# QuantFPFlow: Quantum Amplitude Estimation for Fokker--Planck Policy Optimisation in Continuous Reinforcement Learning

arXiv: https://arxiv.org/abs/2605.16429 · HTML: https://mlsanity.com/paper/2605.16429/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Quantum reinforcement learning, one of 15 directions in Deep reinforcement learning methods.
- Builds on 3 of its 11 references that are in the map.
- First posted on arXiv 14 May 2026.

## Placed in

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

## Builds on (most cited first, 3 of 3)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)

## Abstract (arXiv)

We introduce QuantFPFlow, a reinforcement learning framework that integrates quantum amplitude estimation into the Fokker--Planck~(FP) formulation of stochastic policy optimisation. Classical continuous-space RL agents must estimate the FP partition function Z = int e-V(x)/D,dx at cost calO(1/varepsilon2); QuantFPFlow replaces this with a Grover-amplified amplitude estimator achieving calO(1/varepsilon) -- a provable quadratic speedup. While the full quantum acceleration requires fault-tolerant hardware, the quantum-inspired classical simulation demonstrated here already exhibits the calO(1/varepsilon) algorithmic structure. The estimated stationary distribution rhostar drives a theoretically grounded exploration bonus Raug = Renv + αlog(1/rhostar(s)). This bonus steers the agent toward globally optimal regions of multimodal reward landscapes while simultaneously constraining policy variance through FP diffusion matching. On a continuous-control task specifically designed to expose local-optima failure, QuantFPFlow achieves mean reward 1,295.7 ± 423.2 versus 1,284.0 ± 474.0 for Soft Actor-Critic~(SAC), while discovering the global optimum 10.4,% more frequently (33.9,% vs. 30.7,%). Policy entropy remains near H(π)≈ 6.5,nats throughout training, whereas SAC collapses to 1.5,nats, confirming that FP diffusion matching actively prevents premature convergence. Dimensionality experiments further show computational scaling of calO(d0.35) for QuantFPFlow versus calO(d0.76) for classical FP estimation.