Discrete quantum walk with Hadamard coin. Unlike classical random walks (σ∝√t), quantum walks spread ballistically (σ∝t). Watch interference create the characteristic twin-peak probability distribution.
Coined quantum walk: |ψ⟩ = Σ(αₓ|x,↑⟩ + βₓ|x,↓⟩). Coin step: C⊗I, Shift step: S|x,↑⟩=|x+1,↑⟩, S|x,↓⟩=|x-1,↓⟩. Hadamard coin: (1/√2)[[1,1],[1,-1]]. Position variance grows as t² (ballistic). Twin peaks at ±t/√2 arise from quantum interference. Grover walk: perfect state transfer. Applications: quantum speedup for spatial search (Childs 2002).