A continuous-time quantum walk (CTQW) evolves a quantum state under the Hamiltonian H = −γA, where A is the graph adjacency matrix: |ψ(t)⟩ = e^{−iHt}|ψ(0)⟩. Unlike classical random walks (probability ∝ t^{1/2} spread), CTQWs spread ballistically (∝ t) due to quantum interference. On a line: probability peaks appear at ±γt (Lieb-Robinson bound), with interference fringes between. On a cycle: the walk wraps and interferes with itself. The Anderson localization effect (disorder W > 0) can suppress transport by destructive interference. On complete graphs: the walk visits all nodes coherently in O(1) time — the basis for Grover search speedup (quadratic) and graph traversal algorithms. Probability |ψ_n|² is shown as bar height; phase is shown as color.