Training squared-hinge support vector machines by an explicit QUBO–Ising construction with quantum-annealing execution

Abstract Quantum annealers natively minimize quadratic unconstrained binary optimization (QUBO) problems, yet faithfully compiling continuous convex objectives into discrete binary forms with formal guarantees remains challenging. We present a complete, algebraically verifiable pipeline for training a linear squared-hinge support vector machine on quantum annealing hardware. The construction comprises four stages with rigorous justification: (i) an exact epigraph reformulation eliminating the hinge nonlinearity, (ii) equality conversion via surplus variables with a quadratic penalty whose exactness on the finite binary domain is formally established, (iii) closed-form QUBO coefficients and a provably energy-preserving Ising mapping, and (iv) a moment-based three-component decoder that reconstructs continuous parameters from noisy annealer samples using empirical first- and second-order statistics. We execute this pipeline end-to-end on D-Wave Advantage systems and evaluate under a rigorous protocol with 30 stratified splits, bootstrap confidence intervals, paired tests, and effect sizes. The feature-wise solver achieves 87–89% test accuracy on the Iris benchmark, competitive with classical baselines at this scale. We contribute a fully auditable reduction from convex SVM training to Ising optimization rather than claiming quantum advantage, and explicitly characterize limitations from discretization, embedding overhead, and feature-wise decomposition.