A Simple Quantum Neural Net with a Periodic Activation Function

TL;DR

This paper introduces a simple quantum neural network with a periodic cosine activation function, requiring fewer qubits and gates, and demonstrates its potential for exponential speedup in machine learning tasks.

Contribution

The paper presents a novel quantum neural network architecture with a cosine activation function, showing its efficiency and potential exponential speedup over classical neural networks.

Findings

Network requires only O(n log_2 k) qubits and O(nk) gates.

Numerical experiments on iris and breast cancer datasets show promising results.

Potential for exponential speedup over classical neural networks.

Abstract

In this paper, we propose a simple neural net that requires only $O(nlog_2k)$ number of qubits and $O(nk)$ quantum gates: Here, $n$ is the number of input parameters, and $k$ is the number of weights applied to these parameters in the proposed neural net. We describe the network in terms of a quantum circuit, and then draw its equivalent classical neural net which involves $O(k^n)$ nodes in the hidden layer. Then, we show that the network uses a periodic activation function of cosine values of the linear combinations of the inputs and weights. The backpropagation is described through the gradient descent, and then iris and breast cancer datasets are used for the simulations. The numerical results indicate the network can be used in machine learning problems and it may provide exponential speedup over the same structured classical neural net.