# Fidelity-based Probabilistic Q-learning for Control of Quantum Systems

arXiv: https://arxiv.org/abs/1806.03145 · HTML: https://mlsanity.com/paper/1806.03145/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2018.

## Built on by (most cited first, 10 of 10)

- [Deep Reinforcement Learning with Quantum-inspired Experience Replay](https://mlsanity.com/paper/2101.02034/) (2021)
- [Monte Carlo Tree Search based Hybrid Optimization of Variational Quantum Circuits](https://mlsanity.com/paper/2203.16707/) (2022)
- [Tomography of Quantum States from Structured Measurements via quantum-aware transformer](https://mlsanity.com/paper/2305.05433/) (2023)
- [Learning a quantum computer's capability](https://mlsanity.com/paper/2304.10650/) (2023)
- [Auxiliary Task-based Deep Reinforcement Learning for Quantum Control](https://mlsanity.com/paper/2302.14312/) (2023)
- [Magnetic Field-Based Reward Shaping for Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2307.08033/) (2023)
- [Quantum Stream Learning](https://mlsanity.com/paper/2112.06628/) (2021)
- [A quantum system control method based on enhanced reinforcement learning](https://mlsanity.com/paper/2310.03036/) (2023)
- [Hybrid Quantum-Classical Policy Gradient for Adaptive Control of Cyber-Physical Systems: A Comparative Study of VQC vs. MLP](https://mlsanity.com/paper/2510.06010/) (2025)
- [Lyapunov-Aware Quantum-Inspired Reinforcement Learning for Continuous-Time Vehicle Control: A Feasibility Study](https://mlsanity.com/paper/2510.18852/) (2025)

## Abstract (arXiv)

The balance between exploration and exploitation is a key problem for reinforcement learning methods, especially for Q-learning. In this paper, a fidelity-based probabilistic Q-learning (FPQL) approach is presented to naturally solve this problem and applied for learning control of quantum systems. In this approach, fidelity is adopted to help direct the learning process and the probability of each action to be selected at a certain state is updated iteratively along with the learning process, which leads to a natural exploration strategy instead of a pointed one with configured parameters. A probabilistic Q-learning (PQL) algorithm is first presented to demonstrate the basic idea of probabilistic action selection. Then the FPQL algorithm is presented for learning control of quantum systems. Two examples (a spin- 1/2 system and a lamda-type atomic system) are demonstrated to test the performance of the FPQL algorithm. The results show that FPQL algorithms attain a better balance between exploration and exploitation, and can also avoid local optimal policies and accelerate the learning process.