Avoiding Barren Plateaus with Classical Deep Neural Networks

Abstract: Variational quantum algorithms (VQAs) are among the most promising algorithms in the era of Noisy Intermediate Scale Quantum Devices. Such algorithms are constructed using a parameterization U($\pmb{\theta}$) with a classical optimizer that updates the parameters $\pmb{\theta}$ in order to minimize a cost function $C$. For this task, in general the gradient descent method, or one of its variants, is used. This is a method where the circuit parameters are updated iteratively using the cost function gradient. However, several works in the literature have shown that this method suffers from a phenomenon known as the Barren Plateaus (BP). In this work, we propose a new method to mitigate BPs. In general, the parameters $\pmb{\theta}$ used in the parameterization $U$ are randomly generated. In our method they are obtained from a classical neural network (CNN). We show that this method, besides to being able to mitigate BPs during startup, is also able to mitigate the effect of BPs during the VQA training. In addition, we also show how this method behaves for different CNN architectures.