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

2026-05-19 · Source: cs.LG updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Emerging Technologies & Innovation · Depth: Expert, long

Summary

QuantFPFlow is a novel reinforcement learning framework that integrates quantum amplitude estimation (QAE) into the Fokker–Planck (FP) formulation for stochastic policy optimization in continuous state-action spaces. It addresses the computational bottleneck of estimating the FP partition function, $Z=\int e^{-V(\mathbf{x})/D}\,d\mathbf{x}$, which classically costs $\mathcal{O}(1/\varepsilon^{2})$. QuantFPFlow replaces this with a Grover-amplified amplitude estimator, achieving a provable quadratic speedup with $\mathcal{O}(1/\varepsilon)$ complexity. The framework uses the estimated stationary distribution $\rho^{*}$ to generate a theoretically grounded exploration bonus, $r_{\mathrm{aug}}=r_{\mathrm{env}}+\alpha\log(1/\rho^{*}(s))$, which guides the agent toward global optima in multimodal reward landscapes and constrains policy variance through FP diffusion matching. On a continuous-control task designed to expose local-optima failure, QuantFPFlow achieved a mean reward of $1,295.7\pm 423.2$, slightly outperforming Soft Actor-Critic (SAC)'s $1,284.0\pm 474.0$, and discovered the global optimum 10.4% more frequently (33.9% vs. 30.7%). It also demonstrated superior dimensionality scaling of $\mathcal{O}(d^{0.35})$ compared to classical FP estimation's $\mathcal{O}(d^{0.76})$.

Key takeaway

For AI Scientists and Machine Learning Engineers working on continuous reinforcement learning with multimodal reward landscapes, QuantFPFlow offers a principled approach to overcome local optima. Your teams should consider integrating quantum-inspired amplitude estimation for its $\mathcal{O}(1/\varepsilon)$ speedup in partition function computation and its ability to maintain policy exploration, leading to higher global optimum discovery rates compared to methods like SAC.

Key insights

Quantum amplitude estimation can quadratically speed up Fokker-Planck partition function computation in continuous reinforcement learning.

Principles

• FP consistency prevents policy entropy collapse.
• QAE offers a quadratic speedup for partition function estimation.
• Theory-grounded exploration bonuses improve global optimum discovery.

Method

QuantFPFlow couples a temperature-annealed QAE for $\rho^{*}(s)$ with an FP-Actor using FP-guided gradients and an FP consistency loss to match policy variance to diffusion, all within a TD-learning critic loop.

In practice

• Use QAE for $\mathcal{O}(1/\varepsilon)$ partition function estimation.
• Implement FP consistency to maintain policy exploration.
• Apply exploration bonuses derived from stationary distributions.

Topics

• Quantum Amplitude Estimation
• Fokker-Planck Equation
• Continuous Reinforcement Learning
• Stochastic Policy Optimization
• Exploration Mechanisms

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.