2D Quantum Walk Search Algorithm

This canvas simulator runs the same real discrete-time coined quantum walk as the 2D grid search sim — a Hadamard coin mixes a walker's complex amplitude between left and right at every lattice site, then a shift operator moves each coin component to its neighbor — but on a 1D lattice, so the two hallmark effects are easy to read directly off a plot: the quantum walk's interference produces a double-peaked probability distribution that spreads ballistically (variance ∝ t²), plotted live side by side against a classical random walk on the same lattice, whose diffusive spreading only grows variance ∝ t. Flip on search mode to replace the coin at one site with a π phase-flip oracle and watch probability concentrate there in far fewer steps than the classical walk needs — the same quadratic hitting-time speed-up that underlies Grover-style quantum search.