Neural Network Cost Landscapes as Quantum States

Abdulah Fawaz, Sebastien Piat, Paul Klein, Peter Mountney, Simone Severini

Abstract: Quantum computers promise significant advantages over classical computers for a number of different applications. We show that the complete loss function landscape of a neural network can be represented as the quantum state output by a quantum computer. We demonstrate this explicitly for a binary neural network and, further, show how a quantum computer can train the network by manipulating this state using a well-known algorithm known as quantum amplitude amplification. We further show that with minor adaptation, this method can also represent the meta-loss landscape of a number of neural network architectures simultaneously. We search this meta-loss landscape with the same method to simultaneously train and design a binary neural network.

Keywords: quantum, neural networks, meta-learning

TL;DR: We show that NN parameter and hyperparameter cost landscapes can be generated as quantum states using a single quantum circuit and that these can be used for training and meta-training.