Quantum propagation via Schrödinger evolution on a graph Laplacian
In a continuous-time quantum walk, the walker evolves under H = −γL where L is the graph Laplacian. The state |ψ(t)⟩ = e^{−iHt}|ψ(0)⟩ spreads as a quantum superposition, exhibiting interference and quadratic speedup over classical random walks. This powers quantum search algorithms and transport in photosynthetic complexes.