Figure 16
From: Robustness of quantum reinforcement learning under hardware errors
Simulation results of evaluating the trace of the Hessian matrix for two different hardware-efficient ansatzes with random values of the parameters. The plot on the left is obtained using the layer template shown in the figure for \(n=6\) qubits and \(l = 6\) layers. The plot on the right instead with \(n=5\) and \(l=5\) layers of the template shown in the corresponding inset. The simulations are performed by sampling 2000 random parameter vectors \(\boldsymbol{\theta}_{m}\) with \(\theta _{i} \sim \operatorname{Unif}[0,2\pi [\), evaluating the trace of the Hessian matrix \(\operatorname{Tr} [H(\boldsymbol{\theta})]\), and then building the histogram to show its frequency distribution. In both experiments the measured observable is \(Z^{\otimes n}\). The length of the arrows are respectively: “Numerical 2σ” (black solid line) twice the numerical standard deviation, “Approximation” (dashed red) twice the square root of the approximation in Eq. (B.45), “Bound” (dashed-dotted green) twice the square root of the upper Bound in Eq. (B.41). These parametrized circuits correspond to the templates BasicEntanglinLayer and Simplified2Design defined in Pennylane [80], and used for example in [55] to study barren plateaus