# A Simple Quantum Neural Net with a Periodic Activation Function

arXiv: https://arxiv.org/abs/1804.07633 · HTML: https://mlsanity.com/paper/1804.07633/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2018.

## Built on by (most cited first, 7 of 7)

- [Quantum activation functions for quantum neural networks](https://mlsanity.com/paper/2201.03700/) (2022)
- [The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning](https://mlsanity.com/paper/2212.11826/) (2022)
- [A Quantum Hopfield Associative Memory Implemented on an Actual Quantum Processor](https://mlsanity.com/paper/2105.11590/) (2021)
- [A walk through of time series analysis on quantum computers](https://mlsanity.com/paper/2205.00986/) (2022)
- [A unifying primary framework for quantum graph neural networks from quantum graph states](https://mlsanity.com/paper/2402.13001/) (2024)
- [On the explainability of quantum neural networks based on variational quantum circuits](https://mlsanity.com/paper/2301.05549/) (2023)
- [A Simple Quantum Blockmodeling with Qubits and Permutations](https://mlsanity.com/paper/2311.07726/) (2023)

## Abstract (arXiv)

In this paper, we propose a simple neural net that requires only O(nlog2k) 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(kn) 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.