Fermi Machine -- Quantum Many-Body Solver Derived from Correspondence between Noninteracting and Strongly Correlated Fermions

Abstract

Stimulated by the successful descriptions of strongly correlated electron systems by fractionalized fermions, correspondence between interacting fermions and non-interacting multi-component fermions is formulated in examples of the Hubbard model. The formalism enables constructions of the neural network for a quantum many-body solver represented by coupled noninteracting fermions. After showing the exact correspondence of 1- and 2-site Hubbard model to two-component noninteracting fermions, numerical algorithm of the quantum machine learning for the Hubbard model is proposed. Benchmark for the 4-site systems is successfully presented and promising future directions as well as implications are discussed.