Abstract

     Quantum-inspired artificial neural network is an interesting research area, which combines quantum computing and deep learning. Several models of quantum-inspired neuron with real-valued weights have been proposed, and they were mainly used to build the three-layer feedforward neural networks. In this work, we improve the convolutional neural networks (CNNs) by utilizing the quantum-inspired way of data representation and convolutional operation. Specifically, we first improve the quantum-inspired neuron by exploiting the complex-valued weights, which have richer representational capacity and better non-linearity. Moreover, we extend the method implementing the quantum-inspired neurons to perform convolutional operations, and naturally draw the models of quantum-inspired convolutional neural networks (QICNNs) capable of processing high-dimensional data. Here five specific types of QICNNs are proposed, which are different in the way of implementing the convolutional layers and fully connected layers. We establish the detail mathematical framework to implement the QICNNs. The performances of accuracy, convergence and robustness of the five QICNNs against the classical counterpart are tested using the MNIST and CIFAR-10 datasets.

Introduction

     In the past few years, the field of quantum computing has witnessed many breakthroughs in both quantum processors [1, 2] and quantum algorithms [3–۵]. Quantum computing performs information processing in a quantum mechanical way, that is, encoding the data into an exponentially large Hilbert space and manipulating this data space in a parallel way, which result into the exponential improvements of data representation power and computational power. On the other hand, deep learning is the art of making computers learn how to solve problems based on huge amounts of data, and now faces challenges of storage and computational resources. It is therefore only natural to ask if and how they could be combined to add something new to how machines recognize patterns in data.

     At present, algorithm researches at the junction of quantum computing and deep learning focus on two active directions. One is to search for the real quantum algorithms [3]; such algorithms harness the unique properties of quantum mechanics, including the quantum superposition and entanglement, to encode and process data. The other direction is to develop the so-called quantum-inspired algorithms [6–۱۹]; such algorithms borrow the basic ideas and formalism of quantum computing, such as the way of data representation and complex operations, to improve the existing classical algorithms or even find new algorithms. The salient difference between the two realms of algorithms is that the first kind of algorithms run on the quantum computers, while the second one run on the conventional computers.

Conclusions

     In the present work, we improve the quantum-inspired neurons by exploiting the complex-valued weights to have richer representational capacity and better non-linearity. Then the basic idea of quantum-inspired neuron is extended naturally to perform the complex-valued convolutional operations. By employing the quantum-inspired neurons in the fully connected layers and/or the convolutional operations in the convolutional layers, we develop five types of quantuminspired convolutional neuron networks (QICNNs). The detail mathematical framework to implement the QICNNs are developed, which can be executed based on the common realvalued framework of machine learning. The performances of the five QICNNs are studied using the MNIST and CIFAR-10 dataset. The results show that the QICNN using the quantuminspired neuron in the fully connected layers has the best performance. The performance of classification accuracy, convergent rate and robustness is remarkably higher than the classical template CNN.