# Quantum Deep Learning

arXiv: https://arxiv.org/abs/1412.3489 · HTML: https://mlsanity.com/paper/1412.3489/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2014.

## Built on by (most cited first, 30 of 31)

- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Quantum machine learning for image classification](https://mlsanity.com/paper/2304.09224/) (2023)
- [Quantum Multi-Agent Reinforcement Learning via Variational Quantum Circuit Design](https://mlsanity.com/paper/2203.10443/) (2022)
- [Universal Adversarial Examples and Perturbations for Quantum Classifiers](https://mlsanity.com/paper/2102.07788/) (2021)
- [Introduction to Quantum Reinforcement Learning: Theory and PennyLane-based Implementation](https://mlsanity.com/paper/2108.06849/) (2021)
- [Near-Optimal Quantum Algorithms for Multivariate Mean Estimation](https://mlsanity.com/paper/2111.09787/) (2021)
- [Quantum Distributed Deep Learning Architectures: Models, Discussions, and Applications](https://mlsanity.com/paper/2202.11200/) (2022)
- [Laziness, Barren Plateau, and Noise in Machine Learning](https://mlsanity.com/paper/2206.09313/) (2022)
- [Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data](https://mlsanity.com/paper/2306.07331/) (2023)
- [Quantum Mathematics in Artificial Intelligence](https://mlsanity.com/paper/2101.04255/) (2021)
- [Spectral Bias in Variational Quantum Machine Learning](https://mlsanity.com/paper/2506.22555/) (2025)
- [Evaluating the Performance of Some Local Optimizers for Variational Quantum Classifiers](https://mlsanity.com/paper/2102.08949/) (2021)
- [Review of Ansatz Designing Techniques for Variational Quantum Algorithms](https://mlsanity.com/paper/2212.04913/) (2022)
- [Analogy between Boltzmann machines and Feynman path integrals](https://mlsanity.com/paper/2301.06217/) (2023)
- [Projected Stochastic Gradient Descent with Quantum Annealed Binary Gradients](https://mlsanity.com/paper/2310.15128/) (2023)
- [Quantum advantage for learning shallow neural networks with natural data distributions](https://mlsanity.com/paper/2503.20879/) (2025)
- [Quantum Machine Learning For Classical Data](https://mlsanity.com/paper/2105.03684/) (2021)
- [Modeling stochastic eye tracking data: A comparison of quantum generative adversarial networks and Markov models](https://mlsanity.com/paper/2408.00673/) (2024)
- [Quantum Speedup of Natural Gradient for Variational Bayes](https://mlsanity.com/paper/2106.05807/) (2021)
- [Quantum Measurement Classification with Qudits](https://mlsanity.com/paper/2107.09781/) (2021)
- [An efficient combination strategy for hybird quantum ensemble classifier](https://mlsanity.com/paper/2210.06785/) (2022)
- [KirchhoffNet: A Scalable Ultra Fast Analog Neural Network](https://mlsanity.com/paper/2310.15872/) (2023)
- [Hybrid Quantum Neural Network in High-dimensional Data Classification](https://mlsanity.com/paper/2312.01024/) (2023)
- [Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications](https://mlsanity.com/paper/2509.08911/) (2025)
- [Accelerating Inference for Multilayer Neural Networks with Quantum Computers](https://mlsanity.com/paper/2510.07195/) (2025)
- [Estimating the randomness of quantum circuit ensembles up to 50 qubits](https://mlsanity.com/paper/2205.09900/) (2022)
- [Stochastic Security as a Performance Metric for Quantum-enhanced Generative AI](https://mlsanity.com/paper/2305.07973/) (2023)
- [Neural Crystals](https://mlsanity.com/paper/2311.16111/) (2023)
- [Distribution alignment based transfer fusion frameworks on quantum devices for seeking quantum advantages](https://mlsanity.com/paper/2411.01822/) (2024)

## Abstract (arXiv)

In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on conventional, classical computers. We show that quantum computing not only reduces the time required to train a deep restricted Boltzmann machine, but also provides a richer and more comprehensive framework for deep learning than classical computing and leads to significant improvements in the optimization of the underlying objective function. Our quantum methods also permit efficient training of full Boltzmann machines and multi-layer, fully connected models and do not have well known classical counterparts.