Quantum state classification via complex-valued neural networks

Abstract To efficiently complete quantum information processing tasks, quantum neural networks (QNNs) should be introduced rather than the common classical neural networks, but the QNNs in the current noisy intermediate-scale quantum era cannot perform better than classical neural networks because of scale and the efficiency limits. So if the quantum properties can be introduced into classical neural networks, more efficient classical neural networks may be constructed for tasks in the field of quantum information. Complex numbers play an indispensable role in the standard quantum theory, and constitute an important feature in quantum theory. So if complex numbers are introduced in classical neural networks, they may outperform the common classical neural networks in dealing with the tasks in the quantum information field. In this paper, we verify this conjecture by studying quantum state classification via complex-valued neural networks (CVNNs). The numerical results show that the performance of CVNNs is much better than the real-valued neural network in classifying the entangled states. Our results not only provide a new way to improve the performance of artificial neural networks in quantum state classifiers, but also might shed light on the study of CVNNs in the field of other quantum information processing tasks before the appearance of the universal quantum computer.