Barren Plateaus in Quantum Neural Networks*

Variational quantum-classical algorithms (VQCAs), and more generally Quantum Neural Networks (QNNs), optimize the parameters of a gate sequence, V, to minimize a cost function, C. It is believed that VQCAs and QNNs will enable the first practical applications of noisy quantum computers. Recently it has been shown that the cost training landscape can exhibit the so-called barren-plateau phenomena, where the gradients of C vanish exponentially with the system size and makes the architectures non-scalable. In this talk we first discuss the importance of performing rigorous scaling analysis on the trainability of VQAs and QNNs, and we argue that such study should be a stable for the community. 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 dissipative perceptron-based QNN. For both of these we provide conditions under which the parameter trainability can be guaranteed, and we connect the notion of locality of the cost with its trainability.