Equilibrium quantum many-body methods are encoders from admissible states to represented variables, with exact decoders existing precisely when tasks are constant on encoder fibers.
Structure of Fermion Density Matrices
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A unified framework for functional theories of quantum systems is introduced via scopes of observables and fixed Hamiltonian parts, enabling general proofs of universal functionals, convexity, differentiability, representability, and Hohenberg-Kohn-type uniqueness across variants.
Neural ODEs reproduce 2RDM dynamics from data only when three-particle cumulant correlations are strong, mapping the validity regime of cumulant expansions.
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Unified Framework for Functional Theories of Quantum Systems
A unified framework for functional theories of quantum systems is introduced via scopes of observables and fixed Hamiltonian parts, enabling general proofs of universal functionals, convexity, differentiability, representability, and Hohenberg-Kohn-type uniqueness across variants.