Quantum Tic Tac Toe
The LUMS Math Circle session on September 27, titled "Quantum Tic Tac Toe," was a unique and innovative exploration of quantum mechanics led by Dr. Hassan Jaleel and Dr. Muhammad Faryad. Dr. Jaleel introduced the concept by comparing the classic game of tic tac toe, familiar to most students, with its quantum version, which mirrors the differences between classical and quantum science.
He began by asking students to pair up and play traditional tic tac toe, encouraging them to devise strategies to either win or defend, underscoring that every move in the classical game depends entirely on the opponent’s actions.
In this setup, the game represents local actions, where a player’s move only affects their immediate position. A fundamental rule of classical science – the idea that local positions remain unchanged after measurement – parallels the static nature of marks in classical tic tac toe.
To shift gears, Dr. Faryad introduced students to the core principles of quantum science. In contrast to the fixed positions of classical objects, quantum states are not definite until measured. These states, represented by lists of numbers known as Kets, can exist in superpositions and be entangled with other objects. He explained that after measurement, an object’s state collapses to a specific value, but its behavior before that collapse is indeterminate, belonging to what he called the "Unrealistic Universe."
One of the students raised an important question: if the behavior of quantum objects can only be known after collapse, how can we understand their pre-collapse behavior? Dr. Faryad confirmed that in the quantum realm, before collapse, predicting the behavior is impossible due to its inherent randomness.
In the final part of the session, the students were asked to play "Quantum Tic Tac Toe," using the rules of quantum science. Unlike the classical game, multiple objects (or moves) could be placed in a single box, representing superposition, until one collapsed during measurement. The winner was determined by whose objects, with lower Ket values, appeared in a row, column, or diagonal. Adding to the randomness, the collapse of an object was decided by tossing a coin.
The session vividly illustrated the contrast between the deterministic nature of classical science and the probabilistic, uncertain nature of quantum science, leaving students with a sense of wonder about the mysteries of the universe yet to be discovered.
Special thanks to Ms. Noreen Sohail, Mr. Qamar Hussain, and Mr. Javaid Qayyum (the author of this email) for their continued organizational support.
Here are some highlights from the event:
