Fig. 5: Cost versus number of iterations for the quantum autoencoder problem defined by Eqs. (25)–(26).
From: Cost function dependent barren plateaus in shallow parametrized quantum circuits
In all cases we employed two layers of the ansatz shown in Fig. 4, and we set nA = 1, while increasing nB = 10, 15, …, 100. The top (bottom) axis corresponds to the global cost function \(C_{\rm{G}}^{\prime}\) of Eq. (22) (local cost function \(C_{\rm{L}}^{\prime}\) of (23)). As can be seen, \(C_{\rm{G}}^{\prime}\) can be trained up to nB = 20 qubits, while \(C_{\rm{L}}^{\prime}\) trained in all cases. These results indicate that global cost function presents a barren plateau even for a shallow depth ansatz, and this can be avoided by employing a local cost function.
