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

Leonidas Tam

Keywords: reinforcement learning, ADS/CFT, holography, quantum computing, chaos, quantized gravity

TL;DR: RL aware of Hamiltonian symmetries is used to find quantum computing configurations to test holographic duals of quantized gravity

Abstract:

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.

Submission Number: 51