Fig. 13: Poincaré diagram of fixed points for QNN dynamics with two data.
From: Quantum-data-driven dynamical transition in quantum learning
The top and bottom panels show exponential and polynomial convergence classes with frozen-kernel, frozen-error, mixed-frozen (a–c) and critical point, critical-frozen-kernel, critical-frozen-error (d–f). Colored dots represent different physically accessible fixed points with different initialization of training parameters. Black horizontal and vertical dashed lines indicate \(\det (M)=0\) and \({\rm{tr}}(M)=0\) for reference. Gray dashed curve shows \({\rm{tr}}{(M)}^{2}=4\det (M)\), a criteria to determine whether there exists a spiral surrounding the fixed point. All settings are the same as in Fig. 2.
