VQE Ansatz: Entanglement & Barren Plateaus

This simulator runs a real hardware-efficient VQE ansatz — alternating RY/RZ single-qubit rotation layers with a ring of CNOT entanglers — on a genuine complex statevector of up to 32 amplitudes (5 qubits), then visualizes each qubit's reduced Bloch vector in 3D, obtained by an exact partial trace. A parameter-shift gradient descent minimizes an antiferromagnetic Ising-ring Hamiltonian H = Σ ZᵢZᵢ₊₁, the same class of spin Hamiltonian used as a standard VQE benchmark. Watch the Bloch arrows pull inward as entanglement grows, and watch the average gradient magnitude shrink as the ansatz gets deeper and wider — a small, hands-on demonstration of the barren-plateau training problem that limits today's NISQ-era variational algorithms.