# Application of Quantum Annealing to Training of Deep Neural Networks

arXiv: https://arxiv.org/abs/1510.06356 · HTML: https://mlsanity.com/paper/1510.06356/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2015.

## Built on by (most cited first, 30 of 37)

- [Training an Ising Machine with Equilibrium Propagation](https://mlsanity.com/paper/2305.18321/) (2023)
- [Training Deep Boltzmann Networks with Sparse Ising Machines](https://mlsanity.com/paper/2303.10728/) (2023)
- [Adiabatic Quantum Graph Matching with Permutation Matrix Constraints](https://mlsanity.com/paper/2107.04032/) (2021)
- [Variational inference with a quantum computer](https://mlsanity.com/paper/2103.06720/) (2021)
- [Feature Selection for Recommender Systems with Quantum Computing](https://mlsanity.com/paper/2110.05089/) (2021)
- [Towards Feature Selection for Ranking and Classification Exploiting Quantum Annealers](https://mlsanity.com/paper/2205.04346/) (2022)
- [CaloQVAE : Simulating high-energy particle-calorimeter interactions using hybrid quantum-classical generative models](https://mlsanity.com/paper/2312.03179/) (2023)
- [An efficient probabilistic hardware architecture for diffusion-like models](https://mlsanity.com/paper/2510.23972/) (2025)
- [A Review of Machine Learning Classification Using Quantum Annealing for Real-world Applications](https://mlsanity.com/paper/2106.02964/) (2021)
- [On the challenges of using D-Wave computers to sample Boltzmann Random Variables](https://mlsanity.com/paper/2111.15295/) (2021)
- [Quark: A Gradient-Free Quantum Learning Framework for Classification Tasks](https://mlsanity.com/paper/2210.01311/) (2022)
- [A hybrid quantum-classical approach for inference on restricted Boltzmann machines](https://mlsanity.com/paper/2304.12418/) (2023)
- [Projected Stochastic Gradient Descent with Quantum Annealed Binary Gradients](https://mlsanity.com/paper/2310.15128/) (2023)
- [Training Multi-layer Neural Networks on Ising Machine](https://mlsanity.com/paper/2311.03408/) (2023)
- [Towards Transfer Learning for Large-Scale Image Classification Using Annealing-based Quantum Boltzmann Machines](https://mlsanity.com/paper/2311.15966/) (2023)
- [Assessment of image generation by quantum annealer](https://mlsanity.com/paper/2103.08373/) (2021)
- [Discriminating Quantum States with Quantum Machine Learning](https://mlsanity.com/paper/2112.00313/) (2021)
- [Beyond Ans"atze: Learning Quantum Circuits as Unitary Operators](https://mlsanity.com/paper/2203.00601/) (2022)
- [Three Learning Stages and Accuracy-Efficiency Tradeoff of Restricted Boltzmann Machines](https://mlsanity.com/paper/2209.00873/) (2022)
- [Quantum Image Denoising: A Framework via Boltzmann Machines, QUBO, and Quantum Annealing](https://mlsanity.com/paper/2307.06542/) (2023)
- [Quantum Annealing for Computer Vision Minimization Problems](https://mlsanity.com/paper/2312.12848/) (2023)
- [Implementing Large Quantum Boltzmann Machines as Generative AI Models for Dataset Balancing](https://mlsanity.com/paper/2502.03086/) (2025)
- [Training Multilayer Perceptrons by Sampling with Quantum Annealers](https://mlsanity.com/paper/2303.12352/) (2023)
- [Comparison of D-Wave Quantum Annealing and Gibbs Monte Carlo for Sampling from a Probability Distribution of a Restricted Boltzmann Machine](https://mlsanity.com/paper/2508.10228/) (2025)
- [Quantum Deep Learning: Sampling Neural Nets with a Quantum Annealer](https://mlsanity.com/paper/2107.08710/) (2021)
- [Heuristic for Diverse Kemeny Rank Aggregation based on Quantum Annealing](https://mlsanity.com/paper/2301.05146/) (2023)
- [Mean-Field Assisted Deep Boltzmann Learning with Probabilistic Computers](https://mlsanity.com/paper/2401.01996/) (2024)
- [Adiabatic Quantum Support Vector Machines](https://mlsanity.com/paper/2401.12485/) (2024)
- [Biclustering a dataset using photonic quantum computing](https://mlsanity.com/paper/2405.18622/) (2024)
- [Towards Arbitrary QUBO Optimization: Analysis of Classical and Quantum-Activated Feedforward Neural Networks](https://mlsanity.com/paper/2410.12636/) (2024)

## Abstract (arXiv)

In Deep Learning, a well-known approach for training a Deep Neural Network starts by training a generative Deep Belief Network model, typically using Contrastive Divergence (CD), then fine-tuning the weights using backpropagation or other discriminative techniques. However, the generative training can be time-consuming due to the slow mixing of Gibbs sampling. We investigated an alternative approach that estimates model expectations of Restricted Boltzmann Machines using samples from a D-Wave quantum annealing machine. We tested this method on a coarse-grained version of the MNIST data set. In our tests we found that the quantum sampling-based training approach achieves comparable or better accuracy with significantly fewer iterations of generative training than conventional CD-based training. Further investigation is needed to determine whether similar improvements can be achieved for other data sets, and to what extent these improvements can be attributed to quantum effects.