# Quantum HyperNetworks: Training Binary Neural Networks in Quantum Superposition

arXiv: https://arxiv.org/abs/2301.08292 · HTML: https://mlsanity.com/paper/2301.08292/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 60 references that are in the map.
- First posted on arXiv 19 Jan 2023.

## Builds on (most cited first, 23 of 23)

- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Soft Weight-Sharing for Neural Network Compression](https://mlsanity.com/paper/1702.04008/) (2017)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Unbiased Implicit Variational Inference](https://mlsanity.com/paper/1808.02078/) (2018)
- [Attacking Binarized Neural Networks](https://mlsanity.com/paper/1711.00449/) (2017)
- [BATS: Binary ArchitecTure Search](https://mlsanity.com/paper/2003.01711/) (2020)
- [Training Binary Neural Networks using the Bayesian Learning Rule](https://mlsanity.com/paper/2002.10778/) (2020)
- [Doubly Semi-Implicit Variational Inference](https://mlsanity.com/paper/1810.02789/) (2018)
- [Variational inference with a quantum computer](https://mlsanity.com/paper/2103.06720/) (2021)
- [Quantum algorithms for feedforward neural networks](https://mlsanity.com/paper/1812.03089/) (2018)
- [Efficiency of quantum versus classical annealing in non-convex learning problems](https://mlsanity.com/paper/1706.08470/) (2017)
- [A quantum algorithm for training wide and deep classical neural networks](https://mlsanity.com/paper/2107.09200/) (2021)
- [Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing](https://mlsanity.com/paper/2108.08064/) (2021)
- [Quantum Approximate Optimization Algorithm applied to the binary perceptron](https://mlsanity.com/paper/2112.10219/) (2021)
- [Quantum-Aided Meta-Learning for Bayesian Binary Neural Networks via Born Machines](https://mlsanity.com/paper/2203.17089/) (2022)
- [Accelerating the training of single-layer binary neural networks using the HHL quantum algorithm](https://mlsanity.com/paper/2210.12707/) (2022)
- [Quantum enhanced cross-validation for near-optimal neural networks architecture selection](https://mlsanity.com/paper/1808.09058/) (2018)
- [A Quantum Implementation Model for Artificial Neural Networks](https://mlsanity.com/paper/1609.05884/) (2016)

## Built on by (most cited first, 8 of 8)

- [A Brief Review of Hypernetworks in Deep Learning](https://mlsanity.com/paper/2306.06955/) (2023)
- [Dynamic Inter-treatment Information Sharing for Individualized Treatment Effects Estimation](https://mlsanity.com/paper/2305.15984/) (2023)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Training Multi-layer Neural Networks on Ising Machine](https://mlsanity.com/paper/2311.03408/) (2023)
- [Distributed Quantum Neural Networks on Distributed Photonic Quantum Computing](https://mlsanity.com/paper/2505.08474/) (2025)
- [You Only Measure Once: On Designing Single-Shot Quantum Machine Learning Models](https://mlsanity.com/paper/2509.20090/) (2025)
- [Individualised Treatment Effects Estimation with Composite Treatments and Composite Outcomes](https://mlsanity.com/paper/2502.08282/) (2025)
- [Variational Inference for Quantum HyperNetworks](https://mlsanity.com/paper/2506.05888/) (2025)

## Abstract (arXiv)

Binary neural networks, i.e., neural networks whose parameters and activations are constrained to only two possible values, offer a compelling avenue for the deployment of deep learning models on energy- and memory-limited devices. However, their training, architectural design, and hyperparameter tuning remain challenging as these involve multiple computationally expensive combinatorial optimization problems. Here we introduce quantum hypernetworks as a mechanism to train binary neural networks on quantum computers, which unify the search over parameters, hyperparameters, and architectures in a single optimization loop. Through classical simulations, we demonstrate that our approach effectively finds optimal parameters, hyperparameters and architectural choices with high probability on classification problems including a two-dimensional Gaussian dataset and a scaled-down version of the MNIST handwritten digits. We represent our quantum hypernetworks as variational quantum circuits, and find that an optimal circuit depth maximizes the probability of finding performant binary neural networks. Our unified approach provides an immense scope for other applications in the field of machine learning.