心房顫動之量子傅立葉轉換

心電圖(ECG)是檢測心臟疾病重要工具之一，在醫學領域中具有重要性及不可或缺的臨床應用。其中，心房顫動(AF)為最常見的心律不整類型，可能導致心血管疾病和中風的風險，因此，分析心電圖訊號以識別心房顫動，有助於制定有效的治療方案。在過去的研究中，通常會運用快速傅立葉轉換(FFT)、小波轉換、人工智慧和深度學習等技術，不僅能有效分析ECG訊號的頻率成分，還能區分正常竇性心律人士及心房顫動患者ECG的特徵。然而，隨著數據的增加和疾病模式的複雜性提升，現有的頻率分析方法面臨著準確性及靈敏度的挑戰。近年來，隨著量子計算的興起，量子傅立葉轉換(QFT)利用量子計算的特性，如量子糾纏和疊加，能夠利用較少的時間來處理大規模數據，從而提高分析的效率及準確度。本研究運用臺北榮民總醫院所提供正常竇性心律人士及心房顫動患者的ECG數據，探索QFT在心電圖訊號分析的潛力。實驗結果證明，使用QFT能夠有效分析出與FFT相似的主頻率結果，利用量子計算的先天優勢，QFT在未來醫學研究和臨床應用的潛力及發展性，尤其在實時診斷方面。關鍵詞: 心電圖、心房顫動、快速傅立葉轉換、量子傅立葉轉換

關鍵字

心電圖；心房顫動；快速傅立葉轉換；量子傅立葉轉換

並列摘要

An Electrocardiogram (ECG) is one of the most essential tools for detecting cardiac diseases and has significant and indispensable clinical applications in medicine. Among them, atrial fibrillation (AF) is the most common type of arrhythmia, which may lead to cardiovascular disease and stroke risk. Therefore, analyzing ECG signals to identify AF can help to develop an effective treatment plan. In past studies, techniques such as fast Fourier transform (FFT), wavelet transform, artificial intelligence, and deep learning were commonly used to effectively analyze not only the frequency components of ECG signals but also to differentiate between the characteristics of ECGs from normal sinus rhythm (NSR) individuals and patients with AF. However, with the increase of data and the complexity of disease patterns, the existing frequency analysis methods face the challenge of accuracy and sensitivity. In recent years, with the rise of quantum computing, quantum Fourier transform (QFT) has demonstrated the potential to process large-scale data in less time, thus improving the efficiency and accuracy of analysis. This study explores the QFT in the analysis of ECG data provided by Taipei Veterans General Hospital from NSR people and AF patients. The experimental results show that using QFT can effectively analyze the main frequency results similar to the FFT and utilize the inherent advantages of quantum computing. Keywords: electrocardiogram, atrial fibrillation, fast Fourier transform, quantum Fourier transform