在開放量子系統理論領域中，動力學過程所展現出的非經典特性一直是研究的核心議題之一。這些非經典特性對於理解量子相干性、糾纏動力學以及量子與經典行為之間的轉變扮演著關鍵角色。近年來，一種基於正則哈密頓量集(CHER)的方法被提出，用以系統性地刻畫與量化量子動力學過程中的非經典性。此方法提供了一個嚴謹的理論框架，能夠將微觀哈密頓量的不確定性與可觀測的開放系統行為建立起連結。CHER 方法已被應用於氮-空位中心（N-V center）的自由感應衰減（FID）進行實證，該物理系統在量子資訊處理與量子感測領域中具有重要地位。
然而，若要在實驗上實現 CHER 理論會面臨相當大的挑戰。特別是實作該理論需要進行多次量子過程斷層掃描（QPT），以高時間解析度收集大量實驗數據。這在實驗上相當耗時且成本高昂，尤其是在系統中，由於退相干現象與技術限制，可取得的測量數量相對有限。為了解決這一問題，我們提出利用基於核函數的量子機器學習（QML）模型，從時間上稀疏的資料中估計非經典性。我們的方法運用了量子核在捕捉複雜量子資料相關性方面的優勢，這些相關性往往是傳統模型難以辨識的。
以 N-V 中心的自由感應衰減動力學為例進行展示，模擬退相干過程，並使用 QML 模型學習從可觀測數據映射至對應的非經典性量測。量子學習模型不僅能夠應對資料稀疏的問題，還更具備辨識非經典性等微妙量子特徵的能力。研究成果指出，將量子機器學習應用於量子特性表徵任務中是一項前景可期的方向，尤其能夠減輕未來在實作 CHER 或其他相關理論時的實驗負擔。此工作有效地架起理論量子動力學與資料驅動方法之間的橋樑，為在資料取得受限或成本高昂的實驗條件下量化非經典性，提供了一條可行的實作途徑。

Nonclassical characteristics of dynamical processes constitute a fundamental subject in the theory of open quantum systems, as they underlie phenomena such as quantum coherence, entanglement evolution, and the quantum-to-classical transition. The Canonical Hamiltonian Ensemble Representation (CHER) has recently emerged as a rigorous and general framework for the characterization and quantification of nonclassicality, enabling a direct connection between microscopic Hamiltonian randomness and the observable dynamics of open systems. This theoretical framework has been exemplified in the free induction decay (FID) of nitrogen-vacancy centers in diamond, a platform of significant relevance to quantum information and quantum sensing.
However, the experimental implementation of CHER is technically demanding, as it relies on repeated quantum process tomography (QPT) with high temporal resolution to reconstruct the dynamical map over time. Such requirements pose substantial challenges in practical settings, particularly in solid-state systems where decoherence and measurement limitations restrict data acquisition.
To address this challenge, a kernel-based quantum machine learning (QML) approach is introduced for estimating nonclassicality directly from temporally sparse experimental data. By utilizing quantum kernels, this method captures intricate correlations embedded in the quantum dynamics that are not easily extracted by classical learning models.
Numerical simulations of the FID dynamics of the N-V center are employed to validate the method. This study demonstrates the feasibility of using quantum machine learning as a data-efficient surrogate for QPT-based characterization schemes. The proposed approach offers a scalable and experimentally accessible pathway for quantifying nonclassicality in open quantum systems, effectively bridging theoretical frameworks such as CHER with practical data-driven implementations.

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