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We demonstrate that it is possible to implement a quantum perceptron with asigmoid activation function as an efficient, reversible many-body unitaryoperation. When inserted in a neural network, the perceptron's response isparameterized by the potential exerted by other neurons. We prove that such aquantum neural network is a universal approximator of continuous functions,with at least the same power as classical neural networks. While engineeringgeneral perceptrons is a challenging control problem --also defined in thiswork--, the ubiquitous sigmoid-response neuron can be implemented as aquasi-adiabatic passage with an Ising model. In this construct, the scaling ofresources is favorable with respect to the total network size and is dominatedby the number of layers. We expect that our sigmoid perceptron will haveapplications also in quantum sensing or variational estimation of many-bodyHamiltonians.

Unitary quantum perceptron as efficient universal approximator