# Bayesian Deep Learning on a Quantum Computer

arXiv: https://arxiv.org/abs/1806.11463 · HTML: https://mlsanity.com/paper/1806.11463/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2018.

## Built on by (most cited first, 12 of 12)

- [Quantum Permutation Synchronization](https://mlsanity.com/paper/2101.07755/) (2021)
- [Quantum neural networks form Gaussian processes](https://mlsanity.com/paper/2305.09957/) (2023)
- [Building Continuous Quantum-Classical Bayesian Neural Networks for a Classical Clinical Dataset](https://mlsanity.com/paper/2406.06307/) (2024)
- [Accelerating the training of single-layer binary neural networks using the HHL quantum algorithm](https://mlsanity.com/paper/2210.12707/) (2022)
- [Quantum Bayesian Computation](https://mlsanity.com/paper/2208.08068/) (2022)
- [Bayesian Quantum Orthogonal Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2504.18103/) (2025)
- [Old Rules in a New Game: Mapping Uncertainty Quantification to Quantum Machine Learning](https://mlsanity.com/paper/2507.14919/) (2025)
- [Quantum Speedup of Natural Gradient for Variational Bayes](https://mlsanity.com/paper/2106.05807/) (2021)
- [Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning](https://mlsanity.com/paper/2602.00048/) (2026)
- [Classi|Qrangle Towards a Translation Framework To Bridge The Classical-Quantum Programming Gap](https://mlsanity.com/paper/2406.06764/) (2024)
- [Depth-Based Matrix Classification for the HHL Quantum Algorithm](https://mlsanity.com/paper/2505.22454/) (2025)
- [Spectral Anatomy of Quantum Gaussian Process Kernels](https://mlsanity.com/paper/2605.30952/) (2026)

## Abstract (arXiv)

Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to deep architectures has remained a major challenge. Recent results connected deep feedforward neural networks with Gaussian processes, allowing training without backpropagation. This connection enables us to leverage a quantum algorithm designed for Gaussian processes and develop a new algorithm for Bayesian deep learning on quantum computers. The properties of the kernel matrix in the Gaussian process ensure the efficient execution of the core component of the protocol, quantum matrix inversion, providing an at least polynomial speedup over classical algorithms. Furthermore, we demonstrate the execution of the algorithm on contemporary quantum computers and analyze its robustness with respect to realistic noise models.