Quantum Walk — Decoherence & Localization

A coined quantum walk on the line uses a Hadamard coin to create superposition, spreading as σ ~ t (ballistic) vs classical σ ~ √t (diffusive). Decoherence (random measurement noise) destroys quantum coherence and drives a transition to classical diffusion. Disorder induces Anderson localization, confining the probability distribution exponentially.

Step: 0 | σ = 0