Quantum Annealing Minimum-Gap Explorer

Quantum annealers like D-Wave solve optimization problems by slowly morphing a Hamiltonian from an easy-to-prepare quantum driver into the classical cost function you actually want minimized, letting the system ride its instantaneous ground state down to the answer. This simulator exactly diagonalizes a real 5-spin transverse-field Ising ring — a genuine 32-dimensional Hilbert space, no approximation — at every point of that sweep, so the ground energy, the excitation gap, and every spin's polarization are all physically real numbers, not a canned animation. Pick a ferromagnetic, frustrated antiferromagnetic, or randomly-coupled ring, then watch how geometric frustration shrinks the minimum gap and makes a fast sweep far more likely to jump into the wrong (excited) state — the Landau-Zener effect that limits how fast a real quantum annealer can run.