Barren Plateaus in Quantum Neural Network Training

Training a variational quantum circuit means gradient-descending a cost landscape defined over its rotation angles — but for a broad class of quantum-machine-learning ansätze, that landscape provably flattens exponentially as the number of qubits grows, a phenomenon called a "barren plateau" (McClean et al., 2018). This simulator renders an explicit 3D cost surface C(θ₁,θ₂) whose amplitude is scaled by 2⁻⁽ⁿ⁻²⁾ to match that theoretical concentration, lets you tune qubit count, circuit depth and learning rate, and drops a real gradient-descent marker onto the surface so you can watch training work fine at a few qubits and stall almost completely once the plateau sets in.