In this study, an attempt has been made to investigate an example of magnetic systems with quantum properties called a spin system with a random long-range interaction. Also, classical neural network methods, classical convolutional neural network, hybrid classical-quantum convolutional neural network, and quantum convolutional neural network have been used in search of the superiority of quantum methods over classical ones in the study of quantum materials. Also, the ground state energy of this magnetic system has been estimated by the variational quantum algorithm. In another section, an effort has been made to investigate the changes in the system’s magnetization concerning variations in the coefficients of such a Hamiltonian system. In these analyses, we concluded that classical neural networks and clas- sical convolutional methods are suitable approaches for eva‎luating such a magnetic system. In these studies, we concluded that the classical neural network and classical convergence are appropriate methods for eva‎luating such a magnetic system. The hybrid classical-quantum neural network not only proved comparable to the classical method in most cases studied but also demonstrated certain advantages over classical neural networks in some instances. The quantum convolutional neural network was also categorized as a suitable approach for analyzing such magnetic systems, and this research establishes that this model can be consid- ered as a case study in the pursuit of quantum methods’ superiority for examining quantum systems. Brick-wall model also succeeded in learning such a system and was able to provide correct predictions of the properties of this system. In employing the variational quantum algorithm, it was demonstrated that this method has advantages over exact diagonalization, establishing it as a reliable model in terms of speed and accuracy for investigating quantum systems.

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