DISCRETE QUANTUM WALK

Coin operator · Quantum spreading · Interference · Ballistic vs diffusive
σ ≈ —
|ψ_{t+1}⟩ = S·(C⊗I)|ψ_t⟩
Quantum walk spreads as σ~t (ballistic), unlike classical random walk σ~√t.

Quantum interference creates characteristic double-peak distribution. The Hadamard coin creates asymmetry from |↑⟩ initial state.

Top: Probability |ψ|² vs position.
Bottom: Classical (green) vs quantum (purple) comparison.