Unitary quantum perceptron as efficient universal approximator

TL;DR

This paper introduces a quantum perceptron model with a sigmoid activation function, demonstrating its efficiency, universality in function approximation, and potential applications in quantum sensing and variational estimation.

Contribution

It presents a novel quantum perceptron implementation as a reversible unitary operation and proves its universality as a function approximator, with scalable resource requirements.

Findings

Quantum perceptron implemented as a reversible unitary operation.

Proven to be a universal approximator of continuous functions.

Resource scaling is favorable with network depth.

Abstract

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.