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Reinforcement Learning for Charging Optimization of Inhomogeneous Dicke Quantum Batteries

Xiaobin Song, Siyuan Bai, Da-Wei Wang, Hanxiao Tao, Xizhe Wang, Rebing Wu, Benben Jiang

TL;DR

This work addresses fast charging of inhomogeneous Dicke quantum batteries under partial observability by casting charging as a discrete-time reinforcement-learning problem. Using Soft Actor–Critic, the agent learns piecewise-constant charger coupling policies that maximize terminal ergotropy $\mathcal{E}(\tau)$ while using observables from four regimes, from full state to experimentally accessible correlations. The key finding is that second-order correlations in observables recover most of the performance gap caused by partial information, achieving 94–98% of the full-state baseline, with learned schedules that are nonmyopic and terminal-focused. The results offer a practical route to efficient fast-charging protocols under realistic readout constraints and motivate future POMDP-driven or robust-control extensions for experimental quantum batteries.

Abstract

Charging optimization is a key challenge to the implementation of quantum batteries, particularly under inhomogeneity and partial observability. This paper employs reinforcement learning to optimize piecewise-constant charging policies for an inhomogeneous Dicke battery. We systematically compare policies across four observability regimes, from full-state access to experimentally accessible observables (energies of individual two-level systems (TLSs), first-order averages, and second-order correlations). Simulation results demonstrate that full observability yields near-optimal ergotropy with low variability, while under partial observability, access to only single-TLS energies or energies plus first-order averages lags behind the fully observed baseline. However, augmenting partial observations with second-order correlations recovers most of the gap, reaching 94%-98% of the full-state baseline. The learned schedules are nonmyopic, trading temporary plateaus or declines for superior terminal outcomes. These findings highlight a practical route to effective fast-charging protocols under realistic information constraints.

Reinforcement Learning for Charging Optimization of Inhomogeneous Dicke Quantum Batteries

TL;DR

This work addresses fast charging of inhomogeneous Dicke quantum batteries under partial observability by casting charging as a discrete-time reinforcement-learning problem. Using Soft Actor–Critic, the agent learns piecewise-constant charger coupling policies that maximize terminal ergotropy while using observables from four regimes, from full state to experimentally accessible correlations. The key finding is that second-order correlations in observables recover most of the performance gap caused by partial information, achieving 94–98% of the full-state baseline, with learned schedules that are nonmyopic and terminal-focused. The results offer a practical route to efficient fast-charging protocols under realistic readout constraints and motivate future POMDP-driven or robust-control extensions for experimental quantum batteries.

Abstract

Charging optimization is a key challenge to the implementation of quantum batteries, particularly under inhomogeneity and partial observability. This paper employs reinforcement learning to optimize piecewise-constant charging policies for an inhomogeneous Dicke battery. We systematically compare policies across four observability regimes, from full-state access to experimentally accessible observables (energies of individual two-level systems (TLSs), first-order averages, and second-order correlations). Simulation results demonstrate that full observability yields near-optimal ergotropy with low variability, while under partial observability, access to only single-TLS energies or energies plus first-order averages lags behind the fully observed baseline. However, augmenting partial observations with second-order correlations recovers most of the gap, reaching 94%-98% of the full-state baseline. The learned schedules are nonmyopic, trading temporary plateaus or declines for superior terminal outcomes. These findings highlight a practical route to effective fast-charging protocols under realistic information constraints.

Paper Structure

This paper contains 14 sections, 16 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Dicke Quantum Battery and Charging Dynamics
  3. Reinforcement Learning Framework for Charging Optimization
  4. Environment for the RL agent
  5. Soft Actor–Critic Algorithm
  6. Actor.
  7. Critic and policy evaluation.
  8. Policy improvement.
  9. Simulation Results and Discussion
  10. Simulation Parameters
  11. Experimental Scenarios
  12. Performance Analysis
  13. Discussion
  14. Conclusions

Figures (2)

  • Figure 1: Average ergotropy versus training episodes under four settings of available information, averaged over five random seeds, for three inhomogeneous quantum batteries: (a) Env1, (b) Env2, (c) Env3. The shaded regions represent the standard deviation over five seeds.
  • Figure 2: Best charging protocols among five seeds for four our observable regimes [(a):$E_j(t)$, (b):$E_j(t) + \langle\hat{\sigma}_\alpha^{(i)}\rangle_t$, (c):$E_j(t) + \langle\hat{\sigma}_\alpha^{(i)}\rangle_t + \langle \hat{\sigma}_\alpha ^{(i)}\hat{\sigma}_\beta^{(j)}\rangle_t$, (d):$|\psi(t)\rangle$] and their ergotropy trajectories (e) in Env1.