Quantum Walk: Coin-Flip on Lattice

A quantum walker carries an internal "coin" qubit. At each step, a unitary coin flip (Hadamard or other) evolves the coin, then the lattice position shifts based on coin state. Unlike classical diffusion (σ~√t), quantum walks spread ballistically (σ~t), producing an interference pattern with characteristic twin peaks — a purely quantum signature.

Step: 0 | σ (quantum) = 0 | Spread is ballistic ~ t