Quantum amplitude propagation governed by the graph Laplacian
The continuous-time quantum walk evolves as |psi(t)> = exp(-i*gamma*L*t)|psi_0> where L is the graph Laplacian and gamma is the hopping rate. Unlike classical diffusion, quantum amplitudes interfere, enabling quadratically faster graph search. Node color encodes quantum phase; size encodes probability. Click a node to relocalize.