Discrete Quantum Walk on Integer Line
Ballistic spreading σ~t vs classical diffusive σ~√t; interference from coin superposition
Discrete quantum walk: walker on ℤ with internal coin state |↑⟩,|↓⟩.
Coin operator: C(θ) = [[cos θ, i sin θ],[i sin θ, cos θ]] (unitary).
Shift: S|↑,x⟩=|↑,x+1⟩, S|↓,x⟩=|↓,x−1⟩.
Quantum interference produces ballistic spreading σ~t (vs classical σ~√t).
Hadamard coin (θ=45°) gives asymmetric distribution from unequal initial conditions.