataset_type_code=0% — the framework's diagnostic accuracy is domain-invariant by construction. To the best of our knowledge, ThylerSpectral-Audit-Q is the only pre-execution diagnostic tool integrating EC detection, dequantization filtering, and structural alignment evaluation into a single automated pipeline with an empirical multi-domain phase diagram, validated across 124 configurations spanning 7 data domains and a systematic six-family quantum kernel survey.