# Efficient Quantum Circuits for Machine Learning Activation Functions including Constant T-depth ReLU

arXiv: https://arxiv.org/abs/2404.06059 · HTML: https://mlsanity.com/paper/2404.06059/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 42 references that are in the map.
- First posted on arXiv 9 Apr 2024.

## Builds on (most cited first, 12 of 12)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Deep Learning for Hyperspectral Image Classification: An Overview](https://mlsanity.com/paper/1910.12861/) (2019)
- [On the Computational Efficiency of Training Neural Networks](https://mlsanity.com/paper/1410.1141/) (2014)
- [Systematic Literature Review: Quantum Machine Learning and its applications](https://mlsanity.com/paper/2201.04093/) (2022)
- [Sharpness-aware Low dose CT denoising using conditional generative adversarial network](https://mlsanity.com/paper/1708.06453/) (2017)
- [Simulating a perceptron on a quantum computer](https://mlsanity.com/paper/1412.3635/) (2014)
- [Quantum activation functions for quantum neural networks](https://mlsanity.com/paper/2201.03700/) (2022)
- [Quantum Fan-out: Circuit Optimizations and Technology Modeling](https://mlsanity.com/paper/2007.04246/) (2020)
- [A Q# Implementation of a Quantum Lookup Table for Quantum Arithmetic Functions](https://mlsanity.com/paper/2210.11786/) (2022)

## Built on by (most cited first, 2 of 2)

- [Hybrid Quantum-Classical Recurrent Neural Networks](https://mlsanity.com/paper/2510.25557/) (2025)
- [Hybrid Quantum--Classical Machine Learning Potential with Variational Quantum Circuits](https://mlsanity.com/paper/2508.04098/) (2025)

## Abstract (arXiv)

In recent years, Quantum Machine Learning (QML) has increasingly captured the interest of researchers. Among the components in this domain, activation functions hold a fundamental and indispensable role. Our research focuses on the development of activation functions quantum circuits for integration into fault-tolerant quantum computing architectures, with an emphasis on minimizing T-depth. Specifically, we present novel implementations of ReLU and leaky ReLU activation functions, achieving constant T-depths of 4 and 8, respectively. Leveraging quantum lookup tables, we extend our exploration to other activation functions such as the sigmoid. This approach enables us to customize precision and T-depth by adjusting the number of qubits, making our results more adaptable to various application scenarios. This study represents a significant advancement towards enhancing the practicality and application of quantum machine learning.