A Quantum Machine Learning Algorithm for Solving Binary Constraint Problems

Variational quantum algorithms (VQAs) are a leading approach in quantum machine learning (QML) for training parameterized models on structured tasks. We introduce a variational framework for learning measurement strategies in the Magic Square Game (MSG), encoding its winning condition into a value Hamiltonian and training circuits to minimize the cost, akin to supervised learning on a structured dataset. We validate the method in noiseless simulations and discuss its broader applicability to QML-based strategy discovery.