Coined Quantum Walk on the Line

A quantum particle walks on a discrete line using a Hadamard coin to create superposition of left/right steps. Unlike classical random walks (σ~√t), the quantum walk spreads ballistically (σ~t) and exhibits characteristic interference fringes with two probability peaks.

Steps: 0 / 150

Coin angle θ: 45°

Initial spin: |↑⟩+i|↓⟩

Hadamard coin:
H = (1/√2)[[1,1],[1,-1]]

Spreading:
Quantum: σ ≈ t/√2
Classical: σ ≈ √t

Entanglement entropy of position-spin grows as walk spreads

Step: 0