# Efficient Learning for Deep Quantum Neural Networks

arXiv: https://arxiv.org/abs/1902.10445 · HTML: https://mlsanity.com/paper/1902.10445/

## Key facts

- Cited by 161 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2019.

## Built on by (most cited first, 30 of 161)

- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer](https://mlsanity.com/paper/2102.12846/) (2021)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [Quantum Federated Learning with Quantum Data](https://mlsanity.com/paper/2106.00005/) (2021)
- [lambeq: An Efficient High-Level Python Library for Quantum NLP](https://mlsanity.com/paper/2110.04236/) (2021)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [On Circuit-based Hybrid Quantum Neural Networks for Remote Sensing Imagery Classification](https://mlsanity.com/paper/2109.09484/) (2021)
- [Subtleties in the trainability of quantum machine learning models](https://mlsanity.com/paper/2110.14753/) (2021)
- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [Benchmarking Adversarially Robust Quantum Machine Learning at Scale](https://mlsanity.com/paper/2211.12681/) (2022)
- [Towards quantum enhanced adversarial robustness in machine learning](https://mlsanity.com/paper/2306.12688/) (2023)
- [Entangled Datasets for Quantum Machine Learning](https://mlsanity.com/paper/2109.03400/) (2021)
- [projUNN: efficient method for training deep networks with unitary matrices](https://mlsanity.com/paper/2203.05483/) (2022)
- [On the statistical complexity of quantum circuits](https://mlsanity.com/paper/2101.06154/) (2021)
- [QuantumFed: A Federated Learning Framework for Collaborative Quantum Training](https://mlsanity.com/paper/2106.09109/) (2021)
- [Analytic theory for the dynamics of wide quantum neural networks](https://mlsanity.com/paper/2203.16711/) (2022)
- [Quantum Self-Supervised Learning](https://mlsanity.com/paper/2103.14653/) (2021)
- [The dilemma of quantum neural networks](https://mlsanity.com/paper/2106.04975/) (2021)
- [Learning shallow quantum circuits](https://mlsanity.com/paper/2401.10095/) (2024)
- [FedQNN: Federated Learning using Quantum Neural Networks](https://mlsanity.com/paper/2403.10861/) (2024)
- [Deep Reinforcement Learning with Quantum-inspired Experience Replay](https://mlsanity.com/paper/2101.02034/) (2021)
- [Certified Robustness of Quantum Classifiers against Adversarial Examples through Quantum Noise](https://mlsanity.com/paper/2211.00887/) (2022)
- [Beyond Classical Attention: Quantum Attention for Scalable Computation](https://mlsanity.com/paper/2307.08045/) (2023)
- [QFNN-FFD: Quantum Federated Neural Network for Financial Fraud Detection](https://mlsanity.com/paper/2404.02595/) (2024)
- [Deep learning models for price forecasting of financial time series: A review of recent advancements: 2020-2022](https://mlsanity.com/paper/2305.04811/) (2023)
- [Quantum Annealing Formulation for Binary Neural Networks](https://mlsanity.com/paper/2107.02751/) (2021)
- [Variational Quantum Soft Actor-Critic](https://mlsanity.com/paper/2112.11921/) (2021)

## Abstract (arXiv)

Neural networks enjoy widespread success in both research and industry and, with the imminent advent of quantum technology, it is now a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose the use of quantum neurons as a building block for quantum feed-forward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function and provide both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing the optimisation of deep networks. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.