Discrete Quantum Walk — Hadamard Coin

Ballistic spread vs classical diffusion · superposition & interference

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Step t0
σ quantum0
σ classical0
σ ratio Q/C

About

A quantum walker applies the Hadamard coin at each step: H|↑⟩=(|↑⟩+|↓⟩)/√2. The walker moves right on |↑⟩, left on |↓⟩. Quantum interference creates a ballistic spread σ~t, vs classical random walk σ~√t. Two peaks emerge from initial state. Decoherence destroys coherence, recovering classical behavior.
quantum
classical