Quantum Walk Search Algorithm

This simulator runs a real discrete-time coined quantum walk over an N×N grid: a Grover-diffusion coin mixes amplitude among the four neighboring directions at every unmarked vertex, while the single marked vertex applies a π phase flip instead — the walk's oracle. Iterating the coin-then-shift unitary drives probability to concentrate at the marked vertex after roughly √N steps, the same quadratic speed-up Grover's circuit-model algorithm achieves, but produced by purely local graph dynamics. Click any cell to relocate the target, step through the evolution by hand or let it run, and overlay a classical random walk on the same grid to see its Θ(N) hitting time next to the quantum walk's Θ(√N).