# Fourier Series Guided Design of Quantum Convolutional Neural Networks for Enhanced Time Series Forecasting

arXiv: https://arxiv.org/abs/2404.15377 · HTML: https://mlsanity.com/paper/2404.15377/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 45 references that are in the map.
- First posted on arXiv 23 Apr 2024.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [Semiconductor Defect Detection by Hybrid Classical-Quantum Deep Learning](https://mlsanity.com/paper/2208.03514/) (2022)
- [Residual Tensor Train: A Quantum-inspired Approach for Learning Multiple Multilinear Correlations](https://mlsanity.com/paper/2108.08659/) (2021)

## Built on by (most cited first, 1 of 1)

- [Empirical Characterization of Learning Geometry in Hybrid Quantum Forecasting Models](https://mlsanity.com/paper/2608.19497/) (2026)

## Abstract (arXiv)

In this study, we apply 1D quantum convolution to address the task of time series forecasting. By encoding multiple points into the quantum circuit to predict subsequent data, each point becomes a feature, transforming the problem into a multidimensional one. Building on theoretical foundations from prior research, which demonstrated that Variational Quantum Circuits (VQCs) can be expressed as multidimensional Fourier series, we explore the capabilities of different architectures and ansatz. This analysis considers the concepts of circuit expressibility and the presence of barren plateaus. Analyzing the problem within the framework of the Fourier series enabled the design of an architecture that incorporates data reuploading, resulting in enhanced performance. Rather than a strict requirement for the number of free parameters to exceed the degrees of freedom of the Fourier series, our findings suggest that even a limited number of parameters can produce Fourier functions of higher degrees. This highlights the remarkable expressive power of quantum circuits. This observation is also significant in reducing training times. The ansatz with greater expressibility and number of non-zero Fourier coefficients consistently delivers favorable results across different scenarios, with performance metrics improving as the number of qubits increases.