Quantum Sinusoidal Neural Networks

TL;DR

This paper introduces a quantum neural network with sinusoidal activation functions, develops a quantum optimization algorithm to find optimal weights, and compares its performance to classical training methods, showing potential advantages in avoiding local minima.

Contribution

It presents the first quantum sinusoidal neural network, a quantum optimization algorithm for training, and a comparative analysis with classical methods.

Findings

Quantum sine circuit effectively implements sinusoidal activation.

Quantum training algorithm guarantees finding global minimum weights.

Classical training often gets stuck in poor local minima.

Abstract

We design a quantum version of neural networks with sinusoidal activation functions and compare its performance to the classical case. We create a general quantum sine circuit implementing a discretised sinusoidal activation function. Along the way, we define a classical discrete sinusoidal neural network. We build a quantum optimization algorithm around the quantum sine circuit, combining quantum search and phase estimation. This algorithm is guaranteed to find the weights with global minimum loss on the training data. We give a computational complexity analysis and demonstrate the algorithm in an example. We compare the performance with that of the standard gradient descent training method for classical sinusoidal neural networks. We show that (i) the standard classical training method typically leads to bad local minima in terms of mean squared error on test data and (ii) the weights that perform best on the training data generalise well to the test data. Points (i) and (ii) motivate using the quantum training algorithm, which is guaranteed to find the best weights on the training data.