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

2024-04-23

arXiv.org

AI Summary

Multivariate time series forecasting remains challenging for quantum machine learning models due to limited expressivity and inefficient parameter utilization. Method: This paper proposes a novel one-dimensional quantum convolutional neural network (QCNN) that encodes temporal points as quantum states and leverages the theoretical equivalence between quantum circuits and multidimensional Fourier series to guide architecture design. It integrates data re-uploading, expressivity analysis, and Fourier coefficient spectrum evaluation. Contribution/Results: We are the first to deeply embed Fourier series analysis into QCNN design, revealing that a small number of variational parameters can efficiently generate high-order Fourier components—challenging the conventional trade-off between parameter count and representational power. Experiments across multiple benchmarks demonstrate: (i) consistent improvement in prediction accuracy with increasing qubit count; (ii) stronger performance of highly expressive ansätze, evidenced by richer spectra of non-zero Fourier coefficients; (iii) stable superiority over classical and quantum baselines; and (iv) over 40% higher training efficiency.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

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.

Problem

• Designing quantum convolutional neural networks for time series forecasting
• Exploring quantum circuit expressibility and avoiding barren plateaus
• Enhancing performance with limited parameters via Fourier series framework

Innovation

• 1D quantum convolution for time series
• Fourier series-guided quantum circuit design
• Data reuploading enhances circuit performance