Implicit neural representations have emerged as a powerful paradigm to
represent signals such as images and sounds. This approach aims to utilize
neural networks to parameterize the implicit function of the signal. However,
when representing implicit functions, traditional neural networks such as
ReLU-based multilayer perceptrons face challenges in accurately modeling
high-frequency components of signals. Recent research has begun to explore the
use of Fourier Neural Networks (FNNs) to overcome this limitation. In this
paper, we propose Quantum Implicit Representation Network (QIREN), a novel
quantum generalization of FNNs. Furthermore, through theoretical analysis, we
demonstrate that QIREN possesses a quantum advantage over classical FNNs.
Lastly, we conducted experiments in signal representation, image
superresolution, and image generation tasks to show the superior performance of
QIREN compared to state-of-the-art (SOTA) models. Our work not only
incorporates quantum advantages into implicit neural representations but also
uncovers a promising application direction for Quantum Neural Networks.

我们提出了一种新颖的量子广义傅立叶神经网络（QIREN），其通过理论分析证明了比经典的傅立叶神经网络具有量子优势，并通过信号表示、图像超分辨率和图像生成任务的实验证明了 QIREN 相对于最先进模型的卓越性能。我们的工作不仅将量子优势融入了隐性神经表示中，还揭示了量子神经网络的一个有前景的应用方向。