# An Introduction to Quantum Machine Learning for Engineers

arXiv: https://arxiv.org/abs/2205.09510 · HTML: https://mlsanity.com/paper/2205.09510/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 25 references that are in the map.
- First posted on arXiv 11 May 2022.

## Builds on (most cited first, 2 of 2)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)

## Built on by (most cited first, 22 of 22)

- [Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning](https://mlsanity.com/paper/2304.03398/) (2023)
- [Statistical Complexity of Quantum Learning](https://mlsanity.com/paper/2309.11617/) (2023)
- [Error Mitigation-Aided Optimization of Parameterized Quantum Circuits: Convergence Analysis](https://mlsanity.com/paper/2209.11514/) (2022)
- [Quantum Split Neural Network Learning using Cross-Channel Pooling](https://mlsanity.com/paper/2211.06524/) (2022)
- [Quantum Federated Learning with Entanglement Controlled Circuits and Superposition Coding](https://mlsanity.com/paper/2212.01732/) (2022)
- [Dynamic Estimation Loss Control in Variational Quantum Sensing via Online Conformal Inference](https://mlsanity.com/paper/2505.23389/) (2025)
- [Adversarial Quantum Machine Learning: An Information-Theoretic Generalization Analysis](https://mlsanity.com/paper/2402.00176/) (2024)
- [Neuromorphic Wireless Split Computing with Multi-Level Spikes](https://mlsanity.com/paper/2411.04728/) (2024)
- [QuLTSF: Long-Term Time Series Forecasting with Quantum Machine Learning](https://mlsanity.com/paper/2412.13769/) (2024)
- [Quantum Multi-Agent Reinforcement Learning for Cooperative Mobile Access in Space-Air-Ground Integrated Networks](https://mlsanity.com/paper/2406.16994/) (2024)
- [Adaptive Bayesian Single-Shot Quantum Sensing](https://mlsanity.com/paper/2507.16477/) (2025)
- [Learning Quantum Entanglement Distillation with Noisy Classical Communications](https://mlsanity.com/paper/2205.08561/) (2022)
- [Online Convex Optimization of Programmable Quantum Computers to Simulate Time-Varying Quantum Channels](https://mlsanity.com/paper/2212.05145/) (2022)
- [On the Generalization of Adversarially Trained Quantum Classifiers](https://mlsanity.com/paper/2504.17690/) (2025)
- [Stochastic Quantum Spiking Neural Networks with Quantum Memory and Local Learning](https://mlsanity.com/paper/2506.21324/) (2025)
- [Variational Quantum Integrated Sensing and Communication](https://mlsanity.com/paper/2511.16597/) (2025)
- [Quantum Machine Learning for Distributed Quantum Protocols with Local Operations and Noisy Classical Communications](https://mlsanity.com/paper/2207.11354/) (2022)
- [Variational Quantum Eigensolver with Constraints (VQEC): Solving Constrained Optimization Problems via VQE](https://mlsanity.com/paper/2311.08502/) (2023)
- [QMViT: A Mushroom is worth 16x16 Words](https://mlsanity.com/paper/2407.04708/) (2024)
- [Conservative quantum offline model-based optimization](https://mlsanity.com/paper/2506.19714/) (2025)
- [Adaptive Conformal Prediction for Quantum Machine Learning](https://mlsanity.com/paper/2511.18225/) (2025)
- [Quantum Random Forest for the Regression Problem](https://mlsanity.com/paper/2603.22790/) (2026)

## Abstract (arXiv)

In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parametrized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parametrized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra. It first describes the necessary background, concepts, and tools necessary to describe quantum operations and measurements. Then, it covers parametrized quantum circuits, the variational quantum eigensolver, as well as unsupervised and supervised quantum machine learning formulations.