# Completely Quantum Neural Networks

arXiv: https://arxiv.org/abs/2202.11727 · HTML: https://mlsanity.com/paper/2202.11727/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 23 Feb 2022.

## Builds on (most cited first, 8 of 8)

- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Quantum Annealing Formulation for Binary Neural Networks](https://mlsanity.com/paper/2107.02751/) (2021)
- [Quantum Optimisation of Complex Systems with a Quantum Annealer](https://mlsanity.com/paper/2105.13945/) (2021)
- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)
- [Bayesian Network Structure Learning Using Quantum Annealing](https://mlsanity.com/paper/1407.3897/) (2014)

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

- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Nonnegative/Binary Matrix Factorization for Image Classification using Quantum Annealing](https://mlsanity.com/paper/2311.01028/) (2023)
- [Jet Discrimination with Quantum Complete Graph Neural Network](https://mlsanity.com/paper/2403.04990/) (2024)
- [Qade: Solving Differential Equations on Quantum Annealers](https://mlsanity.com/paper/2204.03657/) (2022)
- [Training Neural Networks with Universal Adiabatic Quantum Computing](https://mlsanity.com/paper/2308.13028/) (2023)
- [Quadratic Unconstrained Binary Optimisation for Training and Regularisation of Binary Neural Networks](https://mlsanity.com/paper/2601.00449/) (2026)
- [From Reachability to Learnability: Geometric Design Principles for Quantum Neural Networks](https://mlsanity.com/paper/2603.03071/) (2026)

## Abstract (arXiv)

Artificial neural networks are at the heart of modern deep learning algorithms. We describe how to embed and train a general neural network in a quantum annealer without introducing any classical element in training. To implement the network on a state-of-the-art quantum annealer, we develop three crucial ingredients: binary encoding the free parameters of the network, polynomial approximation of the activation function, and reduction of binary higher-order polynomials into quadratic ones. Together, these ideas allow encoding the loss function as an Ising model Hamiltonian. The quantum annealer then trains the network by finding the ground state. We implement this for an elementary network and illustrate the advantages of quantum training: its consistency in finding the global minimum of the loss function and the fact that the network training converges in a single annealing step, which leads to short training times while maintaining a high classification performance. Our approach opens a novel avenue for the quantum training of general machine learning models.