DISCRETE QUANTUM WALK
Coin operator · Quantum spreading · Interference · Ballistic vs diffusive
Coin Bias θ
45°
Steps
100
Coin Type
Hadamard
Grover (2D)
DFT Coin
Initial State
|↑⟩ (right-biased)
|↓⟩ (left-biased)
Balanced |↑⟩+i|↓⟩
σ ≈ —
|ψ_{t+1}⟩ = S·(C⊗I)|ψ_t⟩
Quantum walk spreads as σ~t (
ballistic
), unlike classical random walk σ~√t.
Quantum
interference
creates characteristic double-peak distribution. The Hadamard coin creates asymmetry from |↑⟩ initial state.
Top:
Probability |ψ|² vs position.
Bottom:
Classical (green) vs quantum (purple) comparison.
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