Quantum Walk — Coined Walk on a Line (Interference)

The coined quantum walk uses a Hadamard-like coin:
C(θ) = [[cos θ, sin θ],[sin θ, −cos θ]]

After t steps, classical walk spreads as σ ~ √t (diffusive). Quantum walk spreads as σ ~ t (ballistic) — quadratic speedup.

Interference between left-moving and right-moving amplitudes creates the characteristic two-peaked distribution with quantum oscillations between.

Applications: quantum search (Grover, O(√N)), quantum transport in photosynthesis, universal quantum computation.