The first part develops discrete bulk models on hyperbolic tilings, exploring scalar field instability and correlation functions, and proposes electric circuits as experimental platforms. The second part constructs boundary theories as disordered spin chains and analyzes their entanglement via tensor networks. The final part investigates quantum information measures-circuit complexity, geometric quantum discord, and operator algebras-to probe black hole properties in holographic dualities. This work uncovers new insights into holography and bridges theoretical concepts with experimental realizations.
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