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

Area of Science:

• Quantum Computing
• Machine Learning
• Optimization

Background:

• Quantum annealers are designed for Quadratic Unconstrained Binary Optimization (QUBO) problems.
• Compiling continuous convex objectives into discrete binary forms for quantum annealers is challenging.
• Support Vector Machines (SVMs) are a powerful supervised learning model.

Purpose of the Study:

• To present a complete, algebraically verifiable pipeline for training a linear squared-hinge SVM on quantum annealing hardware.
• To demonstrate a rigorous method for reducing convex SVM training to Ising optimization.

Main Methods:

• An epigraph reformulation to eliminate hinge nonlinearity.
• Equality conversion using surplus variables with a formally established quadratic penalty.
• Derivation of closed-form QUBO coefficients and an energy-preserving Ising mapping.
• A moment-based decoder to reconstruct continuous parameters from noisy quantum annealer samples.

Main Results:

• The pipeline was executed end-to-end on D-Wave Advantage systems.
• A feature-wise solver achieved 87-89% test accuracy on the Iris benchmark.
• Performance was competitive with classical baselines at this scale.

Conclusions:

• A fully auditable reduction from convex SVM training to Ising optimization was achieved.
• Limitations including discretization, embedding overhead, and feature-wise decomposition were characterized.
• The study contributes a verifiable method for applying quantum annealing to machine learning tasks.