Quantum Fourier Convolutional Network

The neural network and quantum computing are both significant and appealing fields, with their interactive disciplines promising for large-scale computing tasks that are untackled by conventional computers. However, both developments are restricted by the scope of the hardware development. Nevertheless, many neural network algorithms had been proposed before GPUs became powerful enough for running very deep models. Similarly, quantum algorithms can also be proposed as knowledge reserve before real quantum computers are easily accessible. Specifically, taking advantage of both the neural networks and quantum computation and designing quantum deep neural networks (QDNNs) for acceleration on the Noisy Intermediate-Scale Quantum (NISQ) processors is also an important research problem. As one of the most widely used neural network architectures, convolutional neural network (CNN) remains to be accelerated by quantum mechanisms, with only a few attempts having been demonstrated. In this article, we propose a new hybrid quantum-classical circuit, namely, Quantum Fourier Convolutional Network (QFCN). Our model achieves exponential speedup compared with classical CNN theoretically and improves over the existing best result of quantum CNN. We demonstrate the potential of this architecture by applying it on different deep learning tasks, including traffic prediction and image classification.