Storage properties of a quantum perceptron

Artificial neural networks are central for machine learning algorithms and artificial intelligence. The generalization to quantum artificial networks has inspired a lot of research in recent years. Different architectures for quantum perceptrons have been proposed, but the abilities of such a quantum machine remain debated. In this work, we explore the storage capacity of a specific quantum perceptron architecture. We use techniques of statistical mechanics and connect the storage capacity of the quantum perceptron with the theory of spin glasses. As a result, if the activation threshold is close to zero, the storage capacity of the quantum perceptron scales exponentially with the number of physical spins. If the activation threshold is close to one, the storage capacity decreases rapidly. We validate our result numerically and present a phase transition between the spin glass and para-magnetic phase. Finally, the here presented work inspires further studies of quantum neural networks using techniques of statistical physics.