# A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance

arXiv: https://arxiv.org/abs/2401.11351 · HTML: https://mlsanity.com/paper/2401.11351/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 157 references that are in the map.
- First posted on arXiv 21 Jan 2024.

## Builds on (most cited first, 30 of 45)

- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [The Principles of Deep Learning Theory](https://mlsanity.com/paper/2106.10165/) (2021)
- [Non-convex Optimization for Machine Learning](https://mlsanity.com/paper/1712.07897/) (2017)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [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)
- [Quantum Recommendation Systems](https://mlsanity.com/paper/1603.08675/) (2016)
- [A quantum-inspired classical algorithm for recommendation systems](https://mlsanity.com/paper/1807.04271/) (2018)
- [Stochastic gradient descent for hybrid quantum-classical optimization](https://mlsanity.com/paper/1910.01155/) (2019)
- [Learning to learn with quantum neural networks via classical neural networks](https://mlsanity.com/paper/1907.05415/) (2019)
- [Efficient quantum tomography II](https://mlsanity.com/paper/1612.00034/) (2016)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)
- [Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning](https://mlsanity.com/paper/1910.06151/) (2019)
- [On barren plateaus and cost function locality in variational quantum algorithms](https://mlsanity.com/paper/2011.10530/) (2020)

## Built on by (most cited first, 30 of 32)

- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [A PennyLane-Centric Dataset to Enhance LLM-based Quantum Code Generation using RAG](https://mlsanity.com/paper/2503.02497/) (2025)
- [Towards efficient quantum algorithms for diffusion probabilistic models](https://mlsanity.com/paper/2502.14252/) (2025)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Image Classification with Rotation-Invariant Variational Quantum Circuits](https://mlsanity.com/paper/2403.15031/) (2024)
- [Quantum Generative Adversarial Autoencoders: Learning latent representations for quantum data generation](https://mlsanity.com/paper/2509.16186/) (2025)
- [Regression and Classification with Single-Qubit Quantum Neural Networks](https://mlsanity.com/paper/2412.09486/) (2024)
- [TabularQGAN: A quantum generative model for tabular data synthesis](https://mlsanity.com/paper/2505.22533/) (2025)
- [SimQFL: A Quantum Federated Learning Simulator with Real-Time Visualization](https://mlsanity.com/paper/2508.12477/) (2025)
- [Property-guided Inverse Design of Metal-Organic Frameworks Using Quantum Natural Language Processing](https://mlsanity.com/paper/2405.11783/) (2024)
- [Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise](https://mlsanity.com/paper/2412.11451/) (2024)
- [HQCC: A Hybrid Quantum-Classical Classifier with Adaptive Structure](https://mlsanity.com/paper/2504.02167/) (2025)
- [Superior resilience to poisoning and amenability to unlearning in quantum machine learning](https://mlsanity.com/paper/2508.02422/) (2025)
- [Subsampling Factorization Machine Annealing](https://mlsanity.com/paper/2508.08778/) (2025)
- [Intrinsic preservation of plasticity in continual quantum learning](https://mlsanity.com/paper/2511.17228/) (2025)
- [The Role of Quantum in Hybrid Quantum-Classical Neural Networks: A Realistic Assessment](https://mlsanity.com/paper/2601.04732/) (2026)
- [Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning](https://mlsanity.com/paper/2602.00048/) (2026)
- [Model selection in hybrid quantum neural networks with applications to quantum transformer architectures](https://mlsanity.com/paper/2603.21749/) (2026)
- [HQ-UNet: A Hybrid Quantum-Classical U-Net with a Quantum Bottleneck for Remote Sensing Image Segmentation](https://mlsanity.com/paper/2604.27206/) (2026)
- [Digital-Analog Quantum Machine Learning](https://mlsanity.com/paper/2411.10744/) (2024)
- [The Stabilizer Bootstrap of Quantum Machine Learning with up to 10000 qubits](https://mlsanity.com/paper/2412.11356/) (2024)
- [Single-Qudit Quantum Neural Networks for Multiclass Classification](https://mlsanity.com/paper/2503.09269/) (2025)
- [Supervised Quantum Machine Learning: A Future Outlook from Qubits to Enterprise Applications](https://mlsanity.com/paper/2505.24765/) (2025)
- [Noise tolerance via reinforcement: Learning a reinforced quantum dynamics](https://mlsanity.com/paper/2506.12418/) (2025)
- [On the Generalization Limits of Quantum Generative Adversarial Networks with Pure State Generators](https://mlsanity.com/paper/2508.09844/) (2025)
- [QCSE: A Pretrained Quantum Context-Sensitive Word Embedding for Natural Language Processing](https://mlsanity.com/paper/2509.05729/) (2025)
- [Generative modeling using evolved quantum Boltzmann machines](https://mlsanity.com/paper/2512.02721/) (2025)
- [Hybrid Quantum-Classical Mixture of Experts: Unlocking Topological Advantage via Interference-Based Routing](https://mlsanity.com/paper/2512.22296/) (2025)
- [Quantum Scrambling Born Machine](https://mlsanity.com/paper/2602.17281/) (2026)
- [From Reachability to Learnability: Geometric Design Principles for Quantum Neural Networks](https://mlsanity.com/paper/2603.03071/) (2026)

## Abstract (arXiv)

Quantum machine learning, which involves running machine learning algorithms on quantum devices, has garnered significant attention in both academic and business circles. In this paper, we offer a comprehensive and unbiased review of the various concepts that have emerged in the field of quantum machine learning. This includes techniques used in Noisy Intermediate-Scale Quantum (NISQ) technologies and approaches for algorithms compatible with fault-tolerant quantum computing hardware. Our review covers fundamental concepts, algorithms, and the statistical learning theory pertinent to quantum machine learning.