Symmetry-Aware Entropy Reinforcement Learning for Chaos Accurate Holographic Duals in NISQ Hardware

The construction of hardware-efficient holographic duals requires sparsification of Sachdev-Ye-Kitaev (SYK) Hamiltonians while preserving the dynamics of quantum chaos. In this work, we introduce Symmetry-Aware Reinforcement Learning (SARL) with state-entropy regularization to find suitable hardware configurations for noisy intermediate-scale quantum (NISQ) hardware. By implementing parity-sector auditing to filter artifactual geometries, we map the complexity threshold of pruned SYK models consisting of $N=24$ Majorana fermions, identifying a complexity floor at $M=25$ four-body interaction terms. This configuration represents a 99.98\% reduction from the dense Hamiltonian limit. Our analysis reveals an ultra-sparse regime at 12 four-body terms characterized by marginal reproducibility with a 20\% success rate across independent searches. Using RL for configuration discovery must be paired with rigorous verification. Through an ablation analysis, we show that macroscopic graph motifs, including hub-spoke and core-periphery structures, are necessary prerequisites for connectivity, but insufficient predictors of Gaussian Orthogonal Ensemble (GOE) statistics. A second verification via the normalized participation ratio ($PR/dim$) confirms that a systematic level at $M=25$ produces ergodic, eigenstate thermalization hypothesis (ETH) compliant states across the full energy spectrum. These results delineate empirical sparsity limits for discovering chaotic SYK Hamiltonians and provide a concrete benchmark and open-source codebase for future studies of sparse models in holographic and NISQ settings.