Adiabatic Quantum Optimization: Energy Gap Simulator

Quantum annealers and QAOA both lean on the same physical principle: the adiabatic theorem. This simulator encodes a small MaxCut-style graph problem as an Ising Hamiltonian, interpolates smoothly from an easy-to-prepare initial Hamiltonian to the problem Hamiltonian, and numerically integrates the Schrödinger equation for up to four coupled spins in real time. Watch the instantaneous energy spectrum and its minimum gap as the sweep parameter s advances, then control how fast the sweep runs — slow enough respects the adiabatic condition and the system lands in the true optimum; too fast and it jumps to an excited, wrong answer, exactly as it does on real quantum annealing hardware.