Quantum-Enhanced In-Context Learning for Geopotential Field Estimation: A Theoretical Framework

We establish a theoretical framework for in-context learning (ICL) of Earth's gravitational potential field using transformer architectures, with particular emphasis on the sample complexity advantages afforded by quantum gravimetry. The geopotential, expressed as a truncated spherical harmonic expansion of maximum degree N with K = (N+1)² coefficients, defines a function class for which we characterize ICL learnability. Building on the ICL characterization framework of Hawarey (2026) (i.e. the foundational paper), we prove that the geopotential function class is ICL-Easy: it admits an additive sufficient statistic computable by a single attention layer, enabling transformers to match the sample complexity of…