Fermi machine as an efficient quantum many-body solver based on a novel quantized artificial neural network

Inspired by the successful descriptions of strongly correlated electron systems by fractionalized fermions [1-4], correspondence between interacting fermions and non-interacting multi-component fermions is formulated in examples of the Hubbard model. The formalism enables constructions of an artificial neural network, aiming at efficient quantum many-body solvers represented by coupled noninteracting fermions [5]. After showing the exact correspondences of 1- and 2-site Hubbard models to two-component noninteracting fermions, a numerical algorithm of the quantum machine learning for the Hubbard model is proposed. Benchmark for the 4-site systems is successfully presented, indicating a promising accurate solver for challenging strongly correlated fermion systems. The proposed novel artificial neural network is also expected to reveal quantum entanglement structure through the architecture of hidden layers in the network. Promising future directions as well as implications are discussed.

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[5] M. Imada, J. Phys. Soc. Jpn., 93, 104002 (2024).