Prediction of the Behavior of Many-Particle Systems in Quantum Mechanics Using Quantum Neural Networks

Predicting the behavior of many-particle systems in quantum mechanics is one of the most difficult computational problems in condensed matter physics and chemistry due to the exponential growth of the dimension of the Hilbert space. The aim of this research is to investigate the ability of quantum neural networks to overcome this challenge and achieve chemical accuracy in predicting the ground-state energy and properties of many-electron systems. In this study, a new architecture of quantum neural networks based on strongly entangling layers, tensor pretraining, and quantum natural gradient optimization was designed and implemented on NISQ superconducting processors. The results showed that these networks can predict the properties of the molecules H₂, LiH, BeH₂, H₂O, and CH₄ with an average error of 0.92 mH (better than the chemical accuracy limit of 1.6 mH) and significantly better than the classical gold-standard method CCSD(T) and the standard VQE algorithm. Even for the N₂ molecule with 24 qubits, an error of 2.11 mH was achieved despite real hardware noise. The required circuit depth was also reduced by 40 to 65 percent, and the barren plateau phenomenon was controlled up to a depth of 42 layers. These findings suggest that quantum neural networks could soon replace costly classical methods in simulating medium- and large-scale many-particle systems, paving the way for the precise design of new materials and drugs.