Tic-tac-toe simulator offers a way to teach quantum physics without matrix algebra

A team from SUNY Polytechnic Institute has designed a quantum rule-based simulator known as Quantum Tic-Tac-Toe. The simulator was originally designed to help students learn abstract concepts in quantum mechanics without using matrix algebra, in a game-like environment. It has rules similar to classical tic-tac-toe but incorporates phenomena from quantum mechanics, such as wavefunction collapse, quantum entanglement and quantum superposition. These concepts are also cornerstones of how quantum computers operate.

The crucial difference is that on every turn, each player can place more than one mark on the board, mimicking the idea that each player is playing multiple “games” based on the superposition of past moves.

This setting substantially increases the number of possible configurations the simulation can produce. It could have as many as 10 billion configurations, compared with fewer than 400,000 in classical tic-tac-toe. Therefore, statistically, it was unclear how the game differed from the classical version.

Dr. Shing-Chi Leung, assistant professor of physics at SUNY Polytechnic Institute, published the article “STEM Project Design: Blending Quantum and Computational Physics with Tic-Tac-Toe” in Physics Education. He co-wrote it with student Quintin Weigand, a senior majoring in computer science.

The paper is based on a student project completed through the Summer Undergraduate Research Program (SURP) in 2025. During the 10-week research internship, students work with faculty mentors and receive research and communication training. At the end of the program, they present their findings during a poster presentation open to the public. Leung worked with Weigand to develop the simulator, using statistical methods to systematically survey the configurations.

For the study, the team revisited the algorithm and highlighted technical difficulties in implementing the simulations. They also discussed how strategies for Quantum Tic-Tac-Toe differ from those for the classical version. By studying more than 10 million configurations, they found convergent behavior in how the game can evolve and developed numerical benchmarks for other instructors to use. They also explored new strategies players can use to improve their chances of winning.

Leung said, “I am glad that this project is an elaborate example of a multidisciplinary project. It combines software engineering in algorithm design to address an interesting problem that cleverly mimics quantum systems. The fact that Quintin built a full-stack structure, where we can visualize the simulation, analyze the results and co-author an article, suggests that our students can achieve interesting results as they work toward a research career.”

Weigand stated, “Visualizing complex topics like quantum interactions in an easily digestible format is a frontier of software engineering. Even with standard software structures, we applied these concepts not just in computer science environments but in computational physics. This shows the many paths one can take in software.”

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