We demonstrate that it is possible to implement a quantum perceptron with a
sigmoid activation function as an efficient, reversible many-body unitary
operation. When inserted in a neural network, the perceptron's response is
parameterized by the potential exerted by other neurons. We prove that such a
quantum neural network is a universal approximator of continuous functions,
with at least the same power as classical neural networks. While engineering
general perceptrons is a challenging control problem --also defined in this
work--, the ubiquitous sigmoid-response neuron can be implemented as a
quasi-adiabatic passage with an Ising model. In this construct, the scaling of
resources is favorable with respect to the total network size and is dominated
by the number of layers. We expect that our sigmoid perceptron will have
applications also in quantum sensing or variational estimation of many-body
Hamiltonians.

该研究论文证明了可以利用一个可逆的、多体的单元操作实现具有 Sigmoid 激活函数的量子感知器，并且在神经网络中插入该感知器可以构成一个连续函数的普适逼近器。这一构造中所需的资源随着网络总规模的变大而缩小，并主要由层数决定。最后，该研究还探讨了这种 Sigmoid 感知器在量子传感或多体哈密顿量变分估计方面的应用。