Autonomous Control of Local Pairing in Strongly Correlated Quantum Systems

Designing controls for strongly correlated quantum systems poses a distinctive machine learning (ML) challenge: the search space is high dimensional, feedback is nonlinear and nonconvex, and ground-truth evaluations are costly. We introduce a deep reinforcement learning (RL) framework that autonomously discovers control policies in a controllable Hubbard environment, using exact diagonalization as the oracle. Our geometry-aware dueling DQN, conditioned on a learnable embedding of lattice topology and compact physics state, acts in a discrete vector field space to steer the system toward local electron pairing. Trained via curriculum over Hamiltonian parameters and geometries, the agent achieves high sample efficiency (requiring 10³ -10⁴ ) fewer simulator calls than brute-force search, strong accuracy (R² >0.97) across tetrahedron, octahedron, SC, BCC, and FCC clusters, with 95.5% success on held-out tasks, and generalization to unseen clusters (65% zero-shot success on a cube, rising to 91% after 100 fine-tuning episodes). Mechanistic analysis of the learned policies via retarded Green’s functions reveals Mott-like spectral weight transfer as the driver of pairing enhancement, providing interpretability beyond black-box performance. To contextualize these results, we connect the learned policies to physical design principles uncovered in Hartree–Fock simulations: coordination number governs resilience to Coulomb repulsion, inter-orbital hopping can counterintuitively enhance double occupancy, and external fields squeeze charge localization. Together, the RL framework and physical insights establish a scalable, data-efficient blueprint for controlling pairing phenomena in graph-structured many-body environments, opening pathways for computational and experimental quantum platforms.