Comparative Analysis of Autonomous and Systematic Control Strategies for Hole-Doped Hubbard Clusters: Reinforcement Learning versus Physics-Guided Design

TL;DR

This paper compares physics-guided design and reinforcement learning for controlling hole-doped Hubbard clusters, demonstrating RL's efficiency and effectiveness in complex quantum system optimization.

Contribution

It introduces autonomous deep reinforcement learning with geometry-aware neural architectures for quantum control, outperforming traditional systematic design methods.

Findings

RL achieves R^2 > 0.97 in accuracy

RL attains 95.5% success rate on tasks

RL is 3-4 orders of magnitude more sample-efficient

Abstract

Engineering electron correlations in quantum dot arrays demands navigation of high-dimensional, non-convex parameter spaces where hole doping fundamentally alters the physics. We present a comparative study of two control paradigms for the one-hole, half-filled Hubbard model: (i) systematic physics-guided design and (ii) autonomous deep reinforcement learning with geometry-aware neural architectures. While systematic analysis reveals key design principles, such as field-induced localization for trapping the mobile hole, it becomes computationally intractable for optimization. We show that an autonomous RL agent, benchmarked across five 3D lattices from tetrahedron to FCC, achieves human-competitive accuracy (R^2 > 0.97) and 95.5 percent success on held-out tasks. The agent is 3-4 orders of magnitude more sample-efficient than grid search and outperforms other black-box optimization methods. Transfer learning yields 91 percent few-shot generalization to unseen geometries. This work establishes autonomous RL as a viable and highly efficient framework for rapid optimization and non-obvious strategy discovery in complex quantum systems.