QAOA Max-Cut Contour Map

The Quantum Approximate Optimization Algorithm tackles Max-Cut by alternating a cost unitary and a mixer unitary, then classically tuning the two angles γ and β to maximize the expected number of cut edges. Rather than a rotated 3D terrain, this simulator renders the objective function E(γ,β) it is trying to maximize as a flat 2D topographic contour map, built from a full statevector simulation on a small graph, with colour bands and isolines standing in for elevation. Drag the angle sliders to move a marker across the map and watch the live expectation value change, or launch a finite-difference gradient-ascent climb and watch its traced path hunt for a peak the way a real hybrid quantum-classical training loop does — including getting stuck on a local optimum, the central practical difficulty of variational quantum algorithms.