Feedforward Neural Network Reconstructed from High-order Quantum Systems

Neural Networks (NNs) are widely used because of their superior feature extraction capabilities, among which Feedforward Neural Network (FNN) is used as the basic model for theoretical research. Recently, Quantum Neural Networks (QNNs) based on quantum mechanics have received extensive attention due to their ability to mine quantum correlations and parallel computing. Since two classical bits are required to simulate one qubit (i.e., quantum bit) on a classical computer, it brings challenges for simulating complex quantum operations or building large-scale QNNs on a classical computer. Hardy et al. extended the classical and quantum probability theories to the Generalized Probability Theory (GPT), so it is possible to construct high-order quantum systems. This paper regards the entire feature extraction and integration process of FNN as the evolution process of the high-order quantum system, and then leverages quantum coherence to describe the complex relationship between the features extracted by each layer of the network model. Intuitively, we reconstruct FNN to change the general vector processed by each layer into the state vector of the high-order quantum system. The experimental results on four mainstream datasets show that FNN reconstructed from the high-order quantum system is significantly better than the classical counterpart.