# Exponential improvements for quantum-accessible reinforcement learning

arXiv: https://arxiv.org/abs/1710.11160 · HTML: https://mlsanity.com/paper/1710.11160/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2017.

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

- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Quantum Policy Iteration via Amplitude Estimation and Grover Search -- Towards Quantum Advantage for Reinforcement Learning](https://mlsanity.com/paper/2206.04741/) (2022)
- [Policy Gradients using Variational Quantum Circuits](https://mlsanity.com/paper/2203.10591/) (2022)
- [Quantum policy gradient algorithms](https://mlsanity.com/paper/2212.09328/) (2022)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Quantum Bayesian Networks Can Speed up Reinforcement Learning in Partially Observable Environments](https://mlsanity.com/paper/2507.18606/) (2025)
- [From Classical Data to Quantum Advantage -- Quantum Policy Evaluation on Quantum Hardware](https://mlsanity.com/paper/2509.07614/) (2025)

## Abstract (arXiv)

Quantum computers can offer dramatic improvements over classical devices for data analysis tasks such as prediction and classification. However, less is known about the advantages that quantum computers may bring in the setting of reinforcement learning, where learning is achieved via interaction with a task environment. Here, we consider a special case of reinforcement learning, where the task environment allows quantum access. In addition, we impose certain "naturalness" conditions on the task environment, which rule out the kinds of oracle problems that are studied in quantum query complexity (and for which quantum speedups are well-known). Within this framework of quantum-accessible reinforcement learning environments, we demonstrate that quantum agents can achieve exponential improvements in learning efficiency, surpassing previous results that showed only quadratic improvements. A key step in the proof is to construct task environments that encode well-known oracle problems, such as Simon's problem and Recursive Fourier Sampling, while satisfying the above "naturalness" conditions for reinforcement learning. Our results suggest that quantum agents may perform well in certain game-playing scenarios, where the game has recursive structure, and the agent can learn by playing against itself.