Formulation-Level Auto-Tuning for QUBO-Based Machine Learning: A Case Study Across Multiple Quantum-Inspired Annealers

Research Approach

This paper introduces a two-level auto-tuning framework designed to optimize Support Vector Machines (SVMs) running on quantum-inspired annealers. Because these annealers require the SVM dual problem to be converted into a Quadratic Unconstrained Binary Optimization (QUBO) model, the researchers identified that the quality of the classifier depends not just on standard model parameters, but also on the numerical representation used to discretize continuous variables. The framework uses Optuna to manage an outer loop that selects four coupled hyperparameters: the encoding base (B), bit depth (K), RBF kernel parameter (gamma), and the equality-constraint penalty (xi). In each trial, the framework reconstructs the entire QUBO formulation before passing it to the inner-level annealer for execution.

Experimental Setup

The researchers tested this approach across three distinct quantum-inspired platforms: the Fixstars Amplify Annealing Engine, Toshiba SQBM+, and the Fujitsu Digital Annealer. By using a solver-agnostic procedure, they compared their adaptive framework against a conventional grid search baseline. The experiments covered both linear and nonlinear classification tasks, systematically introducing label noise ranging from 0% to 20%. This setup allowed the team to isolate the impact of formulation-level tuning from the intrinsic search capabilities of the hardware backends.

The results demonstrate that treating the QUBO formulation as a tunable object is superior to static parameter selection. On average, the proposed framework achieved accuracy gains of approximately 0.8 percentage points for linear tasks and 2.1 percentage points for nonlinear tasks compared to grid search. The authors conclude that formulation quality and backend capability are deeply intertwined; task-level feedback from the outer loop effectively compensates for discretization errors, penalty imbalances, and the approximate nature of the underlying annealing solvers.