QAOA Protein Folding: 3D Lattice Walk

This is the genuine three-dimensional companion of the 2D QAOA protein-folding visualization: the same hydrophobic-polar (HP) lattice model — introduced by Ken Dill in 1985 — and the same QAOA cost/mixer circuit pipeline, but the backbone conformation is now a real self-avoiding walk on a 3D cubic lattice (six possible turn directions per bond instead of four on a 2D square lattice), rendered with genuine WebGL depth and a free-orbit camera rather than a flat canvas projection. Hydrophobic (H, orange) and polar (P, blue) residues are placed by the same coarse-graining rule as the 2D original; non-adjacent H residues that land on lattice-neighboring cells form the favorable H-H contacts (yellow, pulsing) whose count sets the HP energy, exactly as in the classic Dill formulation and its turn-encoded QAOA implementations (e.g. Robert et al. 2021, npj Quantum Information). The QAOA Depth slider changes the number of alternating cost/mixer layers shown in the live circuit panel and used in the gate-count estimate; Chain Length reseeds a new self-avoiding walk of that many residues; Reseed draws a fresh random fold at the same length without changing it.