Southwest Quantum Information and Technology

Barren Plateaus in Quantum Neural Networks

Presenting Author: Marco Cerezo, Los Alamos National Laboratory
Contributing Author(s): Akira Sone, Tyler Volkoff, Arthur Pesah, Samson Wang, Andrew T. Sornborger, Lukasz Cincio, Patrick J. Coles

Quantum Neural Networks (QNNs), and Variational Quantum Algorithms (VQAs) have the potential of enabling the first practical applications of quantum machine learning on near-term noisy devices. At their core both QNNs and VQAs train the parameters in a neural networks (or a parametrized quantum circuit) to minimize a cost function which encodes the information of a problem. While many different architectures have been proposed, most of them are heuristic methods with unproven scaling that can guarantee that the optimization can be successful. In fact, one of the few rigorous results which analyze the trainability of the parameters is that the cost landscape can exhibit the so-called barren plateau phenomena, where the cost function gradients vanish exponentially with the system size. In this talk we first discuss the importance of performing rigorous scaling analysis on the trainability of QNNs and VQAs. We then review recent results where we analyze the trainability of two types of QNNs, the first is a parametrized quantum circuit commonly known as a layered hardware efficient ansatz, and the second is a quantum convolutional neural network. For the hardware efficient ansatz, we show that the existence of barren plateaus can be linked to the locality of the cost function. Then, we analyze quantum convolutional neural network and we show that this specific architecture does not exhibit barren plateaus, and hence can be generically trainable.

Read this article online: https://arxiv.org/abs/2001.00550, https://arxiv.org/abs/2011.02966

(Session 5 : Thursday from 12:00pm-2:00 pm)