VQE Ansatz: Ring Diagram & Barren Plateaus (2D)

The same real hardware-efficient VQE ansatz as the 3D geometric simulator — a genuine complex statevector of up to 32 amplitudes, alternating RY/RZ layers, a CNOT entangling ring, and a parameter-shift gradient descent minimizing an antiferromagnetic Ising-ring Hamiltonian H = Σ ZᵢZᵢ₊₁ — redrawn through three 2D-native diagrams instead of 3D Bloch arrows: a qubit coupling-ring graph whose node colors are single-qubit ⟨Zᵢ⟩ expectations and whose edge colors are genuine two-qubit ⟨ZᵢZᵢ₊₁⟩ correlators (the graph-theoretic signature of entanglement), a live energy-vs-iteration curve against the brute-force classical ground energy, and a per-parameter gradient heatmap that visibly dims as the ansatz grows — a direct, quantitative view of the barren-plateau training problem limiting today's NISQ-era variational algorithms.