# The power of quantum neural networks

arXiv: https://arxiv.org/abs/2011.00027 · HTML: https://mlsanity.com/paper/2011.00027/

## Key facts

- Cited by 379 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2020.

## Built on by (most cited first, 30 of 379)

- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [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)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Noisy intermediate-scale quantum (NISQ) algorithms](https://mlsanity.com/paper/2101.08448/) (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)
- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Quantum Self-Attention Neural Networks for Text Classification](https://mlsanity.com/paper/2205.05625/) (2022)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [Experimental quantum adversarial learning with programmable superconducting qubits](https://mlsanity.com/paper/2204.01738/) (2022)
- [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)
- [Capacity and quantum geometry of parametrized quantum circuits](https://mlsanity.com/paper/2102.01659/) (2021)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [Quantum machine learning with differential privacy](https://mlsanity.com/paper/2103.06232/) (2021)
- [Generative quantum machine learning via denoising diffusion probabilistic models](https://mlsanity.com/paper/2310.05866/) (2023)

## Abstract (arXiv)

Fault-tolerant quantum computers offer the promise of dramatically improving machine learning through speed-ups in computation or improved model scalability. In the near-term, however, the benefits of quantum machine learning are not so clear. Understanding expressibility and trainability of quantum models-and quantum neural networks in particular-requires further investigation. In this work, we use tools from information geometry to define a notion of expressibility for quantum and classical models. The effective dimension, which depends on the Fisher information, is used to prove a novel generalisation bound and establish a robust measure of expressibility. We show that quantum neural networks are able to achieve a significantly better effective dimension than comparable classical neural networks. To then assess the trainability of quantum models, we connect the Fisher information spectrum to barren plateaus, the problem of vanishing gradients. Importantly, certain quantum neural networks can show resilience to this phenomenon and train faster than classical models due to their favourable optimisation landscapes, captured by a more evenly spread Fisher information spectrum. Our work is the first to demonstrate that well-designed quantum neural networks offer an advantage over classical neural networks through a higher effective dimension and faster training ability, which we verify on real quantum hardware.