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Life sciences · Preprint
arXiv · September 10, 2026
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This preprint describes a quantum spectral feature extraction method (DOS-QPE) applied to learning structural balance in signed graphs via frustration index prediction on synthetic data. The work is theoretical and exploratory, demonstrating that quantum-derived spectral moments can recover an NP-hard graph property with mean error of 0.4 on synthetic benchmarks; no real-world application, clinical relevance, or peer review is reported.
Theoretical methods development with computational benchmark. Synthetic signed graphs of moderate size, labeled with exact frustration index values; no empirical networks or real-world populations studied.. Intervention: Quantum spectral feature extraction via DOS-QPE (phase estimation) on Ising model instantiation of signed graphs. n = 140,000.
On 1.4×10^5 labeled synthetic graphs, exact density-of-states (DOS) determines frustration index exactly Five standardized moments of the Ising DOS recover the frustration index with mean error of 0.4, below one sign flip DOS-QPE samples spectral density with orders of magnitude fewer quantum shots than Hadamard test-based trace sampling
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This is a theoretical and computational methods paper proposing a novel quantum approach to graph analysis; it demonstrates proof-of-concept on a synthetic benchmark with no clinical, biological, or real-world validation data reported.
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We develop a quantum approach to spectral feature extraction from the density of states (DOS) of a problem-dependent Hamiltonian, and apply it to machine learning on signed graphs. We propose to embed a signed graph as an Ising model instance with positive and negative interactions, and use the standardized moments of the Ising DOS as features for learning. We show that these moments count signed closed walks, are switching-invariant, and are size-free by construction. As a benchmark, we target learning the frustration index, an NP-hard measure of structural balance that can be labeled exactly at moderate size. At zero field, the models can be sampled classically, allowing the quantum extraction procedure to be certified against exact ground truth. We propose DOS-QPE, a phase estimation on a purified maximally mixed probe, which samples the spectral density with orders of magnitude fewer shots than Hadamard test-based trace sampling and feeds the resulting features directly into classically trained models. On $1.4\times10^5$ labeled graphs the exact DOS determines the frustration index, and five moments recover it with a mean error of 0.4, well below one sign flip. Beyond zero field, the underlying trace-estimation problem is DQC1-complete, providing access to spectral features for which no efficient classical sampling method is known. Our work opens routes towards quantum applications in social network balance analysis, spin-glass studies, correlation clustering, and protein-interaction networks.
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