QUANTUM WALK

1D Discrete Quantum Walk — Hadamard Coin & Interference
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A quantum walker on a line uses a coin operator (Hadamard matrix) to create superposition, then shifts left and right simultaneously. Unlike classical random walks (σ∝√t), quantum walks spread ballistically (σ∝t) due to constructive/destructive interference between paths. The initial coin state |↑⟩e^{iφ} breaks left-right symmetry.