# Quantum Neuron: an elementary building block for machine learning on quantum computers

arXiv: https://arxiv.org/abs/1711.11240 · HTML: https://mlsanity.com/paper/1711.11240/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2017.

## Built on by (most cited first, 30 of 35)

- [Quantum Recurrent Neural Networks for Sequential Learning](https://mlsanity.com/paper/2302.03244/) (2023)
- [Quantum activation functions for quantum neural networks](https://mlsanity.com/paper/2201.03700/) (2022)
- [A Leap among Quantum Computing and Quantum Neural Networks: A Survey](https://mlsanity.com/paper/2107.03313/) (2021)
- [Hybrid Classical-Quantum Deep Learning Models for Autonomous Vehicle Traffic Image Classification Under Adversarial Attack](https://mlsanity.com/paper/2108.01125/) (2021)
- [A Classical-Quantum Convolutional Neural Network for Detecting Pneumonia from Chest Radiographs](https://mlsanity.com/paper/2202.10452/) (2022)
- [Quantum Natural Language Processing](https://mlsanity.com/paper/2403.19758/) (2024)
- [Introducing Non-Linear Activations into Quantum Generative Models](https://mlsanity.com/paper/2205.14506/) (2022)
- [Time-Warping Invariant Quantum Recurrent Neural Networks via Quantum-Classical Adaptive Gating](https://mlsanity.com/paper/2301.08173/) (2023)
- [PristiQ: A Co-Design Framework for Preserving Data Security of Quantum Learning in the Cloud](https://mlsanity.com/paper/2404.13475/) (2024)
- [Quantum neural networks force fields generation](https://mlsanity.com/paper/2203.04666/) (2022)
- [The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning](https://mlsanity.com/paper/2212.11826/) (2022)
- [Quantum Splines for Non-Linear Approximations](https://mlsanity.com/paper/2303.05428/) (2023)
- [Graph Neural Networks on Quantum Computers](https://mlsanity.com/paper/2405.17060/) (2024)
- [Quantum Hamiltonian Embedding of Images for Data Reuploading Classifiers](https://mlsanity.com/paper/2407.14055/) (2024)
- [Quantum Cross Entropy and Maximum Likelihood Principle](https://mlsanity.com/paper/2102.11887/) (2021)
- [Enabling Non-Linear Quantum Operations through Variational Quantum Splines](https://mlsanity.com/paper/2303.04788/) (2023)
- [Post-variational quantum neural networks](https://mlsanity.com/paper/2307.10560/) (2023)
- [Fermi-Dirac machines as quantizations of neurons](https://mlsanity.com/paper/2605.24386/) (2026)
- [Predictive control of blast furnace temperature in steelmaking with hybrid depth-infused quantum neural networks](https://mlsanity.com/paper/2504.12389/) (2025)
- [From Digital Humanities to Quantum Humanities: Potentials and Applications](https://mlsanity.com/paper/2103.11825/) (2021)
- [Negational Symmetry of Quantum Neural Networks for Binary Pattern Classification](https://mlsanity.com/paper/2105.09580/) (2021)
- [A Quantum Hopfield Associative Memory Implemented on an Actual Quantum Processor](https://mlsanity.com/paper/2105.11590/) (2021)
- [A supplemental investigation of non-linearity in quantum generative models with respect to simulatability and optimization](https://mlsanity.com/paper/2302.00788/) (2023)
- [Hybrid Quantum Neural Networks for Efficient Protein-Ligand Binding Affinity Prediction](https://mlsanity.com/paper/2509.11046/) (2025)
- [Hybrid Quantum-Classical Recurrent Neural Networks](https://mlsanity.com/paper/2510.25557/) (2025)
- [Quantum-Augmented AI/ML for O-RAN: Hierarchical Threat Detection with Synergistic Intelligence and Interpretability (Technical Report)](https://mlsanity.com/paper/2512.14742/) (2025)
- [On the Behaviour of Pulsed Qubits and their Application to Feed Forward Networks](https://mlsanity.com/paper/2302.10467/) (2023)
- [Hybrid quantum recurrent neural network for remaining useful life prediction of turbofan engines](https://mlsanity.com/paper/2504.20823/) (2025)
- [Selective Feature Re-Encoded Quantum Convolutional Neural Network with Joint Optimization for Image Classification](https://mlsanity.com/paper/2507.02086/) (2025)
- [Collaborative Filtering using Variational Quantum Hopfield Associative Memory](https://mlsanity.com/paper/2508.14906/) (2025)

## Abstract (arXiv)

Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning.