非古典性在動力學過程中的表示一直是開放量子系統研究中備受關注的議題。近年來，基於正則哈密頓量係綜集合表示法 (canonical Hamiltonian ensemble representation, CHER) 的方法被提出，用以量化量子動力學過程的非古典性。然而，由於目前實驗條件的限制，CHER 理論的實際應用仍具挑戰性，且往往需要在量測精度與實驗成本之間取得平衡。
本研究提出一種量子機器學習 (quantum machine learning, QML) 方法，從實驗上可實現的量子系統中擷取具物理意義的資訊，並以鑽石中的氮—空位中心 (NV− center) 作為代表性平台。具體而言，本研究採用量子神經網路(quantum neural networks, QNNs) 學習並表徵 NV− center 系統自由感應衰減(free induction decay, FID) 動力學中所蘊含的非古典特徵。透過以數值產生或模擬之 FID 訊號作為輸入，所提出的框架可用於估計純退相干動力學的非古典性。
此外，QNN 架構之設計考量了電路深度、資料編碼策略與量子位元數等關鍵因素，並與先前變分量子演算法相關研究相呼應。其中，本研究特別分析了重複資料編碼與 ZZ 特徵映射 (ZZ feature map) 結構對模型表達能力與學習效能的影響。
為進一步展示所提出方法的泛化能力與實際應用潛力，本研究亦於 IBM Quantum 真實量子裝置後端執行額外的 NV− center 系統 FID 模擬。結果經過分析以瞭解真實裝置的雜訊與缺陷如何影響所提框架捕捉 FID 動力學中關鍵特徵的能力。
整體而言，本研究展示了 QNN 方法在學習開放量子系統非古典性上的實際應用，並為量子機器學習技術與實驗可實現量子動力學模擬之整合提供了初步方向。

Characterizing nonclassical properties in dynamical processes is a significant topic in open quantum systems. Recently, approaches based on the canonical Hamiltonian ensemble representation (CHER) have been proposed to quantify the nonclassicality of quantum dynamical processes. However, practical implementation remains challenging due to experimental limitations and the trade-off between precision and resource consumption.
In this work, we propose a quantum machine learning (QML) approach to estimate the nonclassicality of pure dephasing dynamics, using the nitrogen-vacancy (NV−) center in diamond as a representative platform. Quantum neural networks (QNNs) are employed to learn nonclassical features from numerically generated or simulated free-induction decay (FID) signals.
The QNN architectures are designed by considering circuit depth, data encoding strategies, and number of qubits. In particular, the effects of repeated data encoding and ZZ feature map structures are analyzed to evaluate their influence on model expressivity and learning performance.
To demonstrate practical applicability, additional FID simulations of the NV center system are performed on IBM Quantum real-device backends. The results are analyzed to investigate how real device noise and imperfections affect the framework’s ability to capture essential FID dynamical features.
Overall, this work demonstrates the potential of QNN-based methods for learning nonclassicality in open quantum systems and provides a step toward integrating quantum machine learning with experimentally realizable quantum dynamical simulations.

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