Quantum Annealing Spectrum Explorer: Avoided Crossings & Landau-Zener

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 2D 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, then plots the entire 32-level energy spectrum as a fan diagram so you can see every avoided crossing the system threads, not just the narrowest one. A live 2D spin-ring diagram tracks every qubit's real-valued polarization, and a dedicated Landau-Zener curve plots the diabatic-jump probability continuously against sweep time so you can see the whole exponential safety margin at a glance. Pick a ferromagnetic, frustrated antiferromagnetic, or randomly-coupled ring and watch how geometric frustration collapses the minimum gap and pushes the safe sweep time out by orders of magnitude.