Making quantum chemistry compressive and expressive: Toward practical ab-initio simulation

Ab-initio quantum chemistry simulations are essential for understanding electronic structure of molecules and materials in almost all areas of chemistry. A broad variety of electronic structure theories and implementations has been developed in the past decades to hopefully solve the many-body Schrödinger equation in an approximate manner on modern computers. In this review, we present recent progress in advancing low-rank electronic structure methodologies that rely on the wavefunction sparsity and compressibility to select the important subset of electronic configurations for both weakly and strongly correlated molecules. Representative chemistry applications that require the many-body treatment beyond traditional density functional approximations are discussed. The low-rank electronic structure theories have further prompted us to highlight compressive and expressive principles that are useful to catalyze idea of quantum learning models. The intersection of the low-rank correlated feature design and the modern deep neural network learning provides new feasibilities to predict chemically accurate correlation energies of unknown molecules that are not represented in the training dataset. The results by others and us are discussed to reveal that the electronic feature sets from an extremely low-rank correlation representation, which is very poor for explicit energy computation, are however sufficiently expressive for capturing and transferring electron correlation patterns across distinct molecular compositions, bond types and geometries.

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