A Game-Theoretic Quantum Algorithm for Solving Magic Squares

Conference · Mon Sep 01 00:00:00 EDT 2025

DOI:https://doi.org/10.1109/QCE65121.2025.00264· OSTI ID:3002500

Chehade, Sarah ^[1]; Delgado, Andrea ^[1]; Wong, Elaine ^[1]

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1. ORNL

Variational quantum algorithms (VQAs) offer a promising near-term approach to finding optimal quantum strategies for playing non-local games. These games test quantum correlations beyond classical limits and enable entanglement verification. In this work, we present a variational framework for the Magic Square Game (MSG), a two-player non-local game with perfect quantum advantage. We construct a value Hamiltonian that encodes the game’s parity and consistency constraints, then optimize parameterize quantum circuits to minimize this cost. Our approach build on the stabilizer formalism, leverages commutation structure for circuit design, and is hardware-efficient. Compared to existing work, our contribution emphasizes algebraic structure an interpretability. We validate our method through numerical experiments and outline generalizations to larger games.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 3002500
• Resource Type: Conference paper/presentation
• Conference Information: IEEE International Conference on Quantum Computing and Engineering - QCE25 - Albuquerque, New Mexico, United States of America - 8/31/2025-9/5/2025
• Country of Publication: United States
• Language: English