Fig. 4: Spectrum gap of the effective Hamiltonian in Schrödinger interpretation of QNN in the example of XXZ model.
From: Dynamical transition in controllable quantum neural networks with large depth
The spectrum gap of Hessian matrix of the effective Shrödinger dynamics in t → ∞ (black). The gapless transition point corresponds to \({O}_{0}={O}_{\min },{O}_{\max }\) (red triangles). The orange line represents the QNTK \({\lim }_{t\to \infty }\overline{K}\). Inset shows the Hessian spectrum of the largest 10 eigenvalues for the three cases \({O}_{0} \gtreqless {O}_{\min }\) marked by triangles. The RPA consists of D = 64 layers (equivalently L = 64 parameters) on n = 2 qubits. The parameters in XXZ model is J = 2.
