# Quantum Deep Hedging

arXiv: https://arxiv.org/abs/2303.16585 · HTML: https://mlsanity.com/paper/2303.16585/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 87 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [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)
- [A Brief Survey of Deep Reinforcement Learning](https://mlsanity.com/paper/1708.05866/) (2017)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Reinforcement Learning with Quantum Variational Circuits](https://mlsanity.com/paper/2008.07524/) (2020)
- [Orthogonal Deep Neural Networks](https://mlsanity.com/paper/1905.05929/) (2019)
- [Group-Invariant Quantum Machine Learning](https://mlsanity.com/paper/2205.02261/) (2022)
- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [Quantum Vision Transformers](https://mlsanity.com/paper/2209.08167/) (2022)
- [A Comparative Analysis of Expected and Distributional Reinforcement Learning](https://mlsanity.com/paper/1901.11084/) (2019)
- [Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits](https://mlsanity.com/paper/2203.09376/) (2022)
- [Input Redundancy for Parameterized Quantum Circuits](https://mlsanity.com/paper/1901.11434/) (2019)
- [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://mlsanity.com/paper/1804.01973/) (2018)
- [Pseudo-dimension of quantum circuits](https://mlsanity.com/paper/2002.01490/) (2020)
- [Enhancing Explainability of Neural Networks through Architecture Constraints](https://mlsanity.com/paper/1901.03838/) (2019)
- [Deep Hedging: Learning to Simulate Equity Option Markets](https://mlsanity.com/paper/1911.01700/) (2019)
- [Quantum Algorithms for Reinforcement Learning with a Generative Model](https://mlsanity.com/paper/2112.08451/) (2021)
- [Introduction to Quantum Reinforcement Learning: Theory and PennyLane-based Implementation](https://mlsanity.com/paper/2108.06849/) (2021)
- [Grassmannian Learning: Embedding Geometry Awareness in Shallow and Deep Learning](https://mlsanity.com/paper/1808.02229/) (2018)
- [Quantum Reinforcement Learning via Policy Iteration](https://mlsanity.com/paper/2203.01889/) (2022)
- [Variational inference with a quantum computer](https://mlsanity.com/paper/2103.06720/) (2021)

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

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [On the relation between trainability and dequantization of variational quantum learning models](https://mlsanity.com/paper/2406.07072/) (2024)
- [Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes](https://mlsanity.com/paper/2304.11247/) (2023)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Training-efficient density quantum machine learning](https://mlsanity.com/paper/2405.20237/) (2024)
- [QuIC: Quantum-Inspired Compound Adapters for Parameter Efficient Fine-Tuning](https://mlsanity.com/paper/2502.06916/) (2025)
- [Trainability issues in quantum policy gradients](https://mlsanity.com/paper/2406.09614/) (2024)
- [Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information](https://mlsanity.com/paper/2407.21138/) (2024)
- [Bayesian Quantum Orthogonal Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2504.18103/) (2025)
- [Distributional Adversarial Attacks and Training in Deep Hedging](https://mlsanity.com/paper/2508.14757/) (2025)
- [Architectures and random properties of symplectic quantum circuits](https://mlsanity.com/paper/2405.10264/) (2024)
- [Exploring Quantum Neural Networks for Demand Forecasting](https://mlsanity.com/paper/2410.16331/) (2024)
- [Quantum Bayesian Networks Can Speed up Reinforcement Learning in Partially Observable Environments](https://mlsanity.com/paper/2507.18606/) (2025)
- [Taming Barren Plateaus in Arbitrary Parameterized Quantum Circuits without Sacrificing Expressibility](https://mlsanity.com/paper/2511.13408/) (2025)
- [Scalable Message-Passing Quantum Graph Neural Networks in the Weisfeiler-Leman Hierarchy](https://mlsanity.com/paper/2606.26873/) (2026)
- [Computing the gradients with respect to all parameters of a quantum neural network using a single circuit](https://mlsanity.com/paper/2307.08167/) (2023)
- [On Quantum Natural Policy Gradients](https://mlsanity.com/paper/2401.08307/) (2024)
- [Variational Quantum Circuit-Based Reinforcement Learning for Dynamic Portfolio Optimization](https://mlsanity.com/paper/2601.18811/) (2026)
- [QnRL: Quantum-Native Reinforcement Learning](https://mlsanity.com/paper/2606.08276/) (2026)
- [Federating Quantum and Classical Computing: A Privacy-Preserving Hybrid Approach](https://mlsanity.com/paper/2609.25082/) (2026)

## Abstract (arXiv)

Quantum machine learning has the potential for a transformative impact across industry sectors and in particular in finance. In our work we look at the problem of hedging where deep reinforcement learning offers a powerful framework for real markets. We develop quantum reinforcement learning methods based on policy-search and distributional actor-critic algorithms that use quantum neural network architectures with orthogonal and compound layers for the policy and value functions. We prove that the quantum neural networks we use are trainable, and we perform extensive simulations that show that quantum models can reduce the number of trainable parameters while achieving comparable performance and that the distributional approach obtains better performance than other standard approaches, both classical and quantum. We successfully implement the proposed models on a trapped-ion quantum processor, utilizing circuits with up to 16 qubits, and observe performance that agrees well with noiseless simulation. Our quantum techniques are general and can be applied to other reinforcement learning problems beyond hedging.