  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.
