在開放量子系統動力學領域，動力學過程中非馬可夫行為的特性化與量化長期以來是研究的核心議題之一。非馬可夫性描述了系統演化過程對歷史狀態的依賴性，這一性質與馬可夫過程的無記憶性形成鮮明對比。由於非馬可夫性涉及複雜的動態特徵，其測量與量化需要深入探討關鍵物理量的時間演化行為。
因此，多種非馬可夫性測量方法相繼提出，通常基於對系統關鍵變數隨時間變化的觀察與分析。在實驗實現層面，測量非馬可夫性往往需要收集大量高精度的時間序列數據，並確保時間解析度足以捕捉動力學過程中的細微變化。然而，這類測量在實際操作中經常面臨挑戰，尤其是在測量設備受到雜訊干擾或時間限制的情況下。為此，開發高效且能在有限數據條件下可靠估計非馬可夫性的技術，成為一項重要的研究課題。
針對上述問題，我們提出了一種基於核函數的量子機器學習模型，旨在從系統的時間演化數據中準確估計非馬可夫性。與傳統方法相比，我們的方法能夠有效處理時間序列數據中的不完全性，並在數據稀疏的條件下保持高準確性。我們通過自旋-玻色子模型生成訓練數據，並將所提出的量子模型與兩種經典模型進行比較。結果表明，量子機器學習模型在預測非馬可夫性方面具有顯著優勢，即使在數據稀疏的情況下，也能可靠地捕捉系統的非馬可夫行為。
研究結果進一步證實，量子機器學習模型相較於某些經典學習方法，能更有效地解析和量化非馬可夫性。該方法不僅能顯著減少估計非馬可夫性所需的實驗工作量，還為開放量子系統動力學的研究提供了新的理論框架和實用工具。

Characterization and quantification of the non-Markovian behaviors of dynamical processes have attracted long-lasting research interest in the field of open quantum system dynamics. Many different measures of non-Markovianity have been proposed based on the temporal variation of certain quantities of interest. Therefore, their experimental realizations would require vast raw data with sufficient time resolution along time axis. In this study, we propose leveraging kernel-based quantum machine learning models to estimate non-Markovianity using sparse temporal data. To demonstrate our approach, we generate the training data according to the spin-boson model. We also compare the quantum model with two classical ones. We find that the quantum model is capable of reliably predicting the non-Markovianity even if the raw data is temporally spare, and the quantum model performs better than some types of classical learning models. Therefore, our approach would be promising in reducing the experimental efforts for estimating the non-Markovianity.

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