# Quantum Machine Learning for Finance

arXiv: https://arxiv.org/abs/2109.04298 · HTML: https://mlsanity.com/paper/2109.04298/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 137 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Deep Reinforcement Learning framework for Autonomous Driving](https://mlsanity.com/paper/1704.02532/) (2017)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Deep Reinforcement Learning for Trading](https://mlsanity.com/paper/1911.10107/) (2019)
- [Trainability of Dissipative Perceptron-Based Quantum Neural Networks](https://mlsanity.com/paper/2005.12458/) (2020)
- [q-means: A quantum algorithm for unsupervised machine learning](https://mlsanity.com/paper/1812.03584/) (2018)
- [Market Making via Reinforcement Learning](https://mlsanity.com/paper/1804.04216/) (2018)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines](https://mlsanity.com/paper/1712.04144/) (2017)
- [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://mlsanity.com/paper/1804.01973/) (2018)
- [Quantum Perceptron Models](https://mlsanity.com/paper/1602.04799/) (2016)
- [Quantum Algorithms for Compositional Natural Language Processing](https://mlsanity.com/paper/1608.01406/) (2016)
- [Experimental kernel-based quantum machine learning in finite feature space](https://mlsanity.com/paper/1906.04137/) (2019)
- [A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver](https://mlsanity.com/paper/1910.09694/) (2019)
- [Sublinear quantum algorithms for training linear and kernel-based classifiers](https://mlsanity.com/paper/1904.02276/) (2019)
- [Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Q](https://mlsanity.com/paper/2005.03247/) (2020)
- [Quantum Differentially Private Sparse Regression Learning](https://mlsanity.com/paper/2007.11921/) (2020)
- [Deep Reinforcement Learning in Quantitative Algorithmic Trading: A Review](https://mlsanity.com/paper/2106.00123/) (2021)
- [Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer](https://mlsanity.com/paper/1508.06182/) (2015)

## Built on by (most cited first, 7 of 7)

- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [Contextual Quantum Neural Networks for Stock Price Prediction](https://mlsanity.com/paper/2503.01884/) (2025)
- [Quorum: Zero-Training Unsupervised Anomaly Detection using Quantum Autoencoders](https://mlsanity.com/paper/2504.13113/) (2025)
- [Quantum version of the k-NN classifier based on a quantum sorting algorithm](https://mlsanity.com/paper/2204.03761/) (2022)
- [Shuffle-QUDIO: accelerate distributed VQE with trainability enhancement and measurement reduction](https://mlsanity.com/paper/2209.12454/) (2022)
- [Empowering Credit Scoring Systems with Quantum-Enhanced Machine Learning](https://mlsanity.com/paper/2404.00015/) (2024)
- [Wavelet-Accelerated Physics-Informed Quantum Neural Network for Multiscale Partial Differential Equations](https://mlsanity.com/paper/2512.08256/) (2025)

## Abstract (arXiv)

Quantum computers are expected to surpass the computational capabilities of classical computers during this decade, and achieve disruptive impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from Quantum Computing not only in the medium and long terms, but even in the short term. This review paper presents the state of the art of quantum algorithms for financial applications, with particular focus to those use cases that can be solved via Machine Learning.