Quantum Random Walk — Interference & Ballistic Spreading
Discrete-time quantum walk: coin operator, probability distribution, σ ∝ t vs √t
Walk Parameters
Steps t =
50
Coin angle θ =
45
°
45°=Hadamard, 0°=identity, 90°=swap
Initial state:
|0⟩
0=|↑⟩, 1=|↓⟩, 2=|+⟩, 3=|i+⟩
Decoherence p =
0.00
▶ Animate Walk
⏹ Stop
Statistics
Mean ⟨x⟩
--
σ (spread)
--
σ/t (ballistic?)
--
P(origin)
--
Entropy S
--
Quantum walk
: σ ∝ t (ballistic)
Classical walk
: σ ∝ √t (diffusive)
Coin C(θ) = [[cosθ, sinθ],[-sinθ, cosθ]]
Interference creates two-peak distribution