# Quantum Implicit Neural Representations

arXiv: https://arxiv.org/abs/2406.03873 · HTML: https://mlsanity.com/paper/2406.03873/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 47 references that are in the map.
- First posted on arXiv 6 Jun 2024.

## Builds on (most cited first, 28 of 28)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [Adversarial Generation of Continuous Images](https://mlsanity.com/paper/2011.12026/) (2020)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Image Generators with Conditionally-Independent Pixel Synthesis](https://mlsanity.com/paper/2011.13775/) (2020)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [Generative Models as Distributions of Functions](https://mlsanity.com/paper/2102.04776/) (2021)
- [Reinforcement Learning with Quantum Variational Circuits](https://mlsanity.com/paper/2008.07524/) (2020)
- [Reconstructing continuous distributions of 3D protein structure from cryo-EM images](https://mlsanity.com/paper/1909.05215/) (2019)
- [Seeing Implicit Neural Representations as Fourier Series](https://mlsanity.com/paper/2109.00249/) (2021)
- [Spatially-Adaptive Pixelwise Networks for Fast Image Translation](https://mlsanity.com/paper/2012.02992/) (2020)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
- [Power and limitations of single-qubit native quantum neural networks](https://mlsanity.com/paper/2205.07848/) (2022)
- [Learning Deep Time-index Models for Time Series Forecasting](https://mlsanity.com/paper/2207.06046/) (2022)

## Built on by (most cited first, 16 of 16)

- [Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2509.14026/) (2025)
- [QKAN-LSTM: Quantum-inspired Kolmogorov-Arnold Long Short-term Memory](https://mlsanity.com/paper/2512.05049/) (2025)
- [Quantum Doubly Stochastic Transformers](https://mlsanity.com/paper/2504.16275/) (2025)
- [Quantum Visual Fields with Neural Amplitude Encoding](https://mlsanity.com/paper/2508.10900/) (2025)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Predictive Performance of Deep Quantum Data Re-uploading Models](https://mlsanity.com/paper/2505.20337/) (2025)
- [QFGN: A Quantum Approach to High-Fidelity Implicit Neural Representations](https://mlsanity.com/paper/2504.19053/) (2025)
- [PALQO: Physics-informed Model for Accelerating Large-scale Quantum Optimization](https://mlsanity.com/paper/2509.20733/) (2025)
- [On the accuracy of implicit neural representations for cardiovascular anatomies and hemodynamic fields](https://mlsanity.com/paper/2510.20970/) (2025)
- [Quantum Implicit Neural Representations for Novel View Synthesis](https://mlsanity.com/paper/2601.05250/) (2026)
- [Quantum Implicit Neural Compression](https://mlsanity.com/paper/2412.19828/) (2024)
- [Towards High-Fidelity Gaussian Splatting with Queried-Convolution Neural Networks](https://mlsanity.com/paper/2512.12898/) (2025)
- [Quantum Visual Word Sense Disambiguation: Unraveling Ambiguities Through Quantum Inference Model](https://mlsanity.com/paper/2512.24687/) (2025)
- [Implementation of Quantum Implicit Neural Representation in Deterministic and Probabilistic Autoencoders for Image Reconstruction/Generation Tasks](https://mlsanity.com/paper/2603.06755/) (2026)
- [Bernstein-Vazirani Networks: Quantum Machine Learning by Interference](https://mlsanity.com/paper/2608.19043/) (2026)
- [SQUARE: Structured Quantum Representation Adapters as Compact Quadratic Feature Maps for Frozen Language Models](https://mlsanity.com/paper/2609.37134/) (2026)

## Abstract (arXiv)

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.