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

Abstract

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.