Information-Geometric Limits on Quantum Simulations of Black Hole Scrambling

Strongly chaotic quantum systems, including black holes, exhibit rapid scrambling of initially local information, posing fundamental challenges for their faithful simulation in finite, noisy quantum devices. Here we introduce the Information-Geometric Scrambling Limit (IGSL), a bound that constrains the temporal window over which genuine quantum scrambling can be observed in finite-depth quantum circuits. By characterizing operator growth through the quantum Fisher information, we show that the exponential sensitivity associated with chaotic dynamics is ultimately curtailed by the combined effects of finite Hilbert-space dimension and decoherence, leading to a noise-dominated regime in which increasing circuit depth no longer enhances physically resolvable scrambling. Our results provide a model-agnostic, information-theoretic criterion for assessing the simulability of strongly chaotic dynamics and establish fundamental limits on the ability of near-term quantum platforms to emulate black hole-like scrambling behavior.