Quantum Tic-Tac-Toe

A qubit simulator built on a tic-tac-toe board. Each cell on the board is a qubit with real complex amplitudes, gate operations, and probabilistic collapse. Not a gimmick — the physics is actually correct.

Built with C++ and SFML 3.

What it is

Each of the 9 cells holds a qubit in superposition. You manipulate qubits using quantum gates via a command line interface, then measure them to collapse their state to 0 or 1. The probabilities are real — amplitudes are stored as complex numbers, gates are matrix multiplications, and measurement samples from the actual probability distribution.

Commands

• select X Y      select a qubit at position X Y (1-indexed)
• hadamard        apply Hadamard gate — puts qubit into 50/50 superposition
• rotateY <deg>   apply Ry gate — shifts probability toward 0 or 1
• rotateZ <deg>   apply Rz gate — rotates phase without changing probability
• measure         collapse the qubit — locks it permanently
• exit            close

How the physics works

A qubit has two complex amplitudes — alpha for |0⟩ and beta for |1⟩. The probability of measuring 0 or 1 is the magnitude squared of each amplitude. Gates are unitary matrices applied to the state vector.

Ry directly shifts probabilities. Ry(180°) on |0⟩ gives 100% chance of measuring 1.

Rz rotates phase only — probabilities don't visibly change. But it changes how subsequent Ry gates behave, making it a trap/setup move.

Hadamard puts the qubit on the equator of the Bloch sphere — perfect 50/50. Applied twice it returns to the original state.

Once measured a qubit is locked. No further gates can be applied.