# Reinforcement learning to learn quantum states for Heisenberg scaling accuracy

arXiv: https://arxiv.org/abs/2412.02334 · HTML: https://mlsanity.com/paper/2412.02334/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Quantum reinforcement learning, one of 15 directions in Deep reinforcement learning methods.
- Builds on 37 of its 102 references that are in the map.
- First posted on arXiv 3 Dec 2024.

## Placed in

- Deep reinforcement learning methods / [Quantum reinforcement learning](https://mlsanity.com/deeprl/quantum-reinforcement-learning/)

## Builds on (most cited first, 30 of 37)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Deep Recurrent Q-Learning for Partially Observable MDPs](https://mlsanity.com/paper/1507.06527/) (2015)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey](https://mlsanity.com/paper/2003.04960/) (2020)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [Sample Efficient Actor-Critic with Experience Replay](https://mlsanity.com/paper/1611.01224/) (2016)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [Learning to learn with quantum neural networks via classical neural networks](https://mlsanity.com/paper/1907.05415/) (2019)
- [Universal Quantum Control through Deep Reinforcement Learning](https://mlsanity.com/paper/1803.01857/) (2018)
- [Discovering Evolution Strategies via Meta-Black-Box Optimization](https://mlsanity.com/paper/2211.11260/) (2022)
- [Challenges and Opportunities in Quantum Optimization](https://mlsanity.com/paper/2312.02279/) (2023)
- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (2020)
- [Learning to Repeat: Fine Grained Action Repetition for Deep Reinforcement Learning](https://mlsanity.com/paper/1702.06054/) (2017)
- [Curriculum reinforcement learning for quantum architecture search under hardware errors](https://mlsanity.com/paper/2402.03500/) (2024)
- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems](https://mlsanity.com/paper/1911.11071/) (2019)
- [Attention-based Quantum Tomography](https://mlsanity.com/paper/2006.12469/) (2020)
- [Experimental neural network enhanced quantum tomography](https://mlsanity.com/paper/1904.05902/) (2019)
- [Meta-Learning for Black-box Optimization](https://mlsanity.com/paper/1907.06901/) (2019)
- [Learning hard quantum distributions with variational autoencoders](https://mlsanity.com/paper/1710.00725/) (2017)
- [Optimizing quantum heuristics with meta-learning](https://mlsanity.com/paper/1908.03185/) (2019)
- [Classification and reconstruction of optical quantum states with deep neural networks](https://mlsanity.com/paper/2012.02185/) (2020)
- [Adaptive Quantum State Tomography with Neural Networks](https://mlsanity.com/paper/1812.06693/) (2018)

## Built on by (most cited first, 1 of 1)

- [One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective](https://mlsanity.com/paper/2607.02292/) (2026)

## Abstract (arXiv)

Learning quantum states is a crucial task for realizing quantum information technology. Recently, neural approaches have emerged as promising methods for learning quantum states. We propose a meta-learning model that utilizes reinforcement learning (RL) to optimize the process of learning quantum states. To improve the data efficiency of the RL, we introduce an action repetition strategy inspired by curriculum learning. The RL agent significantly improves the sample efficiency of learning random quantum states, and achieves infidelity scaling close to the Heisenberg limit. We also show that the RL agent trained using 3-qubit states can generalize to learning up to 5-qubit states. These results highlight the utility of RL-driven meta-learning to enhance the efficiency and generalizability of learning quantum states. Our approach can be applied to improve quantum control, quantum optimization, and quantum machine learning.