測量量子態的物理量在日漸進步的量子計算研究中扮演十分重要的
角色，當問題擴展至更複雜或龐大的量子系統時，對現行的量子電腦
的使用環境和硬體限制仍是一大挑戰。
本研究基於已被廣泛使用的 Randomized Measurement，設計一針
對純度估算之工具。其架構結合古典端方法和量子端的 Randomized
Measurement，追求純度估算時擁有低統計誤差。透過古典機器學習近
似高運算資源消耗的量子電路測量，並在估算量子子系統純度時引入
重要性採樣，其相對於均勻採樣的優勢讓系統可以顯著的減少對運算
資源和時間的需求。
本文將完整的介紹我們的系統架構，接著，從虛擬機和真實機上Product state、GHZ state 實驗開始，延伸至較複雜的 Bell state 之淬火動力學的純度估算結果。我們利用此工具實現精準且高效率的糾纏熵測量，展望在日後亦可被推廣至其他量子系統和物理量的計算。

Measuring the properties of a quantum state plays an important role in the rapidly developing field of quantum computing researches nowadays. When expanding the goal on large-scale or complex quantum systems, one may find it challenging to utilize quantum computers under current hardware conditions and environments.
In this research, we designed a toolbox for purity estimation based on the widely used randomized measurement protocol. A combination of classical machine learning and randomized measurements on the quantum states enables us to pursue low statistical error on purity estimation on both quantum simulators and real machines.
This toolbox improves the efficiency of measuring purity on quantum circuits via classical machine learning and importance sampling. It’s advantage over uniform sampling is the significant reduction on the demand of computational resources and time.
In this thesis, we provide a detailed introduction of the system’s structure. Starting from the product state and GHZ state, we further perform experiments on quench dynamics of Bell state, which exhibits longer range entanglement. Finally, we show that this toolbox realizes measurements of entanglement entropy with higher precision and efficiency. This study is expectedto be applied to other quantum systems and physical quantities in the future.

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