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

• URL: http://arxiv.org/abs/2605.16429v1
• Date: Thu, 14 May 2026 18:35:38 GMT
• Title: QuantFPFlow: Quantum Amplitude Estimation for Fokker--Planck Policy Optimisation in Continuous Reinforcement Learning
• Abstract summary: We introduce textbfFPFlow, a reinforcement learning framework that integrates quantum amplitude estimation into the Fokker-Planck(FP) formulation of policy optimisation.<n>Classical continuous-space agents must estimate the FP partition function $Z = int e-V(mathbfx)/D,dmathbfx$ at cost $calO (1/varepsilon2)$; QuantFlow replaces this with a Grover-amplified amplitude estimator achieving $calO (1/varepsilon)$ -- a
• Score: 0.2538209532048867
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce \textbf{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 $Z = \int e^{-V(\mathbf{x})/D}\,d\mathbf{x}$ at cost $\calO(1/\varepsilon^{2})$; 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 $\Raug = \Renv + α\log(1/\rhostar(s))$. 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 $1{,}295.7 \pm 423.2$ versus $1{,}284.0 \pm 474.0$ for Soft Actor-Critic~(SAC), while discovering the global optimum \textbf{10.4\,\% more frequently} (33.9\,\% vs.\ 30.7\,\%). Policy entropy remains near $H(π)\approx 6.5$\,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 $\calO(d^{0.35})$ for QuantFPFlow versus $\calO(d^{0.76})$ for classical FP estimation.

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